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Applying matrix product operators to model systems with long-range interactions
Open accessAbstract
An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite one-dimensional (1D) system. It does this by embedding sites into an approximation of the infinite ``environment'' of the chain, allowing the sites to relax and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply these techniques to compute the ground state of the Haldane-Shastry model [Phys. Rev. Lett. 60, 635 (1988) and Phys. Rev. Lett. 60, 639 (1988)] and present the results.
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Citations
Cites
The density-matrix renormalization group
Schollwöck, U. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.259 · Cited by 3,323
Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions
Jordan, J., Orús, R., Vidal, G., Verstraete, F., & Cirac, J. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.250602 · Cited by 710
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Cited by
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
OpenMolcas: From Source Code to Insight
Fdez. Galván, I., Vacher, M., Alavi, A., Angeli, C., Aquilante, F., Autschbach, J., Bao, J. J., Bokarev, S. I., Bogdanov, N. A., Carlson, R. K., et al. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b00532 · Cited by 1,114
Quantum trajectories and open many-body quantum systems
Daley, A. J. (2014) · Advances in Physics · doi:10.1080/00018732.2014.933502 · Cited by 853
Time-evolving a matrix product state with long-ranged interactions
Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E., & Pollmann, F. (2015) · Physical Review B · doi:10.1103/physrevb.91.165112 · Cited by 323
Metadata
- Authors
- Crosswhite, G. M., Doherty, A. C., & Vidal, G.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2008-07-14
- Volume
- 78
- Issue
- 3
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1997895393
- Cited by
- 176
- References
- 2
- FWCI
- 0.97
- Type
- journal article
- Language
- en
- Open access
- green
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