Abstract
Driven-dissipative quantum many-body systems have attracted increasing interest in recent years as they lead to novel classes of quantum many-body phenomena. In particular, mean-field calculations predict limit cycle phases, slow oscillations instead of stationary states, in the long-time limit for a number of driven-dissipative quantum many-body systems. Using a cluster mean-field and a self-consistent Mori projector approach, we explore the persistence of such limit cycles as short range quantum correlations are taken into account in a driven-dissipative Heisenberg model.
Highlights
Understanding the phases of quantum many-body systems is one of the central goals of modern physics
We explore the existence of limit cycle phases for the model specified in equation (3) via two methods, selfconsistent Mori projectors and cluster mean field
We timeintegrate the equations of motion of the respective reduced density matrices using both the self-consistent Mori projector method and cluster mean-field theory until t ? γ−1, where the transient behaviour due to the product state initialisation has decayed and the system has either entered into a limit cycle or has reached a timeindependent steady state
Summary
Understanding the phases of quantum many-body systems is one of the central goals of modern physics. Recent advances have provided the opportunity to extend this field into the exploration of the phase diagrams of non-equilibrium quantum systems where excitations which dissipate from the system are replenished using an external driving field [3,4,5]. Experimental platforms, such as cavity arrays, superconducting circuits and polariton waveguides, have introduced a new class of systems where the interplay between coherent driving and incoherent dissipation has led to the discovery of novel phenomena. Realising limit cycles would be the discovery of a new class of phases in driven dissipative quantum many-body systems but could have important technological applications, for example in synchronising quantum many-body devices [10, 17]
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