Criticality revealed through quench dynamics in the Lipkin-Meshkov-Glick model

  title={Criticality revealed through quench dynamics in the Lipkin-Meshkov-Glick model},
  author={Steve Campbell},
  journal={Physical Review B},
  • S. Campbell
  • Published 18 August 2016
  • Physics
  • Physical Review B
We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate and by employing the time-dependent fidelity, we see manifestly different dynamics are present if the system is quenched through the critical point. Furthermore, we show that the average work shows no sensitivity to the quantum phase transition, however the free energy and irreversible work show markedly different rates of change in each phase. Finally, we assess… 

Figures from this paper

Polaron-transformed dissipative Lipkin-Meshkov-Glick model

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.

Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model

: We use the spread complexity of a time evolved state after a sudden quantum quench in the Lipkin-Meshkov-Glick (LMG) model prepared in the ground state as a probe of equilibrium signatures of

Quench dynamics and zero-energy modes: The case of the Creutz model

In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model-describing a system of spinless fermions hopping on

Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects.

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

Dynamical quantum correlations after sudden quenches

We employ the mean-field approach in the fermionic picture of the spin-1/2 XXZ chain to investigate the dynamics of bipartite quantum discord and concurrence under sudden quenching. In the case, when

Thermalization of the Lipkin-Meshkov-Glick model in blackbody radiation

In a recent work, we have derived simple Lindblad-based equations for the thermalization of systems in contact with a thermal reservoir. Here, we apply these equations to the Lipkin-Meshkov-Glick

Nonequilibrium many-body dynamics in supersymmetric quenching

We study the dynamics induced by quenching an ultracold quantum many-body system between two supersymmetric Hamiltonians. Such a quench can be created by carefully changing the external trapping

Nonequilibrium Criticality in Quench Dynamics of Long-Range Spin Models.

A prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model is considered describing the collective interaction of N spins and the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian are investigated.

Wiseman–Milburn control for the Lipkin–Meshkov–Glick model

We apply a measurement-based closed-loop control scheme to the dissipative Lipkin–Meshkov–Glick model. Specifically, we use the Wiseman–Milburn feedback master equation to control its quantum phase

Kibble-Zurek scaling in quantum speed limits for shortcuts to adiabaticity

Geometric quantum speed limits quantify the trade-off between the rate with which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a



Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an

Shortcut to adiabaticity in the Lipkin-Meshkov-Glick model.

A hybrid strategy combining a shortcut to adiabaticity and optimal control that allows for remarkably good performance in suppressing the defect production across the phase transition is developed.

Classical and quantum phase transitions in the Lipkin-Meshkov-Glick model

An analysis of the classical and quantum phase transitions of the Lipkin-Meshkov-Glick model is presented. It is shown that the classical dynamics is ruled by the energy surface of the system.

Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections.

The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism and expectation values of the spin operators are computed in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.

Probing the out-of-equilibrium dynamics of two interacting atoms

We study the out-of-equilibrium dynamics of two interacting atoms in a one-dimensional harmonic trap after a quench by a tightly pinned impurity atom. We make use of an approximate variational

Assisted finite-rate adiabatic passage across a quantum critical point: exact solution for the quantum Ising model.

A transitionless quantum driving through a quantum critical point is designed, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter.

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

We study the ground state fidelity, fidelity susceptibility, and quench dynamics of the extended quantum compass model in a transverse field. This model reveals a rich phase diagram which includes

Dynamical quantum phase transitions in the transverse-field Ising model.

It is shown that the equilibrium quantum phase transition and the dynamical phase transition in the transverse-field Ising model are intimately related.

Exact work statistics of quantum quenches in the anisotropic XY model.

The average work and a quantum fluctuation relation is used to determine the amount of irreversible entropy produced during the quench, eventually revealing how the closing of the excitation gap leads to increased dissipated work.

Infinite-range Ising ferromagnet in a time-dependent transverse magnetic field: Quench and ac dynamics near the quantum critical point

We study an infinite-range ferromagnetic Ising model in the presence of a transverse magnetic field, which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the