Thermal and dissipative effects on the heating transition in a driven critical system

TL;DR

This paper investigates how dissipation and thermal effects influence the heating transition in a driven critical one-dimensional lattice system, combining conformal field theory and exact lattice calculations.

Contribution

It extends the understanding of heating phases in driven critical systems by analyzing thermal initial states and open systems with dissipation, supported by analytical and exact numerical results.

Findings

Heating and non-heating phases persist for thermal initial states.

Spatial structure of heating survives dissipation in open systems.

Signatures of heating phases observed in mutual information and energy density.

Abstract

We study the dissipative dynamics of a periodically driven inhomogeneous critical lattice model in one dimension. The closed system dynamics starting from pure initial states is well-described by a driven Conformal Field Theory (CFT), which predicts the existence of both heating and non-heating phases in such systems. Heating is inhomogeneous and is manifested via the emergence of black-hole like horizons in the system. The robustness of this CFT phenomenology when considering thermal initial states and open systems remains elusive. First, we present analytical results for the Floquet CFT time evolution for thermal initial states. Moreover, using exact calculations of the time evolution of the lattice density matrix, we demonstrate that for short and intermediate times, the closed system phase diagram comprising heating and non-heating phases, persists for thermal initial states on the lattice. Secondly, in the fully open system with boundary dissipators, we show that the nontrivial spatial structure of the heating phase survives particle-conserving and non-conserving dissipations through clear signatures in mutual information and energy density evolution.