Exceptional Spectral Phase in a Dissipative Collective Spin Model

TL;DR

This paper investigates a dissipative collective spin model revealing a novel exceptional spectral phase characterized by unique eigenvalue properties, critical phenomena, and implications for quantum phase transitions and boundary time crystals.

Contribution

It introduces the concept of exceptional spectral phases in dissipative quantum systems, highlighting the presence of second order exceptional points and associated critical phenomena.

Findings

Identification of normal and exceptional Liouvillian spectral phases.

Discovery of a critical line with diverging eigenvalue density.

Linking the exceptional phase to dissipative quantum phase transitions and boundary time crystals.

Abstract

We study a model of a quantum collective spin weakly coupled to a spin-polarized Markovian environment and find that the spectrum is divided into two regions that we name normal and exceptional Liouvillian spectral phases. In the thermodynamic limit, the exceptional spectral phase displays the unique property of being made up exclusively of second order exceptional points. As a consequence, the evolution of any initial density matrix populating this region is slowed down and cannot be described by a linear combination of exponential decays. This phase is separated from the normal one by a critical line in which the density of Liouvillian eigenvalues diverges, a phenomenon analogous to that of excited-state quantum phase transitions observed in some closed quantum systems. In the limit of no bath polarization, this criticality is transferred onto the steady state, implying a dissipative quantum phase transition and the formation of a boundary time crystal.