Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1801.00818 · Physical review. B./Physical review. B

Lipkin-Meshkov-Glick model with Markovian dissipation: A description of a collective spin on a metallic surface

João S. Ferreira, Pedro Ribeiro

Published Nov 26, 2019• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.100.184422

Related papers

PT-symmetry-breaking phase transitions in a Lipkin-Meshkov-Glick dimer

Simon Kothe, Christopher Oliver, Peter Kirton

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.

•Oct 13, 2026•0 citations

PT -symmetry-breaking phase transitions in a Lipkin-Meshkov-Glick dimer

Simon Kothe, Christopher Oliver, Peter Kirton

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.

arXiv:2504.18426•Physical Review A•Aug 13, 2026•0 citations

Bosonic representation of a Lipkin-Meshkov-Glick model with Markovian dissipation

Jan C. Louw, Michael Kästner, Johannes N. Kriel

We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems but takes into account leading-order finite-size corrections to the infinite-system result. As an application, we show that the dissipative Lipkin-Meshkov-Glick model equilibrates by passing through a continuum of thermal states with damped oscillations superimposed, until finally reaching an equilibrium state with a temperature that in general differs from the bath temperature. We discuss limitations of our analytic techniques by comparing to exact numerical results.

arXiv:2004.02232•Physical review. B./Physical review. B•Sep 23, 2020•3 citations

Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model

Tommaso Caneva, Rosario Fazio, Giuseppe E. Santoro

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 ${E}_{\text{res}}$ 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.

arXiv:0806.4455•Physical Review B•Sep 30, 2008•107 citations

Quantum phase transitions in the LMG model by means of quantum information concepts

Octavio Castaños, Ramón López–Peña, Eduardo Nahmad-Achar +1 more

Quantum phase transitions are currently studied in several fields of physics, as examples one finds: in nuclear physics the shape phase transitions within the Interacting Boson Model; in quantum optics two level atoms interacting with a one mode electromagnetic radiation in a cavity; and in condensed matter in the analysis of the behavior of spin systems. In this contribution we employ the fidelity and its susceptibility, two concepts widely used in quantum information theory, to determine the quantum phase transitions of the Lipkin-Meshkov-Glick (LMG) model together with its scaling properties. By means of these concepts, we propose a quantum method to determine the crossings and anti-crossings present in a model Hamiltonian as a function of the control parameters of the model. A review of the separatrix of the LMG model is done to compare the results obtained by means of quantum information concepts with those related with the singular behavior of the energy surface of the model, which is the expectation value of the Hamiltonian with respect to spin coherent states.

Journal of Physics Conference Series•Sep 17, 2012•13 citations

The Lipkin-Meshkov-Glick model from the perspective of theSU(1,1) Richardson-Gaudin models

Sergio Lerma-Hernández, J. Dukelsky

Originally introduced in nuclear physics as a numerical laboratory to test different many-body approximation methods, the Lipkin-Meshkov-Glick (LMG) model has received much attention as a simple enough but non-trivial model with many interesting features for areas of physics beyond the nuclear one. In this contribution we look at the LMG model as a particular example of an SU (1,1) Richardson-Gaudin model. The characteristics of the model are analyzed in terms of the behavior of the spectral-parameters or pairons which determine both eigenvalues and eigenfunctions of the model Hamiltonian. The problem of finding these pairons is mathematically equivalent to obtain the equilibrium positions of a set of electric charges moving in a two dimensional space. The electrostatic problems for the different regions of the model parameter space are discussed and linked to the different energy density of states already identified in the LMG spectrum.

Journal of Physics Conference Series•Mar 18, 2014•6 citations
Motivated by recent prototypes of engineered atomic spin devices, we study a fully connected system of NNN spins 1/21/21/2, modeled by the Lipkin-Meshkov-Glick (LMG) model of a collective spin s=N/2s=N/2s=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-sss limit and 1/s1/s1/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.
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 a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems but takes into account leading-order finite-size corrections to the infinite-system result. As an application, we show that the dissipative Lipkin-Meshkov-Glick model equilibrates by passing through a continuum of thermal states with damped oscillations superimposed, until finally reaching an equilibrium state with a temperature that in general differs from the bath temperature. We discuss limitations of our analytic techniques by comparing to exact numerical results.
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{E}_{\text{res}}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.
Quantum phase transitions are currently studied in several fields of physics, as examples one finds: in nuclear physics the shape phase transitions within the Interacting Boson Model; in quantum optics two level atoms interacting with a one mode electromagnetic radiation in a cavity; and in condensed matter in the analysis of the behavior of spin systems. In this contribution we employ the fidelity and its susceptibility, two concepts widely used in quantum information theory, to determine the quantum phase transitions of the Lipkin-Meshkov-Glick (LMG) model together with its scaling properties. By means of these concepts, we propose a quantum method to determine the crossings and anti-crossings present in a model Hamiltonian as a function of the control parameters of the model. A review of the separatrix of the LMG model is done to compare the results obtained by means of quantum information concepts with those related with the singular behavior of the energy surface of the model, which is the expectation value of the Hamiltonian with respect to spin coherent states.
Originally introduced in nuclear physics as a numerical laboratory to test different many-body approximation methods, the Lipkin-Meshkov-Glick (LMG) model has received much attention as a simple enough but non-trivial model with many interesting features for areas of physics beyond the nuclear one. In this contribution we look at the LMG model as a particular example of an SU (1,1) Richardson-Gaudin model. The characteristics of the model are analyzed in terms of the behavior of the spectral-parameters or pairons which determine both eigenvalues and eigenfunctions of the model Hamiltonian. The problem of finding these pairons is mathematically equivalent to obtain the equilibrium positions of a set of electric charges moving in a two dimensional space. The electrostatic problems for the different regions of the model parameter space are discussed and linked to the different energy density of states already identified in the LMG spectrum.