Quantum critical systems with dissipative boundaries

TL;DR

This paper investigates how dissipative boundaries affect the critical dynamics of quantum many-body systems, revealing distinct early and late-time scaling regimes through models of fermionic wires coupled to Markovian baths.

Contribution

It extends the critical scaling framework to include boundary dissipation effects, providing a unified description of quantum evolution near criticality.

Findings

Identification of an early-time finite-size scaling regime.

Discovery of a late-time scaling regime leading to stationary states.

Extension of critical dynamics scaling to dissipative boundary conditions.

Abstract

We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we consider fermionic wires subject to dissipative interactions at the boundaries, associated with pumping or loss of particles. They are induced by couplings with a Markovian baths, so that the evolution of the system density matrix can be described by a Lindblad master equation. We study the quantum evolution arising from variations of the Hamiltonian and dissipation parameters, starting at t=0 from the ground state of the critical Hamiltonian. Two different dynamic regimes emerge: (i) an early-time regime for times t ~ L, where the competition between coherent and incoherent drivings develops a dynamic finite-size scaling, obtained by extending the scaling framework describing the coherent critical dynamics of the closed system, to allow for the boundary dissipation; (ii) a large-time regime for t ~ L^3 whose dynamic scaling describes the late quantum evolution leading to the t->infty stationary states.