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

Journal of Physics Condensed Matter

Universal frozen spectra after time-dependent symmetry restoring phase transitions

Friedemann Queißer, Patrick Navez, Ralf Schützhold

Published Sep 11, 2013• 2 citations
Publisher

Abstract

For a general O(N) model, we study the time-dependent phase transition from a state with broken symmetry <φ> ≠ 0 to the symmetric phase <φ> = 0. During this non-equilibrium process, the primordial quantum (or thermal) fluctuations of the initial Goldstone modes are frozen and result in a deviation from the final ground (or thermal) state. For very slow transitions, we find that these fluctuations display a universal scaling behaviour. Their spectra are universal functions of a single parameter, which combines the initial frequency of the Goldstone modes and the sweep rate. As a result, the final two-point function [φa(r)φb(r')] is not exponentially suppressed at large distances Δr = r - r' (as it would be in the ground state) but decays polynomially in 1/|Δr|. Finally, we exemplify this universal behaviour for the transition from the super-fluid phase to the Mott state in the Bose-Hubbard model.

DOI
10.1088/0953-8984/25/40/404215

Related papers

Non-thermal excited-state quantum phase transitions

Ricardo Puebla, Armando Relaño

We report a kind of phase transition which takes place in isolated quantum systems with a discrete symmetry. Different phases are separated by a critical energy and recognized by means of an order parameter, which can be experimentally measured. Below the critical energy, the symmetry is broken and the equilibrium state is non-thermal, keeping large amounts of memory of the initial condition. Above, the symmetry is restored and a thermal equilibrium state is reached. We identify two universality classes, one showing a second-order phase transition and represented by the Lipkin-Meshkov-Glick model, and another showing a first-order phase transition and represented by the Dicke model. This work is dedicated to the memory of Joaquín Retamosa .

arXiv:1305.3077•Europhysics Letters (EPL)•Dec 1, 2013•28 citations

Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

A. N. Mikheev, Christian-Marcel Schmied, Thomas Gasenzer

Nonthermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of nonthermal fixed points in a bosonic quantum many-body system by integrating out long-wavelength density fluctuations. The system consists of $N$ distinguishable spatially uniform Bose gases with $\text{U}(N)$-symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relative-phase excitations. It is similar in character to the nonlinear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal nonlocal coupling function depending, in the large-$N$ limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the nonthermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields $N$. Numerical results for $N=3$ allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The predicted and observed exponentially suppressed coherence at short distances takes the form of that of a quasicondensate in low-dimensional equilibrium systems. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.

arXiv:1807.10228•Physical Review A•Jun 24, 2019•38 citations

Quasi-Gaussian approximation: Universality, critical dimension

Jean Zinn‐Justin

This chapter examines the universal properties of phase transitions in the quasi-Gaussian or mean-field approximations. It studies the singularities of thermodynamic functions at the transition point as well as the large-distance behaviour of the two-point correlation function. It summarizes the universal properties in the form of Landau′s theory. It stresses the peculiarities of models with continuous symmetries at low temperature due to the appearance of Goldstone modes. Finally, it evaluates corrections to the quasi-Gaussian approximation and shows that the approximation is only consistent in space dimension larger than four. Exercises are provided at the end of the chapter.

Oxford University Press eBooks•Jul 5, 2007•0 citations

Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling

J. Mumford, W. Kirkby, Duncan H J O’Dell

Abstract As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-particle wave functions following a quench, focusing on two-mode systems that include the two-site Bose–Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space certain characteristic shapes, that we identify as cusp catastrophes, appear under generic conditions. In the vicinity of a cusp the wave function takes on a universal structure described by the Pearcey function and obeys scaling relations which depend on the total number of particles N . In the thermodynamic limit ( N → ∞ ) the cusp becomes singular, but at finite N it is decorated by an interference pattern. This pattern contains an intricate network of vortex–antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench is a δ -kick the problem can be solved analytically and we obtain scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern. Finally, we use these scalings to describe the wave function in the critical regime of a Z 2 symmetry-breaking dynamical phase transition.

arXiv:1609.04502•Journal of Physics B Atomic Molecular and Optical Physics•Jan 4, 2017•15 citations

Universal Phenomenology at Critical Exceptional Points of Nonequilibrium O ( N ) Models

Carl Philipp Zelle, Romain Daviet, Achim Rosch +1 more

In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of O ( N ) field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of 2 N − 3 Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions d < 4 they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for N = 2 , and a generalization for arbitrary N , which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an x y magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium. Published by the American Physical Society 2024

arXiv:2304.09207•Physical Review X•Jun 26, 2024•30 citations

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

Hong-Wei Zhong, Haiqing Xu, Ping-Hua Huang

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.

Chinese Physics Letters•Jul 29, 2008•3 citations
For a general O(N) model, we study the time-dependent phase transition from a state with broken symmetry <φ> ≠ 0 to the symmetric phase <φ> = 0. During this non-equilibrium process, the primordial quantum (or thermal) fluctuations of the initial Goldstone modes are frozen and result in a deviation from the final ground (or thermal) state. For very slow transitions, we find that these fluctuations display a universal scaling behaviour. Their spectra are universal functions of a single parameter, which combines the initial frequency of the Goldstone modes and the sweep rate. As a result, the final two-point function [φa(r)φb(r')] is not exponentially suppressed at large distances Δr = r - r' (as it would be in the ground state) but decays polynomially in 1/|Δr|. Finally, we exemplify this universal behaviour for the transition from the super-fluid phase to the Mott state in the Bose-Hubbard model.
We report a kind of phase transition which takes place in isolated quantum systems with a discrete symmetry. Different phases are separated by a critical energy and recognized by means of an order parameter, which can be experimentally measured. Below the critical energy, the symmetry is broken and the equilibrium state is non-thermal, keeping large amounts of memory of the initial condition. Above, the symmetry is restored and a thermal equilibrium state is reached. We identify two universality classes, one showing a second-order phase transition and represented by the Lipkin-Meshkov-Glick model, and another showing a first-order phase transition and represented by the Dicke model. This work is dedicated to the memory of Joaquín Retamosa .
Nonthermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of nonthermal fixed points in a bosonic quantum many-body system by integrating out long-wavelength density fluctuations. The system consists of NNN distinguishable spatially uniform Bose gases with U(N)\text{U}(N)U(N)-symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relative-phase excitations. It is similar in character to the nonlinear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal nonlocal coupling function depending, in the large-NNN limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the nonthermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields NNN. Numerical results for N=3N=3N=3 allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The predicted and observed exponentially suppressed coherence at short distances takes the form of that of a quasicondensate in low-dimensional equilibrium systems. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.
This chapter examines the universal properties of phase transitions in the quasi-Gaussian or mean-field approximations. It studies the singularities of thermodynamic functions at the transition point as well as the large-distance behaviour of the two-point correlation function. It summarizes the universal properties in the form of Landau′s theory. It stresses the peculiarities of models with continuous symmetries at low temperature due to the appearance of Goldstone modes. Finally, it evaluates corrections to the quasi-Gaussian approximation and shows that the approximation is only consistent in space dimension larger than four. Exercises are provided at the end of the chapter.
Abstract As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-particle wave functions following a quench, focusing on two-mode systems that include the two-site Bose–Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space certain characteristic shapes, that we identify as cusp catastrophes, appear under generic conditions. In the vicinity of a cusp the wave function takes on a universal structure described by the Pearcey function and obeys scaling relations which depend on the total number of particles N . In the thermodynamic limit ( N → ∞ ) the cusp becomes singular, but at finite N it is decorated by an interference pattern. This pattern contains an intricate network of vortex–antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench is a δ -kick the problem can be solved analytically and we obtain scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern. Finally, we use these scalings to describe the wave function in the critical regime of a Z 2 symmetry-breaking dynamical phase transition.
In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of O ( N ) field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of 2 N − 3 Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions d < 4 they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for N = 2 , and a generalization for arbitrary N , which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an x y magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium. Published by the American Physical Society 2024
The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.