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Many-body localization as a large family of localized ground states

Journal Article · · Physical Review B
 [1];  [2]
  1. Université de Toulouse, CNRS, UPS (France); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Université de Toulouse, CNRS, UPS (France)

Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with nonergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. Here, we find that a localized many-body ground state of a given interacting disordered Hamiltonian H0 is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to H0 but more disordered. Lastly, this construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to L=256 sites.

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
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1506401
Alternate ID(s):
OSTI ID: 1490912
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 2 Vol. 99; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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  • Devakul, Trithep; Khemani, Vedika; Pollmann, Frank
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 375, Issue 2108 https://doi.org/10.1098/rsta.2016.0431
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Many-body localization edge in the random-field Heisenberg chain text January 2014
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Finding matrix product state representations of highly-excited eigenstates of many-body localized Hamiltonians text January 2015
Entanglement scaling of excited states in large one-dimensional many-body localized systems text January 2015
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Many body localization and thermalization: insights from the entanglement spectrum text January 2016
Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain text January 2016
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Critical Properties of the Many-Body Localization Transition text January 2016
Obtaining highly excited eigenstates of the localized XX chain via DMRG-X text January 2017
Many-body Localization Transition: Schmidt Gap, Entanglement Length & Scaling text January 2017
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Competing Bose-Glass physics with disorder-induced Bose-Einstein condensation in the doped $S=1$ antiferromagnet Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ at high magnetic fields text January 2017
Time Evolution of Many-Body Localized Systems with the Flow Equation Approach text January 2017
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Cited By (6)

From eigenstate to Hamiltonian: Prospects for ergodicity and localization journal October 2019
Kosterlitz-Thouless scaling at many-body localization phase transitions journal March 2019
Multiscale entanglement clusters at the many-body localization phase transition journal April 2019
Entanglement-Guided Search for Parent Hamiltonians journal April 2019
Entanglement guided search for parent Hamiltonians text January 2018
Kosterlitz-Thouless scaling at many-body localization phase transitions text January 2018

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