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

AIP conference proceedings

Excited-state quantum phase transitions and their manifestations in an extended Dicke model

Pavel Stránský, Michal Kloc, Pavel Cejnar

Published Jan 1, 2017• 2 citations
Publisher

Abstract

An Excited-State Quantum Phase Transition (esqpt) is a singularity observed in quantum energy spectra in the infinite-size limit of the system. It originates in the existence of stationary points in the semiclassical Hamiltonian function. We review the classification of esqpts and present a case study in an extended Dicke model. Finally, we show some preliminary results on the dynamical effect induced by esqpts.

DOI
10.1063/1.5016143

Related papers

Comparative quantum and semiclassical analysis of atom-field systems. I. Density of states and excited-state quantum phase transitions

M. A. Bastarrachea-Magnani, Sergio Lerma-Hernández, Jorge G. Hirsch

We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.

arXiv:1312.2665•Physical Review A•Mar 3, 2014•102 citations

Effects of excited state quantum phase transitions on system dynamics

Francisco Pérez-Bernal, Léa Ferreira dos Santos

This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann. Phys. 323, 1106 (2008). In many‐body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum that propagates to higher energies as the control parameter increases beyond the QPT critical point. The analysis of the spectrum has been a main tool for the detection of these ESQPTs. Studies of the effects of this transition on the system dynamics are more limited. Here, we extend our previous works and show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, because it may take place in systems with long‐range interactions, where the dynamics is usually expected to be very fast. A timely example is the one‐dimensional spin‐1/2 model with infinite‐range Ising interaction studied in experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, the slow dynamics described here occurs in two‐level bosonic or fermionic models with pairing interactions and a Hamiltonian exhibiting a QPT between its limiting and dynamical symmetries. In this work, we compare the results for , and 3.

arXiv:1604.06851•Fortschritte der Physik•Jun 23, 2016•36 citations

Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation

Léa Ferreira dos Santos, Marco Távora, Francisco Pérez-Bernal

Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-$\frac{1}{2}$ system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.

arXiv:1604.04289•Physical Review A•Jul 20, 2016•94 citations

Excited-state quantum phase transitions

Pavel Cejnar, Pavel Stránský, Michal Macek +1 more

Abstract We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. We classify typical ESQPT signatures in the spectra of energy eigenstates with respect to the underlying classical dynamics and outline a variety of quantum systems in which they occur. We describe thermodynamic and dynamic consequences of ESQPTs, like those in microcanonical thermodynamics, quantum quench dynamics, and in the response to nearly adiabatic or periodic driving. We hint at some generalizations of the ESQPT concept in periodic lattices and in resonant tunneling systems.

arXiv:2011.01662•Journal of Physics A Mathematical and Theoretical•Jan 26, 2021•122 citations

Excited-state quantum phase transitions in constrained systems

Jakub Novotný, Pavel Stránský, Pavel Cejnar

Abstract We extend the standard semiclassical theory of excited-state quantum phase transitions (ESQPTs), based on a classification of stationary points in the classical Hamiltonian, to constrained systems. We adopt the method of Lagrange multipliers to find all stationary points and their properties directly from the Hamiltonian constrained by an arbitrary number of integrals of motion, and demonstrate the procedure on an algebraic u ( 3 ) boson model with two independent constraints. We also elaborate the Holstein–Primakoff (HP) mapping, used to eliminate one degree of freedom in bosonic systems constrained by a conserved number of excitations, and address the fact that this mapping leads, in the classical limit, to a compact phase space with singular behaviour that conceals some stationary points at the phase space boundary. It is shown that the HP method reveals all ESQPTs only after constructing a complete atlas of different HP mappings.

arXiv:2412.04240•Journal of Physics A Mathematical and Theoretical•Feb 11, 2025•2 citations

Excited-state quantum phase transitions in Kerr nonlinear oscillators

Qing-Wei Wang, Sha Wu

Excited-state quantum phase transitions (ESQPTs) generalize the concept of quantum phase transitions to excited levels. Here we investigate how such ESQPTs can emerge in Kerr nonlinear oscillators, where a bosonic mode with a Kerr nonlinearity is subject to both coherent (one-photon) and parametric (two-photon) driving. We determine the structure and properties of the complete phase diagram by defining proper dimensionless parameters. Rich phases and phase transitions exist in the phase diagram, including phases with two or four critical energies above the ground-state level and first-order quantum phase transitions. We characterize the ESQPTs by singularities in the density of states, which show universal logarithmic divergence or discontinuity at the critical energies. Furthermore, we find that observables such as the photon number also exhibit singular behaviors at the critical energies and obey scaling laws. These results may extend our understanding of the driven Kerr oscillator and ESQPTs in finite-component systems.

Physical Review A•Dec 24, 2020•21 citations
An Excited-State Quantum Phase Transition (esqpt) is a singularity observed in quantum energy spectra in the infinite-size limit of the system. It originates in the existence of stationary points in the semiclassical Hamiltonian function. We review the classification of esqpts and present a case study in an extended Dicke model. Finally, we show some preliminary results on the dynamical effect induced by esqpts.
We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.
This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann. Phys. 323, 1106 (2008). In many‐body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum that propagates to higher energies as the control parameter increases beyond the QPT critical point. The analysis of the spectrum has been a main tool for the detection of these ESQPTs. Studies of the effects of this transition on the system dynamics are more limited. Here, we extend our previous works and show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, because it may take place in systems with long‐range interactions, where the dynamics is usually expected to be very fast. A timely example is the one‐dimensional spin‐1/2 model with infinite‐range Ising interaction studied in experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, the slow dynamics described here occurs in two‐level bosonic or fermionic models with pairing interactions and a Hamiltonian exhibiting a QPT between its limiting and dynamical symmetries. In this work, we compare the results for , and 3.
Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-12\frac{1}{2}21​ system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.
Abstract We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. We classify typical ESQPT signatures in the spectra of energy eigenstates with respect to the underlying classical dynamics and outline a variety of quantum systems in which they occur. We describe thermodynamic and dynamic consequences of ESQPTs, like those in microcanonical thermodynamics, quantum quench dynamics, and in the response to nearly adiabatic or periodic driving. We hint at some generalizations of the ESQPT concept in periodic lattices and in resonant tunneling systems.
Abstract We extend the standard semiclassical theory of excited-state quantum phase transitions (ESQPTs), based on a classification of stationary points in the classical Hamiltonian, to constrained systems. We adopt the method of Lagrange multipliers to find all stationary points and their properties directly from the Hamiltonian constrained by an arbitrary number of integrals of motion, and demonstrate the procedure on an algebraic u ( 3 ) boson model with two independent constraints. We also elaborate the Holstein–Primakoff (HP) mapping, used to eliminate one degree of freedom in bosonic systems constrained by a conserved number of excitations, and address the fact that this mapping leads, in the classical limit, to a compact phase space with singular behaviour that conceals some stationary points at the phase space boundary. It is shown that the HP method reveals all ESQPTs only after constructing a complete atlas of different HP mappings.
Excited-state quantum phase transitions (ESQPTs) generalize the concept of quantum phase transitions to excited levels. Here we investigate how such ESQPTs can emerge in Kerr nonlinear oscillators, where a bosonic mode with a Kerr nonlinearity is subject to both coherent (one-photon) and parametric (two-photon) driving. We determine the structure and properties of the complete phase diagram by defining proper dimensionless parameters. Rich phases and phase transitions exist in the phase diagram, including phases with two or four critical energies above the ground-state level and first-order quantum phase transitions. We characterize the ESQPTs by singularities in the density of states, which show universal logarithmic divergence or discontinuity at the critical energies. Furthermore, we find that observables such as the photon number also exhibit singular behaviors at the critical energies and obey scaling laws. These results may extend our understanding of the driven Kerr oscillator and ESQPTs in finite-component systems.