Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems

Abstract

The tensor network states (TNS) methods combined with Monte Carlo (MC) techniques have been proved a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling techniques, by mapping the energy function of the TNS to that of a classical dynamical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.

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• Solving frustrated quantum many-particle models with convolutional neural networks
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• Tunneling frustration induced peculiar supersolid phases in the extended Bose-Hubbard model
• Exotic Spin Phases in Two Dimensional Spin-orbit Coupled Models: Importance of Quantum Fluctuation Effects
• Projected entangled pair states study of anisotropic-exchange magnets on triangular lattice