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arXiv:1812.00643 · Physical Review A

Cluster methods for the description of a driven-dissipative spin model

Dolf Huybrechts, Michiel Wouters

Published Apr 29, 2019• 18 citations
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Abstract

We study the influence of short-range quantum correlations and classical spatial correlations on the phase diagram of the dissipative XYZ model by using a Gutzwiller Monte Carlo method and a cluster Gutzwiller ansatz for the wave function. Considering lattices of finite size we confirm the emergence of a region with ferromagnetic correlations and two paramagnetic regions and show the emergence of a region with a buildup of ferromagnetic correlations completely missed by mean-field theory. The inclusion of short-range quantum correlations causes drastic alterations of the mean-field correlation functions but our results show that the inclusion of long-range quantum correlations or the use of more sophisticated methods is needed to quantitatively match the exact results. A study of the susceptibility tensor shows that reciprocity is broken, a feature not observed in closed quantum systems. Furthermore, increasing the magnetic field suppresses the magnetization; this is also in contrast with closed quantum systems.

DOI
10.1103/physreva.99.043841

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We study the influence of short-range quantum correlations and classical spatial correlations on the phase diagram of the dissipative XYZ model by using a Gutzwiller Monte Carlo method and a cluster Gutzwiller ansatz for the wave function. Considering lattices of finite size we confirm the emergence of a region with ferromagnetic correlations and two paramagnetic regions and show the emergence of a region with a buildup of ferromagnetic correlations completely missed by mean-field theory. The inclusion of short-range quantum correlations causes drastic alterations of the mean-field correlation functions but our results show that the inclusion of long-range quantum correlations or the use of more sophisticated methods is needed to quantitatively match the exact results. A study of the susceptibility tensor shows that reciprocity is broken, a feature not observed in closed quantum systems. Furthermore, increasing the magnetic field suppresses the magnetization; this is also in contrast with closed quantum systems.
We use the Gutzwiller Monte Carlo approach to simulate the dissipative XYZXYZXYZ model in the vicinity of a dissipative phase transition. This approach captures classical spatial correlations together with the full on-site quantum behavior while neglecting nonlocal quantum effects. By considering finite two-dimensional lattices of various sizes, we identify a ferromagnetic and two paramagnetic phases, in agreement with earlier studies. The greatly reduced numerical complexity of the Gutzwiller Monte Carlo approach facilitates efficient simulation of relatively large lattice sizes. The inclusion of the spatial correlations allows to capture parts of the phase diagram that are completely missed by the widely applied Gutzwiller decoupling of the density matrix.
We study the dynamical properties of a driven-dissipative Bose-Hubbard model in the strongly interacting regime through a quantum trajectory approach with a cluster Gutzwiller Ansatz for the wave function. This allows us to take classical and quantum correlations into account. By studying the dynamical hysteresis surface that arises by sweeping through the coherent driving strength we show that the phase diagram for this system is in qualitative correspondence with the Gutzwiller mean-field result. However, quantitative differences are present and the inclusion of classical and quantum correlations causes a significant shift of the critical parameters. Additionally, we show that approximation techniques relying on a unimodal distribution such as the mean field and 1/z1/z1/z expansion drastically underestimate the particle number fluctuations. Finally, we show that a proposed mapping of the driven-dissipative many-body Bose-Hubbard model onto a single driven-dissipative Kerr model is not accurate for parameters in the hysteresis regime.
Abstract We generalize the numerical linked-cluster expansion (NLCE) method to study the dissipative quantum many-body system. We apply the NLCE to the triangular strip and two-dimensional lattice system. We investigate the dynamics and steady-state properties of the dissipative XYZ model where the coherent dynamics is governed by the anisotropic Heisenberg Hamiltonian while the nonunitary process is induced by the incoherent spin flips. By comparing with the quantum trajectory simulations, the NLCE results show good performance in capturing the dynamics of system with short-range correlations. For strong and long-range correlated system, the larger size clusters in the series should be included. The NLCE study for the magnetic susceptibility also signals the steady-state paramagnetic-ferromagnetic phase transition in the two-dimensional case.
We investigate the steady-state phase diagram of the dissipative spin-1/2 XYZ model on a two-dimensional triangular lattice, in which each site is coupled to a local environment. By means of cluster mean-field approximation, we find that the steady-state phases of the system are rather rich, in particular there exist various types of nonuniform antiferromagnetic phases due to the geometrical frustration. As the short-range correlations are included in the analysis, the numerical results show that the oscillatory phase disappears while the triantiferromagnetic and biantiferromagnetic phases remain to exist in the thermodynamic limit. Moreover, the existence of the spin-density-wave phase, which is missed by the single-site mean-field analysis, is also revealed by the spin-structure factor.
In this work we study the effects of quantum fluctuations in a disordered magnetic system. We consider a cluster-spin Ising model with antiferromagnetic short range interactions (J0) and disordered long range interactions (J) between clusters, where the system is under the influence of a transverse magnetic field Γ. The analytic treatment of the model is done by the replica method and Trotter formalism, in which a cluster mean field, replica symmetric and static approximations are used. This allows us to obtain an effective model of a single cluster that is exactly diagonalized. Thermodynamic quantities like order parameter and free energy are obtained then, the phase diagrams are analyzed. They are shown in temperature versus J0=J phase diagrams for some intensities of Γ. With Γ = 0, when we decrease the temperature (for lower intensities of J0=J) a continuous phase transition between the paramagnetic and cluster spin glass state (CSG) is found. When we increase the ratio J0=J, the system presents the antiferromagnetic phase (AF). The CSG state and the AF phase are separated by first order transitions. In the intermediate region of disorder, there exist a small interval in the AF-PM transition that is first order. When Γ is increased, the transitions PM-AF and PM-VSC decrease toward critical points in the lower and higher disorder, respectively. It is worth to note, in the intermediate range of disorder, that the transition CSG-AF disappears, letting a PM phase between them, even for zero temperature. Besides that, the first-order region, in the PM-AF transition, turns into a second order phase transition, changing its criticality in the low temperature regime. Our results show that quantum fluctuations affects the phase transitions of the model being capable to suppress and/or change his criticality. The present work suggests a model and a mechanism of the change in the criticality away from the quantum critical point, helping the investigation of this interesting and recent topic.
We investigate the effect of short-range correlations on the dynamical phase diagram of quantum many-body systems with long-range interactions. Focusing on Ising spin chains with power-law decaying interactions and accounting for short-range correlations by a cluster mean field theory we show that short-range correlations are responsible for the emergence of a chaotic dynamical region. Analyzing the fine details of the phase diagram, we show that the resulting chaotic dynamics bears close analogies with that of a tossed coin.