SciPost Phys. 10, 044 (2021) ·
published 22 February 2021
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We numerically study the possibility of many-body localization transition in
a disordered quantum dimer model on the honeycomb lattice. By using the
peculiar constraints of this model and state-of-the-art exact diagonalization
and time evolution methods, we probe both eigenstates and dynamical properties
and conclude on the existence of a localization transition, on the available
time and length scales (system sizes of up to N=108 sites). We critically
discuss these results and their implications.
SciPost Phys. 10, 019 (2021) ·
published 28 January 2021
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Within the tensor network framework, the (positive) thermal density operator
can be approximated by a double layer of infinite Projected Entangled Pair
Operator (iPEPO) coupled via ancilla degrees of freedom. To investigate the
thermal properties of the spin-1/2 Heisenberg model on the square lattice, we
introduce a family of fully spin-$SU(2)$ and lattice-$C_{4v}$ symmetric on-site
tensors (of bond dimensions $D=4$ or $D=7$) and a plaquette-based
Trotter-Suzuki decomposition of the imaginary-time evolution operator. A
variational optimization is performed on the plaquettes, using a full (for
$D=4$) or simple (for $D=7$) environment obtained from the single-site Corner
Transfer Matrix Renormalization Group fixed point. The method is benchmarked by
a comparison to quantum Monte Carlo in the thermodynamic limit. Although the
iPEPO spin correlation length starts to deviate from the exact exponential
growth for inverse-temperature $\beta \gtrsim 2$, the behavior of various
observables turns out to be quite accurate once plotted w.r.t the inverse
correlation length. We also find that a direct $T=0$ variational energy
optimization provides results in full agreement with the
$\beta\rightarrow\infty$ limit of finite-temperature data, hence validating the
imaginary-time evolution procedure. Extension of the method to frustrated
models is described and preliminary results are shown.
SciPost Phys. 6, 050 (2019) ·
published 29 April 2019
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We study the many-body localization (MBL) properties of a chain of
interacting fermions subject to a quasiperiodic potential such that the
non-interacting chain is always delocalized and displays multifractality.
Contrary to naive expectations, adding interactions in this systems does not
enhance delocalization, and a MBL transition is observed. Due to the local
properties of the quasiperiodic potential, the MBL phase presents specific
features, such as additional peaks in the density distribution. We furthermore
investigate the fate of multifractality in the ergodic phase for low potential
values. Our analysis is based on exact numerical studies of eigenstates and
dynamical properties after a quench.
Francesca Pietracaprina, Nicolas Macé, David J. Luitz, Fabien Alet
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
many-body localization (MBL) transition, using shift-invert 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
mid-spectrum 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.
