The open Lipkin-Meshkov-Glick (LMG) model provides a prototype of a dissipative phase transition which can be analyzed using mean-field theory. By combining the physics of this model with those of a quantum analog of a parity-time reversal symmetry breaking transition we analyze the steady state phase diagram of a pair of coupled LMG models. Their competition generates a complex phase diagram with multiple steady-state phases and emergent dynamical regimes absent from either constituent model, including chaos characterized by the maximum Lyapunov exponent. We show that the effects predicted from mean-field theory survive in the full quantum model.
The open Lipkin-Meshkov-Glick (LMG) model provides a prototype of a dissipative phase transition which can be analyzed using mean-field theory. By combining the physics of this model with those of a quantum analog of a parity-time reversal symmetry breaking transition we analyze the steady state phase diagram of a pair of coupled LMG models. Their competition generates a complex phase diagram with multiple steady-state phases and emergent dynamical regimes absent from either constituent model, including chaos characterized by the maximum Lyapunov exponent. We show that the effects predicted from mean-field theory survive in the full quantum model.
The open Lipkin-Meshkov-Glick (LMG) model provides a prototype of a dissipative phase transition which can be analyzed using mean-field theory. By combining the physics of this model with those of a quantum analog of a parity-time reversal symmetry breaking transition we analyze the steady state phase diagram of a pair of coupled LMG models. Their competition generates a complex phase diagram with multiple steady-state phases and emergent dynamical regimes absent from either constituent model, including chaos characterized by the maximum Lyapunov exponent. We show that the effects predicted from mean-field theory survive in the full quantum model.
We study the dynamics of the Lipkin-Meshkov-Glick (LMG) model with a finite number of spins. In the thermodynamic limit, the ground state of the LMG model with an isotropic Hamiltonian in the broken phase breaks to a mean-field ground state with a certain direction. However, when the spin number N is finite, the exact ground state is always unique and is not given by a classical mean-field ground state. Here, we prove that when N is large but finite, through a tiny external perturbation, a localized state which is close to a mean-field ground state can be prepared, which mimics spontaneous symmetry breaking. Also, we find the localized in-plane spin polarization oscillates with two different frequencies $\ensuremath{\sim}O(1/N)$, and the lifetime of the localized state is long enough to exhibit this oscillation. We numerically test the analytical results and find that they agree very well with each other. Finally, we link the phenomena to quantum time crystals and time quasicrystals.
Motivated by recent prototypes of engineered atomic spin devices, we study a fully connected system of N spins 1/2, modeled by the Lipkin-Meshkov-Glick (LMG) model of a collective spin s=N/2 in the presence of Markovian dissipation processes. We determine and classify the different phases of the dissipative LMG model with Markovian dissipation, including the properties of the steady state and the dynamic behavior in the asymptotic long-time regime. Employing variational methods and a systematic approach based on the Holstein-Primakoff mapping, we determine the phase diagram and the spectral and steady-state properties of the Liouvillian by studying both the infinite-s limit and 1/s corrections. Our approach reveals the existence of different kinds of dynamical phases and phase transitions, multistability, and regions where the dynamics is recurrent. We provide a classification of critical and noncritical Liouvillians according to their spectral and steady-state properties.
We investigate the Lipkin-Meshkov-Glick model coupled to a thermal bath. Since the isolated model itself exhibits a quantum phase transition, we explore the critical signatures of the open system. Starting from a system-reservoir interaction written in positive-definite form, we find that the position of the critical point remains unchanged, in contrast to the popular mean-field prediction. Technically, we employ the polaron transform to be able to study the full crossover regime from the normal to the symmetry-broken phase, which allows us to investigate the fate of quantum-critical points subject to dissipative environments. The signatures of the phase transition are reflected in observables such as magnetization, stationary mode occupation, or waiting-time distributions.
We study the adiabatic dynamics of the Lipkin-Meshkov-Glick (LMG) model close to its quantum critical point by linearly switching the transverse field from an initial large value to zero. We concentrate our attention on the residual energy after the quench in order to characterize the level of diabaticity of the evolution. As a function of the characteristic time of the quench $\ensuremath{\tau}$ we identify three different regimes. For fast quenches the residual energy Eres is almost independent on $\ensuremath{\tau}$. For slower quenches a second intermediate region appears in which a powerlike decay emerges with ${E}_{\text{res}}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}3/2}$. By further slowing the quench rate, we find a third large-$\ensuremath{\tau}$ regime characterized by a different power law, ${E}_{\text{res}}\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}2}$. All these findings can be accounted for by means of an effective Landau-Zener approximation for the finite-size LMG model. We complete our description of the adiabatic dynamics of the LMG model through the analysis of the entanglement entropy of the evolved state.
The Lipkin-Meshkov-Glick (LMG) model originally describes a Fermionic many-body system in nuclear physics. However, in recent years, it has been widely found in condensed matter physics, quantum information systems, and quantum optics, and it is of wider and wider interest. Previous studies on this model mainly focused on the physics under the thermal dynamical limit, such as quantum phase transitions and quantum entanglement. There are also some researches about LMG model with finite size in some special limits, but the finite-size effect on energy spectrum is not very clear yet. This is the main motivation of this work. In this paper, the exact diagonalization method and the quantum perturbation theory are used to calculate and analyze the energy-level structure of the LMG model at a finite N. To solve it, we first map this model into the angular-momentum space to obtain a reduced LMG model. By this mapping, the dimension of Hilbert space is reduced to N+1 from 2N. The exact solution of its energy levels can be obtained easily in the U(1) limit where the total spin is conserved. We find that the levels are woven into a fishing-net structure in the U(1) limit. While away from the U(1) limit, the crossings between even and odd levels will open a gap, and the system's energy levels will be grouped into pairs with an odd and an even level, forming some bound states, called doublet states, and the parity of each doublet state will oscillate as the Zeeman field increases. This work gives the values of the critical Zeeman field for the parity crossings. These critical values shift as the interacting parameters and disappear at zero in the Z2 limit. In the Z2 limit, the system energy levels form splittings near the zero Zeeman field. In this article, we analytically calculate the relationship between these energy gaps and the Zeeman field. For odd and even number N, the parity of each state has a different behavior. Specifically, the ground state and the doublet excited states of the system with odd N will suffer a parity reversion at zero Zeeman field, while the states with even N will not. By tuning the interacting parameters, we also study the crossover from the U(1) limit to the Z2 limit. The parity oscillation we find in this system is a very important physical phenomenon, which also exists in some other systems like optical cavity quantum electrodynamics and magnetic molecule system.