Damian Hofmann, Giammarco Fabiani, Johan H. Mentink, Giuseppe Carleo, Michael A. Sentef
SciPost Phys. 12, 165 (2022) ·
published 18 May 2022
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Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent variational Monte Carlo (t-VMC). In particular, stable and accurate time propagation over long time scales has been observed in the square-lattice Heisenberg model using the Restricted Boltzmann machine architecture. However, achieving similar performance in other systems has proven to be more challenging. In this article, we focus on the two-leg Heisenberg ladder driven out of equilibrium by a pulsed excitation as a benchmark system. We demonstrate that unmitigated noise is strongly amplified by the nonlinear equations of motion for the network parameters, which causes numerical instabilities in the time evolution. As a consequence, the achievable accuracy of the simulated dynamics is a result of the interplay between network expressiveness and measures required to remedy these instabilities. We show that stability can be greatly improved by appropriate choice of regularization. This is particularly useful as tuning of the regularization typically imposes no additional computational cost. Inspired by machine learning practice, we propose a validation-set based diagnostic tool to help determining optimal regularization hyperparameters for t-VMC based propagation schemes. For our benchmark, we show that stable and accurate time propagation can be achieved in regimes of sufficiently regularized variational dynamics.
SciPost Phys. 7, 004 (2019) ·
published 5 July 2019
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We investigate the efficiency of the recently proposed Restricted Boltzmann
Machine (RBM) representation of quantum many-body states to study both the
static properties and quantum spin dynamics in the two-dimensional Heisenberg
model on a square lattice. For static properties we find close agreement with
numerically exact Quantum Monte Carlo results in the thermodynamical limit. For
dynamics and small systems, we find excellent agreement with exact
diagonalization, while for systems up to N=256 spins close consistency with
interacting spin-wave theory is obtained. In all cases the accuracy converges
fast with the number of network parameters, giving access to much bigger
systems than feasible before. This suggests great potential to investigate the
quantum many-body dynamics of large scale spin systems relevant for the
description of magnetic materials strongly out of equilibrium.
Marion M. S. Barbeau, Martin Eckstein, Mikhail I. Katsnelson, Johan H. Mentink
SciPost Phys. 6, 027 (2019) ·
published 5 March 2019
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In order to have a better understanding of ultrafast electrical control of
exchange interactions in multi-orbital systems, we study a two-orbital Hubbard
model at half filling under the action of a time-periodic electric field. Using
suitable projection operators and a generalized time-dependent canonical
transformation, we derive an effective Hamiltonian which describes two
different regimes. First, for a wide range of non-resonant frequencies, we find
a change of the bilinear Heisenberg exchange $J_{\textrm{ex}}$ that is
analogous to the single-orbital case. Moreover we demonstrate that also the
additional biquadratic exchange interaction $B_{\textrm{ex}}$ can be enhanced,
reduced and even change sign depending on the electric field. Second, for
special driving frequencies, we demonstrate a novel spin-charge coupling
phenomenon enabling coherent transfer between spin and charge degrees of
freedom of doubly ionized states. These results are confirmed by an exact
time-evolution of the full two-orbital Mott-Hubbard Hamiltonian.
