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Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points
Open accessAbstract
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finite-entanglement scaling in one-dimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.
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Cites
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Entanglement 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
“Using equation (68), it has been possible to calculate this exponent exactly [109], obtaining”
BackgroundVariational optimization algorithms for uniform matrix product states
Zauner-Stauber, V., Vanderstraeten, L., Fishman, M. T., Verstraete, F., & Haegeman, J. (2018) · Physical Review B · doi:10.1103/physrevb.97.045145 · Cited by 270
Tensor Network Contractions: Methods and Applications to Quantum Many-Body Systems
Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture Notes in Physics · doi:10.1007/978-3-030-34489-4 · Cited by 176
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Fishman, M. T., Vanderstraeten, L., Zauner-Stauber, V., Haegeman, J., & Verstraete, F. (2018) · Physical Review B · doi:10.1103/physrevb.98.235148 · Cited by 128
Matrix product states and variational methods applied to critical quantum field theory
Milsted, A., Haegeman, J., & Osborne, T. J. (2013) · Physical Review D · doi:10.1103/physrevd.88.085030 · Cited by 88
Metadata
- Authors
- Pollmann, F., Mukerjee, S., Turner, A. M., & Moore, J. E.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2009-06-26
- Volume
- 102
- Issue
- 25
- Pages
- 255701-255701
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2085739341
- Cited by
- 364
- References
- 9
- FWCI
- 7.43
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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