Exponentially slow thermalization and the robustness of Hilbert space fragmentation (2401.11294v1)
Abstract: The phenomenon of Hilbert space fragmentation, whereby dynamical constraints fragment Hilbert space into many disconnected sectors, provides a simple mechanism by which thermalization can be arrested. However, little is known about how thermalization occurs in situations where the constraints are not exact. To study this, we consider a situation in which a fragmented 1d chain with pair-flip constraints is coupled to a thermal bath at its boundary. For product states quenched under Hamiltonian dynamics, we numerically observe an exponentially long thermalization time, manifested in both entanglement dynamics and the relaxation of local observables. To understand this, we study an analogous model of random unitary circuit dynamics, where we rigorously prove that the thermalization time scales exponentially with system size. Slow thermalization in this model is shown to be a consequence of strong bottlenecks in configuration space, demonstrating a new way of producing anomalously slow thermalization dynamics.
- J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
- M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
- M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature 452, 854 (2008).
- R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annual Review of Condensed Matter Physics 6, 15 (2015).
- F. Alet and N. Laflorencie, Many-body localization: An introduction and selected topics, Comptes Rendus Physique 19, 498 (2018), quantum simulation / Simulation quantique.
- V. Khemani, M. Hermele, and R. Nandkishore, Localization from hilbert space shattering: From theory to physical realizations, Phys. Rev. B 101, 174204 (2020).
- S. Moudgalya and O. I. Motrunich, Hilbert space fragmentation and commutant algebras, Phys. Rev. X 12, 011050 (2022a).
- M. van Horssen, E. Levi, and J. P. Garrahan, Dynamics of many-body localization in a translation-invariant quantum glass model, Physical Review B 92, 100305 (2015).
- P. Brighi, M. Ljubotina, and M. Serbyn, Hilbert space fragmentation and slow dynamics in particle-conserving quantum east models, SciPost Physics 15, 093 (2023).
- M. Will, R. Moessner, and F. Pollmann, Realization of hilbert space fragmentation and fracton dynamics in 2d, arXiv preprint arXiv:2311.05695 (2023).
- Y. Li, P. Sala, and F. Pollmann, Hilbert space fragmentation in open quantum systems, Physical Review Research 5 (2023).
- T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum newton’s cradle, Nature 440, 900 (2006).
- M. T. Batchelor and A. Kuniba, Temperley-lieb lattice models arising from quantum groups, Journal of Physics A: Mathematical and General 24, 2599 (1991).
- B. Aufgebauer and A. Klümper, Quantum spin chains of temperley–lieb type: periodic boundary conditions, spectral multiplicities and finite temperature, Journal of Statistical Mechanics: Theory and Experiment 2010, P05018 (2010).
- S. Moudgalya and O. I. Motrunich, Hilbert space fragmentation and commutant algebras, Physical Review X 12, 011050 (2022b).
- R. Lyons and Y. Peres, Probability on trees and networks, Vol. 42 (Cambridge University Press, 2017).
- M. Fishman, S. White, and E. Stoudenmire, The itensor software library for tensor network calculations, SciPost Physics Codebases , 004 (2022).
- V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
- L. Santos, Integrability of a disordered heisenberg spin-1/2 chain, Journal of Physics A: Mathematical and General 37, 4723 (2004).
- V. B. Bulchandani, D. A. Huse, and S. Gopalakrishnan, Onset of many-body quantum chaos due to breaking integrability, Physical Review B 105, 214308 (2022).
- O. Hart, Exact mazur bounds in the pair-flip model and beyond, arXiv preprint arXiv:2308.00738 (2023).
- W. Woess, Random walks on infinite graphs and groups, 138 (Cambridge university press, 2000).
- D. A. Levin and Y. Peres, Markov chains and mixing times, Vol. 107 (American Mathematical Soc., 2017).
- Q. Gao, P. Zhang, and X. Chen, Information scrambling in free fermion systems with a sole interaction (2023), arXiv:2310.07043 [quant-ph] .
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
