Multistability of Driven-Dissipative Quantum Spins

Abstract

We study the dynamics of coupled quantum spins one-half on a lattice with nearest-neighbour "XY" (flip-flop) interactions, driven by external fields and subject to dissipation. The meanfield limit of the model manifests bistable parameter regions of two coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to meanfield by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product-operators in one-and two-dimensional lattices. Correlations are shown to wash the meanfield bistability in dimension one, leading to a unique steady state. In dimension two and higher, we find that multistability is again possible in the thermodynamic limit. It is accompanied by jumps between the different steady states, each showing a critical slowing down in the convergence of perturbations towards the steady state. Experiments with trapped ions can realize the model and possibly answer open questions in the nonequilibrium many-body dynamics of these quantum systems, beyond the system sizes accessible to present numerics. *

Nonequilibrium magnetic phases in spin lattices with gain and loss

“…In the context of spin systems, a lot of previous work on this topic has been focused on the effect of dissipation on the stationary phases of the transverse field Ising and related XYZ models [4,7,12,14,20,22,30,32]. While the equilibrium properties of such models are well known, a general problem in the study of their dissipative counterparts is that reliable numerical simulations are only available in one dimension (1D), where, due to the added damping and (nonequilibrium) fluctuations, typically no sharp transitions occur [14,32]. Notable exceptions to this rule are certain classes of boundarydriven spin models, where dissipation only occurs at the ends [4,10,30].…”

“…Notable exceptions to this rule are certain classes of boundarydriven spin models, where dissipation only occurs at the ends [4,10,30]. In 2D and higher dimensions, where phase transitions are more easily engineered, exact numerical sim-ulations are restricted to rather small lattices [14,20,22,32], while predictions from mean-field theory are still questionable. Therefore, most of our more reliable insights about dissipative phase transitions are currently based on studies of zero-dimensional models, involving, for example, a collective spin S system [1,3,6,24,28,29], a weakly nonlinear bosonic mode [41][42][43], or combinations of both [2,17,26].…”

Dissipation-induced bistability in the two-photon Dicke model

“…As soon as one considers the quantum steadystate, however, only one solution is found 72 . This apparent contradiction can be solved by considering the full Liouvillian spectrum, where the onset of bistability is in close relation to the emergence of criticality 19,73,74 . Indeed, several models presenting bistable behaviour at the mean-field level proved to display a genuine first-order phase transition in the thermodynamic limit of a full quantum model 56,[75][76][77][78][79][80][81][82] .…”

On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices

“…They have subsequently been extended to finite temperatures [7,8], and to open quantum systems and density-matrix evolution [9,10]. Such methods have been very fruitful in exploring the nonequilibrium steady states (NESS) of driven-dissipative one-dimensional systems, using matrix product operators (MPO) [11][12][13][14][15][16][17][18][19][20][21]. These methods can also be extended beyond one dimension, either by mapping a finite two-dimensional lattice onto a one-dimensional chain [22]-see Ref.…”

“…These methods can also be extended beyond one dimension, either by mapping a finite two-dimensional lattice onto a one-dimensional chain [22]-see Ref. [21] for a driven-dissipative implementation-or via the projected entangled pair state (PEPS) algorithm [23][24][25][26]. The PEPS approach represents the two-dimensional lattice directly as a tensor network [3,4], and allows a direct simulation of an infinite (translationally invariant) lattice (iPEPS).…”