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

Area of Science:

• Statistical mechanics
• Condensed matter physics
• Computational physics

Background:

• Many-particle systems on lattices present computational challenges.
• Ratchets with volume exclusion and time-periodic drives exhibit complex dynamics.
• Traditional trajectory sampling can be computationally intensive for steady-state statistics.

Purpose of the Study:

• To develop an efficient computational method for steady-state current statistics in 1D ratchets.
• To approximate the distribution of many-body configurations using binary tree tensor network states.
• To investigate the effects of both typical and rare trajectories on system behavior.

Main Methods:

• Utilizing binary tree tensor network (BTTN) states to represent many-body configurations.
• Employing the Gillespie method for stochastic trajectory evolution.
• Applying the density matrix renormalization group (DMRG) algorithm for BTTN initialization.
• Propagating BTTN states in time using the time-dependent variational principle (TDVP) algorithm.

Main Results:

• The BTTN-TDVP approach successfully computes steady-state current statistics for a 1D ratchet model.
• The method provides a variational approximation to the distribution over many-body configurations.
• The approach accounts for the influence of both typical and rare trajectories.

Conclusions:

• Binary tree tensor network states offer a powerful alternative to trajectory sampling for studying interacting lattice models.
• The BTTN-TDVP strategy is beneficial for systems with time-dependent driving and volume exclusion.
• This approach is extendable to other complex interacting lattice models.