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arXiv:1211.2683 · Physical Review E

ac-driven quantum phase transition in the Lipkin-Meshkov-Glick model

Georg Engelhardt, V. M. Bastidas, Clive Emary, Tobias Brandes

Published May 8, 2013• 35 citations
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Abstract

We establish a set of nonequilibrium quantum phase transitions in the Lipkin-Meshkov-Glick model under monochromatic modulation of the interparticle interaction. We show that the external driving induces a rich phase diagram that characterizes the multistability in the system. Interestingly, the number of stable configurations can be tuned by increasing the amplitude of the driving field. Furthermore, by studying the quantum evolution, we demonstrate that the system exhibits a set of quantum phases that correspond to dynamically stabilized states.

DOI
10.1103/physreve.87.052110

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We establish a set of nonequilibrium quantum phase transitions in the Lipkin-Meshkov-Glick model under monochromatic modulation of the interparticle interaction. We show that the external driving induces a rich phase diagram that characterizes the multistability in the system. Interestingly, the number of stable configurations can be tuned by increasing the amplitude of the driving field. Furthermore, by studying the quantum evolution, we demonstrate that the system exhibits a set of quantum phases that correspond to dynamically stabilized states.
It is of high interest, in the context of adiabatic quantum computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.
Abstract The dynamical properties of the Lipkin–Meshkov–Glick model with longitudinal and transverse fields are studied by considering quantum quenches. The model describes a many-body quantum system with long-range interactions. A semiclassical analysis is performed to obtain the critical points of quantum phase transitions. These critical points consist in the static separatrix, which is found by analyzing the stability structure of the semiclassical potential and is useful in the identification of ground state and excited states quantum phase transitions, and in the dynamical separatrix, which depends on initial conditions and is found by studying the classical equations of motion for the Hamiltonian. The static and dynamical separatrices divide the parameter space in regions of different dynamical behavior, and it is found that both separatrices play an important role in the determination of the occurrences of the dynamical quantum phase transitions. Graphical abstract
We establish a set of nonequilibrium quantum phase transitions in the Dicke model by considering a monochromatic nonadiabatic modulation of the atom-field coupling. For weak driving the system exhibits a set of sidebands which allow the circumvention of the no-go theorem which otherwise forbids the occurrence of superradiant phase transitions. At strong driving we show that the system exhibits a rich multistable structure and exhibits both first- and second-order nonequilibrium quantum phase transitions.
Monitored quantum system have sparked great interest in recent years due to the possibility of observing measurement-induced phase transitions (MIPTs) in the full-counting statistics of quantum trajectories. Here, we investigate the dynamics of the Lipkin-Meshkov-Glick model, composed of NNN all-to-all interacting spins 1/21/21/2, under a weak external monitoring. In the thermodynamic limit, we derive a set of semiclassical stochastic equations describing the evolution of the expectation values of global spin observables. Our results show that the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ does not commute with the long-time limit: while for any finite NNN the average over trajectories is expected to converge towards a trivial steady state, in the thermodynamic limit a MIPT appears. The transition is not affected by postselection issues, as it is already visible at the level of ensemble averages. We derive a quantitative theoretical picture explaining the nature of the transition within our semiclassical approach.
The basic Lipkin-Meshkov-Glick model displays a second-order ground-state quantum phase transition and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The alternative ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground-state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.