Luis Colmenarez, Paul A. McClarty, Masudul Haque, David J. Luitz
SciPost Phys. 7, 064 (2019) ·
published 21 November 2019

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Ergodic quantum manybody systems satisfy the eigenstate thermalization
hypothesis (ETH). However, strong disorder can destroy ergodicity through
manybody localization (MBL)  at least in one dimensional systems  leading
to a clear signal of the MBL transition in the probability distributions of
energy eigenstate expectation values of local operators. For a paradigmatic
model of MBL, namely the randomfield Heisenberg spin chain, we consider the
full probability distribution of eigenstate correlation functions across the
entire phase diagram. We find gaussian distributions at weak disorder, as
predicted by pure ETH. At intermediate disorder  in the thermal phase  we
find further evidence for anomalous thermalization in the form of heavy tails
of the distributions. In the MBL phase, we observe peculiar features of the
correlator distributions: a strong asymmetry in $S_i^z S_{i+r}^z$ correlators
skewed towards negative values; and a multimodal distribution for spinflip
correlators. A quantitative quasidegenerate perturbation theory calculation of
these correlators yields a surprising agreement of the full distribution with
the exact results, revealing, in particular, the origin of the multiple peaks
in the spinflip correlator distribution as arising from the resonant and
offresonant admixture of spin configurations. The distribution of the
$S_i^zS_{i+r}^z$ correlator exhibits striking differences between the MBL and
Anderson insulator cases.
SciPost Phys. 5, 045 (2018) ·
published 6 November 2018

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We provide a pedagogical review on the calculation of highly excited
eigenstates of disordered interacting quantum systems which can undergo a
manybody localization (MBL) transition, using shiftinvert exact
diagonalization. We also provide an example code at
https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the
simulational parameters of the random field Heisenberg spin chain, we provide a
practical guide on how to perform efficient computations. We present data for
midspectrum eigenstates of spin chains of sizes up to $L=26$. This work is
also geared towards readers with interest in efficiency of parallel sparse
linear algebra techniques that will find a challenging application in the MBL
problem.
David J. Luitz, Yevgeny Bar Lev, Achilleas Lazarides
SciPost Phys. 3, 029 (2017) ·
published 25 October 2017

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Using a numerically exact method we study the stability of dynamical
localization to the addition of interactions in a periodically driven isolated
quantum system which conserves only the total number of particles. We find that
while even infinitesimally small interactions destroy dynamical localization,
for weak interactions density transport is significantly suppressed and is
asymptotically diffusive, with a diffusion coefficient proportional to the
interaction strength. For systems tuned away from the dynamical localization
point, even slightly, transport is dramatically enhanced and within the largest
accessible systems sizes a diffusive regime is only pronounced for sufficiently
small detunings.
SciPost Phys. 2, 011 (2017) ·
published 24 March 2017

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Using quantum Monte Carlo simulations, we compute the participation
(ShannonR\'enyi) entropies for groundstate wave functions of Heisenberg
antiferromagnets for onedimensional (line) subsystems of length $L$ embedded
in twodimensional ($L\times L$) square lattices. We also study the line
entropy at finite temperature, i.e. of the diagonal elements of the density
matrix, for threedimensional ($L\times L\times L$) cubic lattices. The
breaking of SU(2) symmetry is clearly captured by a universal logarithmic
scaling term $l_q\ln L$ in the R\'enyi entropies, in good agreement with the
recent fieldtheory results of Misguish, Pasquier and Oshikawa
[arXiv:1607.02465]. We also study the dependence of the log prefactor $l_q$ on
the R\'enyi index $q$ for which a transition is detected at $q_c\simeq 1$.
Submissions
Submissions for which this Contributor is identified as an author:
Dr Luitz: "We thank the referee for contr..."
in Report on Absence of dynamical localization in interacting driven systems