From eigenstate to Hamiltonian: Prospects for ergodicity and localization
Abstract
Here, this paper addresses the so-called inverse problem which consists in searching for (possibly multiple) parent target Hamiltonian(s), given a single quantum state as input. Starting from ψ0, an eigenstate of a given local Hamiltonian Η0, we ask whether or not there exists another parent Hamiltonian ΗP for ψ0, with the same local form as H0. Focusing on one-dimensional quantum disordered systems, we extend the recent results obtained for Bose-glass ground states [M. Dupont and N. Laflorencie, Phys. Rev. B 99, 020202(R) (2019)2469-995010.1103/PhysRevB.99.020202] to Anderson localization, and the many-body localization (MBL) physics occurring at high energy. We generically find that any localized eigenstate is a very good approximation for an eigenstate of a distinct parent Hamiltonian, with an energy variance σ$$_P^2$$(L)=⟨$$H^2_P$$⟩ψ0-(ΗP)$$_{ψ_0}^2$$ vanishing as a power law of system size L. This decay is microscopically related to a chain-breaking mechanism, also signaled by bottlenecks of vanishing entanglement entropy. A similar phenomenology is observed for both Anderson and MBL. In contrast, delocalized ergodic many-body eigenstates uniquely encode the Hamiltonian in the sense that σ$$_P^2$$(L) remains finite at the thermodynamic limit, i.e., L → +∞. Finally, as a direct consequence, the ergodic-MBL transition can be very well captured from the scaling of σ$$_P^2$$(L).
- Authors:
-
[1];
[2];
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Université de Toulouse, CNRS, UPS (France)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; French National Research Agency (ANR); CALMIP; GENCI
- OSTI Identifier:
- 1580943
- Grant/Contract Number:
- AC02-05CH11231; ANR-16-CE30-0023-02; ANR-11-IDEX-0002-02; 2018-P0677; 2019-P0677; 2018-A0030500225
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 13; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Dupont, Maxime, Macé, Nicolas, and Laflorencie, Nicolas. From eigenstate to Hamiltonian: Prospects for ergodicity and localization. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.134201.
Dupont, Maxime, Macé, Nicolas, & Laflorencie, Nicolas. From eigenstate to Hamiltonian: Prospects for ergodicity and localization. United States. doi:10.1103/physrevb.100.134201.
Dupont, Maxime, Macé, Nicolas, and Laflorencie, Nicolas. Mon .
"From eigenstate to Hamiltonian: Prospects for ergodicity and localization". United States. doi:10.1103/physrevb.100.134201. https://www.osti.gov/servlets/purl/1580943.
@article{osti_1580943,
title = {From eigenstate to Hamiltonian: Prospects for ergodicity and localization},
author = {Dupont, Maxime and Macé, Nicolas and Laflorencie, Nicolas},
abstractNote = {Here, this paper addresses the so-called inverse problem which consists in searching for (possibly multiple) parent target Hamiltonian(s), given a single quantum state as input. Starting from ψ0, an eigenstate of a given local Hamiltonian Η0, we ask whether or not there exists another parent Hamiltonian ΗP for ψ0, with the same local form as H0. Focusing on one-dimensional quantum disordered systems, we extend the recent results obtained for Bose-glass ground states [M. Dupont and N. Laflorencie, Phys. Rev. B 99, 020202(R) (2019)2469-995010.1103/PhysRevB.99.020202] to Anderson localization, and the many-body localization (MBL) physics occurring at high energy. We generically find that any localized eigenstate is a very good approximation for an eigenstate of a distinct parent Hamiltonian, with an energy variance σ$_P^2$(L)=⟨$H^2_P$⟩ψ0-(ΗP)$_{ψ_0}^2$ vanishing as a power law of system size L. This decay is microscopically related to a chain-breaking mechanism, also signaled by bottlenecks of vanishing entanglement entropy. A similar phenomenology is observed for both Anderson and MBL. In contrast, delocalized ergodic many-body eigenstates uniquely encode the Hamiltonian in the sense that σ$_P^2$(L) remains finite at the thermodynamic limit, i.e., L → +∞. Finally, as a direct consequence, the ergodic-MBL transition can be very well captured from the scaling of σ$_P^2$(L).},
doi = {10.1103/physrevb.100.134201},
journal = {Physical Review B},
number = 13,
volume = 100,
place = {United States},
year = {2019},
month = {10}
}
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