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

The European Physical Journal B

Sensitivity to initial conditions on dynamical quantum phase transitions

D.S. Lohr-Robles, M. Grether, E. López-Moreno, Peter Oto Hess

Published Jul 1, 2026• 0 citations
Publisher

Abstract

Abstract The dynamical properties of a many-body quantum system are studied in terms of its initial conditions and control parameters in the framework of the Lipkin–Meshkov–Glick model through a quantum quench process. The initial collective pseudospin is considered to lie on the equator of the Bloch sphere and the dynamical phase diagrams are constructed for various values of the polar angle. The two types of dynamical quantum phase transitions (DQPTs) are studied in detail: DQPTs-I, which manifest as non-analyticities of an order parameter as a function of the control parameter; and DQPTs-II, which occur when the rate function of the Loschmidt echo has non-analytical behavior at critical times. By considering relevant domains of the anisotropic parameters of the spin interactions and many examples of initial states, the influence of the initial conditions on both types of DQPTs is examined. The results are presented with emphasis put on the interacting parameters and the initial preparation of the system for their application on experimental settings.

DOI
10.1140/epjb/s10051-026-01209-z

Related papers

Dynamical quantum phase transitions in the Lipkin–Meshkov–Glick model with longitudinal and transverse magnetic fields

D.S. Lohr-Robles, M. Grether, Enrique López‐Moreno +1 more

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

The European Physical Journal B•Dec 1, 2025•1 citation

Exotic signature of dynamical quantum phase transition in the time evolution of an engineered initial state

Sirshendu Bhattacharyya, Subinay Dasgupta

Abstract Dynamical phase transition in quantum many body systems is usually studied by taking it in the ground state and then quenching a parameter to a new value. We investigate here the dynamics when one performs the time evolution of a generic state and observe that the rate function related to the Loschmidt echo shows non-analytic behavior of two types, one related, and the other unrelated, to the appearance of a quantum phase transition. Specifically, we consider a quantum Ising chain in an initial configuration which is a generic superposition of the eigenstates, and follow its dynamics under the transverse Ising Hamiltonian with a constant field. Depending on the the configuration of the initial state, some singularities appear in the rate function which do not correspond to the equilibrium phase transition of the Hamiltonian. However another class of singularity is found having a connection with the quantum critical point. Some features of the singularities of the rate function have been derived analytically and it is observed that the occupancy of quasiparticle eigenstates plays the key role in triggering the non-analyticities.

arXiv:1912.00207•Journal of Physics A Mathematical and Theoretical•May 1, 2020•6 citations

Dynamical Quantum Phase transitions and Recurrences in the Non-Equilibrium BCS model

Colin Rylands, Victor M. Galitski

Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur.

arXiv:2001.10084•Jan 27, 2020•4 citations

Dynamical quantum phase transitions on random networks

Tomohiro Hashizume, Felix Herbort, Joseph Tindall +1 more

Abstract We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse-field Ising model on ensembles of Erdős–Rényi networks of size N. These networks consist of vertices connected randomly with probability p ( 0 < p ⩽ 1 ). Using analytical derivations and numerical techniques, we compare the characteristics of the transitions for p < 1 against the fully connected network (p = 1). We analytically show that the overlap between the wave function after a quench and the wave function of the fully connected network after the same quench deviates by at most O ( N − 1 / 2 ) . For a DQPT defined by an order parameter, the critical point remains unchanged for all p. For a DQPT defined by the rate function of the Loschmidt echo, we find that the rate function deviates from the p = 1 limit near vanishing points of the overlap with the initial state, while the critical point remains independent for all p. Our analysis suggests that this divergence arises from persistent non-trivial global many-body correlations absent in the p = 1 limit.

arXiv:2503.04891•New Journal of Physics•Jun 1, 2025•0 citations

Correlations and dynamical quantum phase transitions in an interacting topological insulator

Wing Chi Yu, Pedro D Sacramento, Yanchao Li +1 more

Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite that DQPTs are defined and signaled by the nonanalyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the noninteracting case, and upon the addition of repulsive intracell interactions. On the other hand, the intercell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in nonequilibrium quantum many-body systems.

arXiv:2105.02449•Physical review. B./Physical review. B•Aug 4, 2021•33 citations

Nonequilibrium Dynamical Quantum Phase Transitions in the Extended Agassi Model

Ritesh Kumar Palai, Rajiv Kumar, Venktesh Singh +1 more

We investigate dynamical quantum phase transitions (DQPTs) in the extended Agassi model following sudden quenches of same level pairing ($Σ$), monopole-monopole ($χ$) and cross level pairing ($Λ$) strengths. Using exact diagonalization, we characterize the non-equilibrium dynamics through the Loschmidt echo and intensive return-rate function. Quenches across equilibrium phase boundaries produce cusp-like structures in the return rate that shows non-analyticities with increasing system size. Equilibrium finite size to large scaling identifies the $χ$-driven transition as a second order phase transition similar to mean-field, Dicke, and Lipkin-Meshkov-Glick (LMG) models critical behaviour with the exponent of the order parameter $β\simeq 1/2$, while the $Σ$- and $Λ$-driven transitions are first order. We further characterize the associated dynamical singularities through a local scaling exponent $α$, with $α_χ\simeq 2/3$, $α_Λ\simeq 1/3$, and $α_Σ\simeq 3/2$ of all three parameters. The distinct scaling behaviours across the parameter channels show that dynamical criticality is not determined solely by the equilibrium order of the transition, revealing multiple dynamical scaling regimes. These non-analyticities are associated with the Fisher zeros of the Loschmidt amplitude, which cross the real time axis at critical times and the time derivatives of the return-rate function to characterize the order of DQPTs within the extended Agassi model.

quant-pharXiv:2610.23096•Oct 19, 2026•0 citations
Abstract The dynamical properties of a many-body quantum system are studied in terms of its initial conditions and control parameters in the framework of the Lipkin–Meshkov–Glick model through a quantum quench process. The initial collective pseudospin is considered to lie on the equator of the Bloch sphere and the dynamical phase diagrams are constructed for various values of the polar angle. The two types of dynamical quantum phase transitions (DQPTs) are studied in detail: DQPTs-I, which manifest as non-analyticities of an order parameter as a function of the control parameter; and DQPTs-II, which occur when the rate function of the Loschmidt echo has non-analytical behavior at critical times. By considering relevant domains of the anisotropic parameters of the spin interactions and many examples of initial states, the influence of the initial conditions on both types of DQPTs is examined. The results are presented with emphasis put on the interacting parameters and the initial preparation of the system for their application on experimental settings.
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
Abstract Dynamical phase transition in quantum many body systems is usually studied by taking it in the ground state and then quenching a parameter to a new value. We investigate here the dynamics when one performs the time evolution of a generic state and observe that the rate function related to the Loschmidt echo shows non-analytic behavior of two types, one related, and the other unrelated, to the appearance of a quantum phase transition. Specifically, we consider a quantum Ising chain in an initial configuration which is a generic superposition of the eigenstates, and follow its dynamics under the transverse Ising Hamiltonian with a constant field. Depending on the the configuration of the initial state, some singularities appear in the rate function which do not correspond to the equilibrium phase transition of the Hamiltonian. However another class of singularity is found having a connection with the quantum critical point. Some features of the singularities of the rate function have been derived analytically and it is observed that the occupancy of quasiparticle eigenstates plays the key role in triggering the non-analyticities.
Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur.
Abstract We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse-field Ising model on ensembles of Erdős–Rényi networks of size N. These networks consist of vertices connected randomly with probability p ( 0 < p ⩽ 1 ). Using analytical derivations and numerical techniques, we compare the characteristics of the transitions for p < 1 against the fully connected network (p = 1). We analytically show that the overlap between the wave function after a quench and the wave function of the fully connected network after the same quench deviates by at most O ( N − 1 / 2 ) . For a DQPT defined by an order parameter, the critical point remains unchanged for all p. For a DQPT defined by the rate function of the Loschmidt echo, we find that the rate function deviates from the p = 1 limit near vanishing points of the overlap with the initial state, while the critical point remains independent for all p. Our analysis suggests that this divergence arises from persistent non-trivial global many-body correlations absent in the p = 1 limit.
Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite that DQPTs are defined and signaled by the nonanalyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the noninteracting case, and upon the addition of repulsive intracell interactions. On the other hand, the intercell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in nonequilibrium quantum many-body systems.
We investigate dynamical quantum phase transitions (DQPTs) in the extended Agassi model following sudden quenches of same level pairing (ΣΣΣ), monopole-monopole (χχχ) and cross level pairing (ΛΛΛ) strengths. Using exact diagonalization, we characterize the non-equilibrium dynamics through the Loschmidt echo and intensive return-rate function. Quenches across equilibrium phase boundaries produce cusp-like structures in the return rate that shows non-analyticities with increasing system size. Equilibrium finite size to large scaling identifies the χχχ-driven transition as a second order phase transition similar to mean-field, Dicke, and Lipkin-Meshkov-Glick (LMG) models critical behaviour with the exponent of the order parameter β≃1/2β\simeq 1/2β≃1/2, while the ΣΣΣ- and ΛΛΛ-driven transitions are first order. We further characterize the associated dynamical singularities through a local scaling exponent ααα, with αχ≃2/3α_χ\simeq 2/3αχ​≃2/3, αΛ≃1/3α_Λ\simeq 1/3αΛ​≃1/3, and αΣ≃3/2α_Σ\simeq 3/2αΣ​≃3/2 of all three parameters. The distinct scaling behaviours across the parameter channels show that dynamical criticality is not determined solely by the equilibrium order of the transition, revealing multiple dynamical scaling regimes. These non-analyticities are associated with the Fisher zeros of the Loschmidt amplitude, which cross the real time axis at critical times and the time derivatives of the return-rate function to characterize the order of DQPTs within the extended Agassi model.