Continuous Dissipative Phase Transitions without Symmetry Breaking

TL;DR

This paper demonstrates that second-order dissipative phase transitions can occur without spontaneous symmetry breaking, challenging the traditional understanding that SSB is necessary for such critical phenomena in open quantum systems.

Contribution

The authors analytically prove that SSB is not required for second-order DPTs and illustrate this with models where criticality persists without symmetry breaking.

Findings

Second-order DPTs can occur without SSB.

Criticality can be retained while removing SSB.

The steady state remains unique after the transition.

Abstract

The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Dissipative phase transitions (DPTs) of second order are often connected with SSB, in close analogy with well-known thermal second-order PTs in closed quantum and classical systems. That is, a second-order DPT should disappear by preventing the occurrence of SSB. Here, we prove this statement to be wrong, showing that, surprisingly, SSB is not a necessary condition for the occurrence of second-order DPTs in out-of-equilibrium open quantum systems. We analytically prove this result using the Liouvillian theory of dissipative phase transitions, and demonstrate this anomalous transition in a paradigmatic laser model, where we can arbitrarily remove SSB while retaining criticality, and on a $Z_2$-symmetric model of a two-photon Kerr resonator. This new type of phase transition cannot be interpreted as a "semiclassical" bifurcation, because, after the DPT, the system steady state remains unique.