From eigenstate to Hamiltonian: Prospects for ergodicity and localization

Journal Article · Mon Oct 07 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.100.134201· OSTI ID:1580943

Dupont, Maxime  ^[1]; Macé, Nicolas  ^[2]; Laflorencie, Nicolas ^[2]

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

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 Η_P 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-(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).

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; French National Research Agency (ANR); CALMIP; GENCI
• Grant/Contract Number: AC02-05CH11231; ANR-16-CE30-0023-02; ANR-11-IDEX-0002-02; 2018-P0677; 2019-P0677; 2018-A0030500225
• OSTI ID: 1580943
• Journal Information: Physical Review. B, Vol. 100, Issue 13; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY