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

TL;DR

This paper introduces a tensor network approach using binary tree tensor network states and the time-dependent variational principle to compute steady-state currents in a driven, interacting 1D lattice system, offering an alternative to trajectory sampling methods.

Contribution

The paper develops a novel tensor network method combining BTTN states and TDVP for efficiently computing steady states in time-periodically driven many-body systems.

Findings

Successfully applied to ratchet current calculations

Can handle rare trajectories in steady-state analysis

Offers a potentially more efficient alternative to trajectory sampling

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.