Stationary states of dissipative many-body quantum systems via matrix product operators

Jian Cui, J. I. Cirac, Mari Carmen Bañuls

We present a new variational method based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus, allowing for a faster convergence when the steady state is a MPO with small bond dimension. Our numerical simulations for several dissipative spin models over a wide range of parameters illustrate the performance of the method and show that, indeed, the stationary state is often well described by a MPO of very moderate dimensions.

Vasily E Tarasov

Jérémy Faupin, François Nicoleau

David Wellnitz, Guillermo Preisser, Vincenzo Alba +2 more

The operator space entanglement entropy, or simply "operator entanglement" (OE), is an indicator of the complexity of quantum operators and of their approximability by matrix product operators (MPOs). We study the OE of the density matrix of 1D many-body models undergoing dissipative evolution. It is expected that, after an initial linear growth reminiscent of unitary quench dynamics, the OE should be suppressed by dissipative processes as the system evolves to a simple stationary state. Surprisingly, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial "rise and fall," the OE can rise again, increasing logarithmically at long times. Using a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, we demonstrate that this growth is inherent to a U(1) conservation law. We argue that in an XXZ spin model and a Bose-Hubbard model the OE grows universally as 1/4log_{2}t at long times and as 1/2log_{2}t for a Fermi-Hubbard model. We trace this behavior back to anomalous classical diffusion processes.

Viacheslav Aleksandrovich Krivorol, Mikhail Yu. Nalimov

Zihan Cheng, Andrew C. Potter

We present a numerical method to simulate nonequilibrium Floquet steady states of one-dimensional periodically driven many-body systems coupled to a dissipative bath, based on a matrix product operator ansatz for the Floquet density matrix in frequency space. This method enables access to large systems beyond the reach of exact simulations, while retaining the periodic micromotion information. An excited-state extension of this technique allows computation of the dynamical approach to the steady state. We benchmark our method with a driven-dissipative Ising model and apply it to study the possibility of stabilizing prethermal discrete time-crystalline order by coupling to a cold bath.