Title: 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 ψ ₀, an eigenstate of a given local Hamiltonian Η ₀, we ask whether or not there exists another parent Hamiltonian Η _P for ψ ₀, with the same local form as H ₀. 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-(Η _P)$$_{ψ_0}^2$$ 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:

Dupont, Maxime  ^[1];

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Macé, Nicolas  ^[2];

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Laflorencie, Nicolas ^[2]

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+ Show Author Affiliations

1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2. Université de Toulouse, CNRS, UPS (France)

Publication Date:

2019-10-07

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