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.
Emil Viñas Boström, Martin Claassen, James W. McIver, Gregor Jotzu, Angel Rubio, Michael A. Sentef
SciPost Phys. 9, 061 (2020) ·
published 30 October 2020
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Driving a two-dimensional Mott insulator with circularly polarized light breaks time-reversal and inversion symmetry, which induces an optically-tunable synthetic scalar spin chirality interaction in the effective low-energy spin Hamiltonian. Here, we show that this mechanism can stabilize topological magnon excitations in honeycomb ferromagnets and in optical lattices. We find that the irradiated quantum magnet is described by a Haldane model for magnons that hosts topologically-protected edge modes. We study the evolution of the magnon spectrum in the Floquet regime and via time propagation of the magnon Hamiltonian for a slowly varying pulse envelope. Compared to similar but conceptually distinct driving schemes based on the Aharanov-Casher effect, the dimensionless light-matter coupling parameter $\lambda = eEa/\hbar\omega$ at fixed electric field strength is enhanced by a factor $\sim 10^5$. This increase of the coupling parameter allows to induce a topological gap of the order of $\Delta \approx 2$ meV with realistic laser pulses, bringing an experimental realization of light-induced topological magnon edge states within reach.
