Exact Solutions and New Insights into the Driven-Dissipative Ising Model

Exact solutions for many-body quantum systems far from thermal equilibrium are comparatively scarce. For example, a quantum Ising chain subject to dissipation in the bulk can no longer be mapped to free fermions. At small dissipation, however, integrability is only weakly broken, and a description in terms of a generalized Gibbs ensemble becomes available. Using this framework, I present an exact, but nontrivial, equation governing the nonlinear dynamics of the driven-dissipative Ising model in terms of fermions. We find that the analytical solution is in excellent agreement with exact matrix-product-state numerical simulations even for moderate values of dissipation. As an aside, we show that the steady state of the driven-dissipative Ising model is sensitive to the quantum critical point of the Ising model in the absence of dissipation. We explain this feature by analogy with fermions and with the aid of the exact solution. Our work provides new insights into the nature of many-body dynamics of quantum simulators in the presence of noise.