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arXiv · 2201.04107

Computing time-periodic steady-state currents via the time evolution of tensor network states

Nils E. Strand·Hadrien Vroylandt·Todd R. Gingrich
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Abstract

We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group (DMRG) algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted in a companion letter, but the approach extends naturally to other interacting lattice models with time-dependent driving. Though trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy could be more favorable.

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Nils E. Strand, Hadrien Vroylandt, Todd R. Gingrich. 2022-01-11. Computing time-periodic steady-state currents via the time evolution of tensor network states. https://doi.org/10.1063/5.0099741

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