From eigenstate to Hamiltonian: Prospects for ergodicity and localization

Maxime Dupont, Nicolas Macé, and Nicolas Laflorencie
Phys. Rev. B 100, 134201 – Published 7 October 2019

Abstract

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 H0, we ask whether or not there exists another parent Hamiltonian HP 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)] 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 σP2(L)=HP2Ψ0HPΨ02 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 σP2(L) remains finite at the thermodynamic limit, i.e., L+. As a direct consequence, the ergodic-MBL transition can be very well captured from the scaling of σP2(L).

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
8 More
  • Received 31 July 2019

DOI:https://doi.org/10.1103/PhysRevB.100.134201

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Maxime Dupont1,2, Nicolas Macé3, and Nicolas Laflorencie3

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 3Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 100, Iss. 13 — 1 October 2019

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×