Is the efficiency of classical simulations of quantum dynamics related to integrability?
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Efficiency of time evolution of quantum observables, and thermal states of quenched Hamiltonians, is studied using time-dependent density-matrix renormalization group method in a family of generic quantum spin chains which undergo a transition from integrable to nonintegrable-quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-product operators with rank D(epsilon)(t), such that evolution of a long chain is accurate within fidelity error epsilon up to time t. We found that the rank generally increases exponentially D(epsilon)(t) proportional to exp(const t), unless the model system was integrable in which case we found polynomial increase.
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If the QPT is described by a CFT, it is characterized by a central charge c.
“If the QPT is described by a CFT (a specific subclass of one-dimensional critical systems), it is characterized by a central charge c . The central charge appears ubiquitously [187].”
From Can one trust quantum simulators? (2012) · cites this paper as [187]
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References 15 · Cited by 138
Research works printed but not linked: 1
- [1]G. Vidal, Phys. Rev. Lett. 91 , 147902 (2003); ibid. 93 , 040502 (2004); S. R. White and A. E. Feiguin, Phys. Rev. Lett. 93 , 076401 (2004); A. J. Daley, C. Kollath, U. Schollw¨ ock and G. Vidal, J. Stat. Mech. 4 , P04005 (2005); G. Vidal, cond-mat/0605597 . · arXiv
- Authors
- Prosen, T., & Žnidarič, M.
- Affiliations
- University of Ljubljana (SI)
- ORCID
- Prosen, Tomaž
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2007-01-11
- Volume
- 75
- Issue
- 1
- Pages
- 015202-015202
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2018882833
- Cited by
- 138
- References
- 15
- Citations by year
- 2026: 12 · 2025: 11 · 2024: 8 · 2023: 9 · 2022: 11 · 2021: 12 · 2020: 11 · 2019: 10 · 2018: 3 · 2017: 3 · 2016: 3 · 2015: 2 · 2014: 6 · 2013: 1 · 2012: 5
- FWCI
- 5.09
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (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 Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Keywords
- classical simulation of quantum dynamics, integrability, quantum chaos, time-dependent density matrix renormalization group, matrix product operators, quantum spin chains, quench dynamics, thermal states
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