General Entanglement Scaling Laws from Time Evolution
Open accessAbstract
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
According to the Lieb-Robinson theorem, after a sufficiently large time, states can become strongly entangled.
“Indeed, this fact is related to correlation and entanglement spreading according to the Lieb-Robinson theorem that states that, after a sufficiently large time, states can become strongly entangled ([91-96], see also [97]).”
From Can one trust quantum simulators? (2012) · cites this paper as [92]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793 · see citing works
Bhatia, R. (1997) · Graduate texts in mathematics · doi:10.1007/978-1-4612-0653-8 · Cited by 2,334 · see citing works
Persistent Entanglement in Arrays of Interacting Particles
Briegel, H. J., & Raussendorf, R. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.910 · Cited by 1,950 · see citing works
Scaling of entanglement close to a quantum phase transition
Osterloh, A., Amico, L., Falci, G., & Fazio, R. (2002) · Nature · doi:10.1038/416608a · Cited by 1,860 · see citing works
Srednicki, M. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.666 · Cited by 1,858 · see citing works
Entanglement in a simple quantum phase transition
Osborne, T. J., & Nielsen, M. A. (2002) · Physical Review A · doi:10.1103/physreva.66.032110 · Cited by 1,472 · see citing works
Self-citationThe finite group velocity of quantum spin systems
Lieb, E. H., & Robinson, D. W. (1972) · Communications in Mathematical Physics · doi:10.1007/bf01645779 · Cited by 1,463 · see citing works
Quantum source of entropy for black holes
Bombelli, L., Koul, R. K., Lee, J., & Sorkin, R. D. (1986) · Physical Review D · doi:10.1103/physrevd.34.373 · Cited by 1,439 · see citing works
Finitely correlated states on quantum spin chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099178 · Cited by 1,422 · see citing works
Quantum Communication through an Unmodulated Spin Chain
Bose, S. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.207901 · Cited by 1,407 · see citing works
Time Dependence of Correlation Functions Following a Quantum Quench
Calabrese, P., & Cardy, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.136801 · Cited by 1,190 · see citing works
Perfect State Transfer in Quantum Spin Networks
Christandl, M., Datta, N., Ekert, A., & Landahl, A. J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.187902 · Cited by 1,179 · see citing works
Thermodynamic limit of density matrix renormalization.
Östlund, S., & Rommer, S. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.3537 · Cited by 1,077 · see citing works
Multiparty entanglement in graph states
Hein, M., Eisert, J., & Briegel, H. J. (2004) · Physical Review A · doi:10.1103/physreva.69.062311 · Cited by 1,035 · see citing works
Self-citationDynamics of a Quantum Phase Transition
Zurek, W. H., Dorner, U., & Zoller, P. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.105701 · Cited by 812 · see citing works
Matrix product states represent ground states faithfully
Verstraete, F., & Cirac, J. I. (2006) · Physical Review B · doi:10.1103/physrevb.73.094423 · Cited by 730 · see citing works
Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order
Bravyi, S., Hastings, M. B., & Verstraete, F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.050401 · Cited by 664 · see citing works
Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
Verstraete, F., Wolf, M. M., Perez-Garcia, D., & Cirac, J. I. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.220601 · Cited by 580 · see citing works
Spectral Gap and Exponential Decay of Correlations
Hastings, M. B., & Koma, T. (2006) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0030-4 · Cited by 580 · see citing works
Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture
Gioev, D., & Klich, I. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.100503 · Cited by 498 · see citing works
Violation of the Entropic Area Law for Fermions
Wolf, M. M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010404 · Cited by 463 · see citing works
Entanglement properties of the harmonic chain
Audenaert, K., Eisert, J., Plenio, M. B., & Werner, R. F. (2002) · Physical Review A · doi:10.1103/physreva.66.042327 · Cited by 409 · see citing works
Self-citationGround state entanglement in quantum spin chains
Latorre, J. I., Rico, E., & Vidal, G. (2004) · Quantum Information and Computation · doi:10.26421/qic4.1-4 · Cited by 408 · see citing works
Lieb-Robinson Bounds and the Exponential Clustering Theorem
Nachtergaele, B., & Sims, R. (2006) · Communications in Mathematical Physics · doi:10.1007/s00220-006-1556-1 · Cited by 404 · see citing works
Hastings, M. B., & Wen, X.-G. (2005) · Physical Review B · doi:10.1103/physrevb.72.045141 · Cited by 401 · see citing works
Entropy, Entanglement, and Area: Analytical Results for Harmonic Lattice Systems
Plenio, M. B., Eisert, J., Dreißig, J., & Cramer, M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.060503 · Cited by 384 · see citing works
Self-citationEntanglement entropy dynamics of Heisenberg chains
Chiara, G. D., Montangero, S., Calabrese, P., & Fazio, R. (2006) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2006/03/p03001 · Cited by 337 · see citing works
Spectral gap and exponential decay of correlationsPreprint
Hastings, M. B., & Koma, T. (2013) · Cited by 333 · see citing works
Ground state entanglement in quantum spin chains
Latorre, J. I., Rico, E., & Vidal, G. (2003) · CaltechAUTHORS (California Institute of Technology) · Cited by 301 · see citing works
Bipartite entanglement and entropic boundary law in lattice spin systems
Hamma, A., Ionicioiu, R., & Paolo Zanardi, A. (2005) · Physical Review A · doi:10.1103/physreva.71.022315 · Cited by 298 · see citing works
Entanglement in the XY spin chain
Its, A. R., Jin, B.-Q., & Korepin, V. E. (2005) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/13/011 · Cited by 278 · see citing works
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
Plenio, M. B., Hartley, J., & Eisert, J. (2004) · New Journal of Physics · doi:10.1088/1367-2630/6/1/036 · Cited by 270 · see citing works
Self-citationGround state entanglement and geometric entropy in the Kitaev model
Hamma, A., Ionicioiu, R., & Paolo Zanardi, A. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.01.060 · Cited by 250 · see citing works
Propagation of quantum information through a spin system
Osborne, T. J., & Linden, N. (2004) · Physical Review A · doi:10.1103/physreva.69.052315 · Cited by 236 · see citing works
Self-citationThree-Spin Interactions in Optical Lattices and Criticality in Cluster Hamiltonians
Pachos, J. K., & Plenio, M. B. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.056402 · Cited by 233 · see citing works
Entanglement-area law for general bosonic harmonic lattice systems
Cramer, M., Eisert, J., Plenio, M. B., & Dreißig, J. (2006) · Physical Review A · doi:10.1103/physreva.73.012309 · Cited by 219 · see citing works
Self-citationTowards Quantum Entanglement in Nanoelectromechanical Devices
Eisert, J., Plenio, M. B., Bose, S., & Hartley, J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.190402 · Cited by 199 · see citing works
Self-citationOn the entanglement entropy for an XY spin chain
Peschel, I. (2004) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2004/12/p12005 · Cited by 153 · see citing works
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
Plenio, M. B., Hartley, J., & Eisert, J. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 151 · see citing works
Self-citationEntanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
Keating, J. P., & Mezzadri, F. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.050501 · Cited by 125 · see citing works
Entanglement in Spin Chains and Lattices with Long-Range Ising-Type Interactions
Dür, W., Hartmann, L., Hein, M., Lewenstein, M., & Briegel, H. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.097203 · Cited by 121 · see citing works
Single-copy entanglement in critical quantum spin chains
Eisert, J., & Cramer, M. (2005) · Physical Review A · doi:10.1103/physreva.72.042112 · Cited by 98 · see citing works
Self-citationCorrelations, spectral gap and entanglement in harmonic quantum systems on generic lattices
Cramer, M., & Eisert, J. (2006) · New Journal of Physics · doi:10.1088/1367-2630/8/5/071 · Cited by 90 · see citing works
Self-citationImproved Transfer of Quantum Information Using a Local Memory
Giovannetti, V., & Burgarth, D. K. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.030501 · Cited by 79 · see citing works
Excitation and entanglement transfer versus spectral gap
Hartmann, M. J., Reuter, M. E., & Plenio, M. B. (2006) · New Journal of Physics · doi:10.1088/1367-2630/8/6/094 · Cited by 70 · see citing works
Toeplitz Determinants with One Fisher–Hartwig Singularity
Ehrhardt, T., & Silbermann, B. (1997) · Journal of Functional Analysis · doi:10.1006/jfan.1996.3074 · Cited by 51 · see citing works
Bethe ansatz for the Temperley–Lieb loop model with open boundaries
de Gier, J., & Pyatov, P. (2004) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2004/03/p002 · Cited by 49 · see citing works
Entropy growth of shift-invariant states on a quantum spin chain
Fannes, M., Haegeman, B., & Mosonyi, M. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1623616 · Cited by 31 · see citing works
Flagged first, then by citations
1 of the 49 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- [32]S. Bose, Phys. Rev. Lett. 91 , 207901 (2003); M. Christandl, N. Datta, A. Ekert, and A.J. Landahl, ibid. 92 , 187902 (2004); V. Giovannetti and D. Burgarth, ibid. 96 , 030501 (2006); T.J. Osborne and N. Linden, quant-ph/0312141; M.B. Plenio, J. Hartley, and J. Eisert, New J. Phys. 6 , 36 (2004); M.J. Hartmann, M.E. Reuter, and M.B. Plenio, ibid. 8 , 94 (2006). · arXiv
Cited by
Sorted by citations
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745 · see citing works
<i>Colloquium</i> : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873 · see citing works
Self-citationEntanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688 · see citing works
Quantum many-body systems out of equilibrium
Eisert, J., Friesdorf, M., & Gogolin, C. (2015) · Nature Physics · doi:10.1038/nphys3215 · Cited by 1,255 · see citing works
Self-citationEquilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
Gogolin, C., & Eisert, J. (2016) · Reports on Progress in Physics · doi:10.1088/0034-4885/79/5/056001 · Cited by 1,024 · see citing works
Self-citationLight-cone-like spreading of correlations in a quantum many-body system
Cheneau, M., Barmettler, P., Poletti, D., Endres, M., Schauß, P., Fukuhara, T., Gross, C., Bloch, I., Kollath, C., & Kuhr, S. (2012) · Nature · doi:10.1038/nature10748 · Cited by 864 · see citing works
Quasiparticle engineering and entanglement propagation in a quantum many-body system
Jurcevic, P., Lanyon, B. P., Hauke, P., Hempel, C., Zoller, P., Blatt, R., & Roos, C. F. (2014) · Nature · doi:10.1038/nature13461 · Cited by 863 · see citing works
Reduced density matrices and entanglement entropy in free lattice models
Peschel, I., & Eisler, V. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504003 · Cited by 792 · see citing works
Quantum entanglement in condensed matter systems
Laflorencie, N. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.008 · Cited by 790 · see citing works
Quantum quenches in extended systems
Calabrese, P., & Cardy, J. (2007) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2007/06/p06008 · Cited by 656 · see citing works
Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems
Cramer, M., Dawson, C. M., Eisert, J., & Osborne, T. J. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.030602 · Cited by 462 · see citing works
Self-citationEntanglement and correlation functions following a local quench: a conformal field theory approach
Calabrese, P., & Cardy, J. (2007) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2007/10/p10004 · Cited by 406 · see citing works
Fagotti, M., & Calabrese, P. (2008) · Physical Review A · doi:10.1103/physreva.78.010306 · Cited by 369 · see citing works
Quantum Noise as an Entanglement Meter
Klich, I., & Levitov, L. S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.100502 · Cited by 356 · see citing works
Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model
Läuchli, A. M., & Kollath, C. (2008) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2008/05/p05018 · Cited by 327 · see citing works
Holographic evolution of entanglement entropy
Abajo-Arrastia, J., Aparício, J., & López, E. (2010) · Journal of High Energy Physics · doi:10.1007/jhep11(2010)149 · Cited by 304 · see citing works
Can one trust quantum simulators?
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/8/082401 · Cited by 315 · see citing works
Entanglement Entropy for the Long-Range Ising Chain in a Transverse Field
Koffel, T., Lewenstein, M., & Tagliacozzo, L. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.267203 · Cited by 255 · see citing works
Prethermalization and universal dynamics in near-integrable quantum systems
Langen, T., Gasenzer, T., & Schmiedmayer, J. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/06/064009 · Cited by 239 · see citing works
Efficient tomography of a quantum many-body system
Lanyon, B. P., Maier, C., Holzäpfel, M., Baumgratz, T., Hempel, C., Jurcevic, P., Dhand, I., Buyskikh, A. S., Daley, A. J., Cramer, M., et al. (2017) · Nature Physics · doi:10.1038/nphys4244 · Cited by 243 · see citing works
Entanglement Renormalization for Quantum Fields in Real Space
Haegeman, J., Osborne, T. J., Verschelde, H., & Verstraete, F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.100402 · Cited by 239 · see citing works
Self-citationKitaev Chains with Long-Range Pairing
Vodola, D., Lepori, L., Ercolessi, E., Gorshkov, A. V., & Pupillo, G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.156402 · Cited by 228 · see citing works
Propagation of Correlations in Quantum Lattice Systems
Nachtergaele, B., Ogata, Y., & Sims, R. (2006) · Journal of Statistical Physics · doi:10.1007/s10955-006-9143-6 · Cited by 220 · see citing works
Post-matrix product state methods: To tangent space and beyond
Haegeman, J., Osborne, T. J., & Verstraete, F. (2013) · Physical Review B · doi:10.1103/physrevb.88.075133 · Cited by 225 · see citing works
Self-citationA short review on entanglement in quantum spin systems
Latorre, J. I., & Riera, A. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504002 · Cited by 224 · see citing works
Complexity and entanglement for thermofield double states
Chapman, S., Eisert, J., Hackl, L., Heller, M. P., Jefferson, R., Marrochio, H., & Myers, R. (2019) · SciPost Physics · doi:10.21468/scipostphys.6.3.034 · Cited by 210 · see citing works
Self-citationEmergence of coherence and the dynamics of quantum phase transitions
Braun, S. G., Friesdorf, M., Hodgman, S. S., Schreiber, M., Ronzheimer, J. P., Riera, A., del Rey, M., Bloch, I., Eisert, J., & Schneider, U. (2015) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1408861112 · Cited by 190 · see citing works
Self-citationEvolution of entanglement after a local quench
Eisler, V., & Peschel, I. (2007) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2007/06/p06005 · Cited by 179 · see citing works
Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases
Kiefer-Emmanouilidis, M., Unanyan, R. G., Fleischhauer, M., & Sirker, J. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.243601 · Cited by 179 · see citing works
Autocorrelations and thermal fragility of anyonic loops in topologically quantum ordered systems
Nussinov, Z., & Ortíz, G. (2008) · Physical Review B · doi:10.1103/physrevb.77.064302 · Cited by 178 · see citing works
Entanglement scrambling in 2d conformal field theory
Asplund, C. T., Bernamonti, A., Galli, F., & Hartman, T. (2015) · Journal of High Energy Physics · doi:10.1007/jhep09(2015)110 · Cited by 170 · see citing works
Osborne, T. J. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/2/022001 · Cited by 164 · see citing works
Self-citationBreakdown of Quasilocality in Long-Range Quantum Lattice Models
Eisert, J., van den Worm, M., Manmana, S. R., & Kästner, M. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.260401 · Cited by 162 · see citing works
Self-citationEntanglement entropy from charge statistics: Exact relations for noninteracting many-body systems
Song, H., Flindt, C., Rachel, S., Klich, I., & Hur, K. L. (2011) · Physical Review B · doi:10.1103/physrevb.83.161408 · Cited by 163 · see citing works
Entanglement entropy of excited statesPreprint
Alba, V., Fagotti, M., & Superiore, S. N. (2009) · Cited by 177 · see citing works
Entanglement entropy of excited states
Alba, V., Fagotti, M., & Calabrese, P. (2009) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2009/10/p10020 · Cited by 159 · see citing works
Bounds on the Speed of Information Propagation in Disordered Quantum Spin Chains
Burrell, C. K., & Osborne, T. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.167201 · Cited by 134 · see citing works
Self-citationExploring Local Quantum Many-Body Relaxation by Atoms in Optical Superlattices
Cramer, M., Flesch, A., McCulloch, I. P., Schollwöck, U., & Eisert, J. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.063001 · Cited by 136 · see citing works
Self-citationLieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
Nachtergaele, B., Raz, H., Schlein, B., & Sims, R. (2008) · Communications in Mathematical Physics · doi:10.1007/s00220-008-0630-2 · Cited by 128 · see citing works
Many-Body Localization Implies that Eigenvectors are Matrix-Product States
Friesdorf, M., Werner, A. H., Brown, W., Scholz, V. B., & Eisert, J. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.170505 · Cited by 114 · see citing works
Self-citationFinite Speed of Quantum Scrambling with Long Range Interactions
Chen, C.-F., & Lucas, A. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.250605 · Cited by 113 · see citing works
The theory of spin noise spectroscopy: a review
Sinitsyn, N. A., & Pershin, Y. V. (2016) · Reports on Progress in Physics · doi:10.1088/0034-4885/79/10/106501 · Cited by 115 · see citing works
Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions
Kuwahara, T., & Saito, K. (2020) · Physical Review X · doi:10.1103/physrevx.10.031010 · Cited by 110 · see citing works
Adiabatic Preparation of Topological Order
Hamma, A., & Lidar, D. A. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.030502 · Cited by 114 · see citing works
Relationship between quantum walks and relativistic quantum mechanics
Chandrashekar, C. M., Banerjee, S., & Srikanth, R. (2010) · Physical Review A · doi:10.1103/physreva.81.062340 · Cited by 109 · see citing works
Probing local relaxation of cold atoms in optical superlattices
Flesch, A., Cramer, M., McCulloch, I. P., Schollwöck, U., & Eisert, J. (2008) · Physical Review A · doi:10.1103/physreva.78.033608 · Cited by 102 · see citing works
Self-citationEntanglement Entropy beyond the Free Case
Barthel, T., Dusuel, S., & Vidal, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.220402 · Cited by 102 · see citing works
Entanglement entropy in collective models
Vidal, J., Dusuel, S., & Barthel, T. (2007) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2007/01/p01015 · Cited by 102 · see citing works
Chen, Y., & Vidal, G. (2014) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2014/10/p10011 · Cited by 102 · see citing works
Barthel, T. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/7/073010 · Cited by 88 · see citing works
Entanglement in a periodic quench
Eisler, V., & Peschel, I. (2008) · Annalen der Physik · doi:10.1002/andp.200810299 · Cited by 87 · see citing works
Entanglement dynamics in short- and long-range harmonic oscillators
Nezhadhaghighi, M. G., & Rajabpour, M. A. (2014) · Physical Review B · doi:10.1103/physrevb.90.205438 · Cited by 81 · see citing works
Statistics Dependence of the Entanglement Entropy
Cramer, M., Eisert, J., & Plenio, M. B. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.220603 · Cited by 83 · see citing works
Self-citationFundamentals of universality in one-way quantum computation
Nest, M. V. D., Dür, W., Miyake, A., & Briegel, H. J. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/6/204 · Cited by 97 · see citing works
Magic-state resource theory for the ground state of the transverse-field Ising model
Oliviero, S. F. E., Leone, L., & Hamma, A. (2022) · Physical Review A · doi:10.1103/physreva.106.042426 · Cited by 97 · see citing works
Entanglement View of Dynamical Quantum Phase Transitions
Nicola, S. D., Michailidis, A. A., & Serbyn, M. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.040602 · Cited by 81 · see citing works
Complexity and entanglement for thermofield double states
Chapman, S., Eisert, J., Hackl, L., Heller, M. P., Jefferson, R., Marrochio, H., & Myers, R. C. (2019) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-25515 · Cited by 80 · see citing works
Self-citationQuasilocality and Efficient Simulation of Markovian Quantum Dynamics
Barthel, T., & Kliesch, M. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.230504 · Cited by 69 · see citing works
Quantum Entanglement in Random Physical States
Hamma, A., Santra, S., & Paolo Zanardi, A. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.040502 · Cited by 71 · see citing works
Renormalization group constructions of topological quantum liquids and beyond
Swingle, B. G., & McGreevy, J. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.045127 · Cited by 73 · see citing works
Improved Thermal Area Law and Quasilinear Time Algorithm for Quantum Gibbs States
Kuwahara, T., Alhambra, A. M., & Anshu, A. (2021) · Physical Review X · doi:10.1103/physrevx.11.011047 · Cited by 66 · see citing works
An Invariant of Topologically Ordered States Under Local Unitary Transformations
Haah, J. (2016) · Communications in Mathematical Physics · doi:10.1007/s00220-016-2594-y · Cited by 66 · see citing works
Spectral functions and time evolution from the Chebyshev recursion
Wolf, F. A., Justiniano, J. A., McCulloch, I. P., & Schollwöck, U. (2015) · Physical Review B · doi:10.1103/physrevb.91.115144 · Cited by 65 · see citing works
Time evolution of many-body localized systems in two spatial dimensions
Kshetrimayum, A., Goihl, M., & Eisert, J. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.235132 · Cited by 64 · see citing works
Self-citationInformation propagation and equilibration in long-range Kitaev chains
Regemortel, M. V., Sels, D., & Wouters, M. (2016) · Physical Review A · doi:10.1103/physreva.93.032311 · Cited by 59 · see citing works
Information propagation for interacting-particle systems
Schuch, N., Harrison, S. K., Osborne, T. J., & Eisert, J. (2011) · Physical Review A · doi:10.1103/physreva.84.032309 · Cited by 60 · see citing works
Self-citationTightening the Lieb-Robinson Bound in Locally Interacting Systems
Wang, Z., & Hazzard, K. R. A. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.010303 · Cited by 61 · see citing works
Preparing and probing atomic Majorana fermions and topological order in optical lattices
Kraus, C. V., Diehl, S., Zoller, P., & Baranov, M. A. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/11/113036 · Cited by 60 · see citing works
Lieb-Robinson Bounds and the Simulation of Time-Evolution of Local Observables in Lattice Systems
Kliesch, M., Gogolin, C., & Eisert, J. (2014) · Mathematical physics studies · doi:10.1007/978-3-319-06379-9_17 · Cited by 56 · see citing works
Self-citationSupersonic Quantum Communication
Eisert, J., & Gross, D. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.240501 · Cited by 58 · see citing works
Self-citationEntangling Power and Quantum Circuit Complexity
Eisert, J. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.020501 · Cited by 56 · see citing works
Self-citationTopological order following a quantum quench
Tsomokos, D. I., Hamma, A., Zhang, W., Haas, S., & Rosario Fazio, B. (2009) · Physical Review A · doi:10.1103/physreva.80.060302 · Cited by 56 · see citing works
Area law of noncritical ground states in 1D long-range interacting systems
Kuwahara, T., & Saito, K. (2020) · Nature Communications · doi:10.1038/s41467-020-18055-x · Cited by 62 · see citing works
Dell’Anna, L., Salberger, O., Barbiero, L., Trombettoni, A., & Korepin, V. E. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.155140 · Cited by 61 · see citing works
Scaling of entanglement entropy in the (branching) multiscale entanglement renormalization ansatz
Evenbly, G., & Vidal, G. (2014) · Physical Review B · doi:10.1103/physrevb.89.235113 · Cited by 54 · see citing works
Time asymptotics and entanglement generation of Clifford quantum cellular automata
Gütschow, J., Uphoff, S., Werner, R. F., & Zimborás, Z. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3278513 · Cited by 48 · see citing works
Fidelity Witnesses for Fermionic Quantum Simulations
Gluza, M., Kliesch, M., Eisert, J., & Aolita, L. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.190501 · Cited by 49 · see citing works
Self-citationMaking Almost Commuting Matrices Commute
Hastings, M. B. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-009-0877-2 · Cited by 53 · see citing works
Dynamical Simulation of Integrable and Nonintegrable Models in the Heisenberg Picture
Muth, D., Unanyan, R. G., & Fleischhauer, M. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.077202 · Cited by 49 · see citing works
Hastings, M. B. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3149556 · Cited by 50 · see citing works
Logarithmic entanglement lightcone in many-body localized systems
Deng, D., Li, X., Pixley, J. H., Wu, Y.-L., & Sarma, S. D. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.024202 · Cited by 49 · see citing works
Area law of noncritical ground states in 1D long-range interacting systems
Kuwahara, T., & Saito, K. (2020) · RePEc: Research Papers in Economics · Cited by 49 · see citing works
Explicit Hamiltonians inducing volume law for entanglement entropy in fermionic lattices
Gori, G., Paganelli, S., Sharma, A., Sodano, P., & Trombettoni, A. (2015) · Physical Review B · doi:10.1103/physrevb.91.245138 · Cited by 47 · see citing works
Dynamics of Pair Correlations in the Attractive Lieb-Liniger Gas
Muth, D., & Fleischhauer, M. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.150403 · Cited by 47 · see citing works
Bounds in nonequilibrium quantum dynamics
Gong, Z., & Hamazaki, R. (2022) · International Journal of Modern Physics B · doi:10.1142/s0217979222300079 · Cited by 49 · see citing works
Lieb-Robinson Bounds and the Speed of Light from Topological Order
Hamma, A., Markopoulou, F., Prémont-Schwarz, I., & Simone Severini, B. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.017204 · Cited by 44 · see citing works
Scalable reconstruction of unitary processes and Hamiltonians
Holzäpfel, M., Baumgratz, T., Cramer, M., & Plenio, M. B. (2015) · Physical Review A · doi:10.1103/physreva.91.042129 · Cited by 41 · see citing works
Locality Estimates for Quantum Spin Systems
Nachtergaele, B., & Sims, R. (2009) · New Trends in Mathematical Physics · doi:10.1007/978-90-481-2810-5_39 · Cited by 49 · see citing works
Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
Métivier, D., Bachelard, R., & Kästner, M. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.210601 · Cited by 38 · see citing works
Sun, Z., Wu, Y.-Y., Xu, J., Huang, H., Zhan, B.-F., Wang, B., & Duan, C.-B. (2014) · Physical Review A · doi:10.1103/physreva.89.022101 · Cited by 41 · see citing works
Quantum quenches in two spatial dimensions using chain array matrix product states
James, A. J. A., & Konik, R. (2015) · Physical Review B · doi:10.1103/physrevb.92.161111 · Cited by 38 · see citing works
Lieb-Robinson bounds for commutator-bounded operators
Prémont-Schwarz, I., Hamma, A., Klich, I., & Markopoulou-Kalamara, F. (2010) · Physical Review A · doi:10.1103/physreva.81.040102 · Cited by 37 · see citing works
Lieb-Robinson Bound and Almost-Linear Light Cone in Interacting Boson Systems
Kuwahara, T., & Saito, K. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.070403 · Cited by 38 · see citing works
Rajabpour, M. A. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/06/063109 · Cited by 37 · see citing works
Light-cone velocities after a global quench in a noninteracting model
Najafi, K., Rajabpour, M. A., & Viti, J. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.205103 · Cited by 36 · see citing works
Dynamics with autoregressive neural quantum states: Application to critical quench dynamics
Donatella, K., Denis, Z., Le Boité, A., & Ciuti, C. (2023) · Physical Review A · doi:10.1103/physreva.108.022210 · Cited by 36 · see citing works
Computational Difficulty of Global Variations in the Density Matrix Renormalization Group
Eisert, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.260501 · Cited by 35 · see citing works
Self-citationEntanglement entropy in dynamic quantum-coherent conductors
Thomas, K. H., & Flindt, C. (2015) · Physical Review B · doi:10.1103/physrevb.91.125406 · Cited by 32 · see citing works
Lower bounds for ballistic current and noise in non-equilibrium quantum steady states
Doyon, B. (2015) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2015.01.007 · Cited by 29 · see citing works
Locally Accurate Tensor Networks for Thermal States and Time Evolution
Alhambra, A. M., & Cirac, J. I. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040331 · Cited by 29 · see citing works
- Authors
- Eisert, J., & Osborne, T. J.
- Affiliations
- London Institute for Mathematical Sciences (GB)
- Royal Holloway University of London (GB)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-10-12
- Volume
- 97
- Issue
- 15
- Pages
- 150404-150404
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2062419763
- Cited by
- 201
- References
- 49
- Citations by year
- 2026: 4 · 2025: 14 · 2024: 9 · 2023: 4 · 2022: 7 · 2021: 7 · 2020: 8 · 2019: 11 · 2018: 8 · 2017: 7 · 2016: 15 · 2015: 10 · 2014: 12 · 2013: 9 · 2012: 18
- FWCI
- 9.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- quantum spin chains, geometric entropy, Lieb-Robinson bound, sudden quench, quantum phase transitions, gapped ground states, fermionic systems, quantum information
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
