Dissipative dynamics at first-order quantum transitions

TL;DR

This paper studies how dissipation influences the out-of-equilibrium quantum dynamics at first-order quantum transitions in the 1D quantum Ising model, revealing a nontrivial dynamic scaling regime when dissipation scales with the energy gap.

Contribution

It introduces an analysis of dissipative effects at first-order quantum transitions, highlighting a dynamic scaling behavior analogous to continuous transitions but with exponentially suppressed energy gaps.

Findings

Dynamic scaling occurs when dissipation scales with the energy gap.

At first-order transitions, the energy gap is exponentially suppressed with system size.

Dissipative effects can induce nontrivial out-of-equilibrium dynamics at quantum transitions.

Abstract

We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $\Delta$ of the lowest levels of the Hamiltonian, i.e., $u\sim \Delta$. However, unlike continuous quantum transitions where $\Delta$ is power-law suppressed, at first-order quantum transitions $\Delta$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).