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We present an approach based upon binary tree tensor network (BTTN) statesfor computing steady-state current statistics for a many-particle 1D ratchetsubject to volume exclusion interactions. The ratcheted particles, which moveon a lattice with periodic boundary conditions subject to a time-periodicdrive, can be stochastically evolved in time to sample representativetrajectories via a Gillespie method. In lieu of generating realizations oftrajectories, a BTTN state can variationally approximate a distribution overthe vast number of many-body configurations. We apply the density matrixrenormalization group (DMRG) algorithm to initialize BTTN states, which arethen propagated in time via the time-dependent variational principle (TDVP)algorithm to yield the steady-state behavior, including the effects of bothtypical and rare trajectories. The application of the methods to ratchetcurrents is highlighted in a companion letter, but the approach extendsnaturally to other interacting lattice models with time-dependent driving.Though trajectory sampling is conceptually and computationally simpler, wediscuss situations for which the BTTN TDVP strategy could be more favorable.

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