Phase diagram of the dissipative quantum Ising model on a square lattice

Abstract

The competition between interactions and dissipative processes in a quantum many-body system can drive phase transitions of different order. Exploiting a combination of cluster methods and quantum trajectories, we show how the systematic inclusion of (classical and quantum) nonlocal correlations at increasing distances is crucial to determine the structure of the phase diagram, as well as the nature of the transitions in strongly interacting spin systems. In practice, we focus on the paradigmatic dissipative quantum Ising model: in contrast to the non-dissipative case, its phase diagram is still a matter of debate in the literature. When dissipation acts along the interaction direction, we predict important quantitative modifications of the position of the first-order transition boundary. In the case of incoherent relaxation in the field direction, our approach confirms the presence of a second-order transition, while does not support the possible existence of multicritical points. Potentially, these results can be tested in up-to-date quantum simulators of Rydberg atoms. arXiv:1810.08112v2 [cond-mat.stat-mech]

Multistability of Driven-Dissipative Quantum Spins

“…1(a) of Ref. [52], in a somewhat larger Ω range, showing a rather sharp change around Ω ≈ 1.5. The simulation accounts for a lattice of 100 2 sites, and the results have been verified to converge in N and t. The mean steady-state z magnetization for the same parameters.…”

“…5(b) can be compared with the results plotted in Fig. 1(a) of [52], which were obtained using a cluster MF approach for different cluster sizes. In the notation of Ref.…”

“…In the notation of Ref. [52], J z Z = −V /γ and Ω = (h x /γ)/2, making the parameters in the plots identical (with only a somewhat larger range taken here for the abscissa). The MFQF curve that we obtain contains a further noticeable feature around Ω ≈ 1.5, with a relatively sharper change in magnetization.…”

“…In one-dimensional (1D) lattices with nearest-neighbour (NN) interactions, the MF bistability is found to be replaced by a crossover driven by large quantum fluctuations [39,45,50,51]. In contrast, in certain 2D NN models, MF bistability has been found by approximate methods to be replaced by a firstorder phase-transition between two states, for nonlinear bosons using a truncated Wigner approximation [39,51], and for Ising spins using a variational ansatz acounting for nearest-neighbors correlations [45], a cluster mean field approach [52] and two-dimensional tensor network states [53]. In a parameter region around the jump, the convergence towards the steady state was found to slow down [45,51], a phenomenon related to the closing of the gap in the spectrum of the Liouvillian superoperator [54].…”

Numerical linked-cluster expansion for the dissipative XYZ model on a triangular lattice

“…Usually the evolution of a dissipative quantum many-body system is governed by the Lindblad master equation under Markovian approximation [30]. The steady state can be obtained by either evolving the master equation for a sufficient long time or diagonalizing exactly the Liouvillian [31]. Because the steady-state solutions in the thermodynamic limit have been proven to be remarkably difficult, some approximations are imposed to the density matrix, such as the single-site and cluster Gutzwiller mean-field factorizations [12,18,16,[32][33][34], to unravel the many-body master equation.…”