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 B Atomic Molecular and Optical Physics

Spatiotemporal scales of dynamical quantum phase transitions in the Bose–Hubbard model

Jia 李 Li 佳, Yajiang Hao

Published Apr 21, 2026• 0 citations
Publisher

Abstract

Abstract We investigate the spatial and temporal scales of dynamical quantum phase transitions (DQPTs) in the one-dimensional Bose–Hubbard model in the strong interaction limit. Using Jordan–Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo (LE), and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system LE, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical DQPTs using the subsystem LE. It is expected that the present results provide a reliable foundation for further experimental investigations.

DOI
10.1088/1361-6455/ae62bd

Related papers

Spatiotemporal scales of dynamical quantum phase transitions in the Bose-Hubbard model

Li, Jia, Hao, Yajiang

We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.

arXiv:2512.11314•Dec 12, 2025•0 citations

Critical exponent of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strongly interacting limit

Jia Li, Yajiang Hao

We analytically investigated the dynamical quantum phase transitions in the Bose-Hubbard model using the Loschmidt echo as an observable, revealing that after a quench, the global Loschmidt echo exhibits cusp singularities with a logarithmically divergent rate function near criticality and a critical exponent of zero. Through extensive calculations across various system sizes and initial states, we have demonstrated that in the strongly interacting regime, the critical singularity of dynamical quantum phase transitions exhibits consistency across different model details and initial product states (charge-density wave states). Moreover, we find that modifying the harmonic potential well not only preserves the phase transition but also enables precise control over the transition timing.

arXiv:2510.21578•Physical Review A•Nov 17, 2025•2 citations

Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid

Mateusz Łącki, Markus Heyl

In this paper, we revisit collapse and revival oscillations in superfluids suddenly quenched by strong local interactions for the case of a one-dimensional Bose-Hubbard model. As the main result, we identify the inherent nonequilibrium quantum many-body character of these oscillations by revealing that they are controlled by a sequence of underlying dynamical quantum phase transitions in the real-time evolution after the quench, which manifest as temporal nonanalyticities in return probabilities or Loschmidt echos. Specifically, we find that the timescale of the collapse and revival oscillations is, first, set by the frequency at which dynamical quantum phase transitions appear, and is, second, of emergent nonequilibrium nature, since it is not only determined by the final Hamiltonian but also depends on the initial condition.

arXiv:1812.02209•Physical review. B./Physical review. B•Mar 18, 2019•32 citations

Dynamical scaling of Loschmidt echo in non-Hermitian systems

Jia-Chen Tang, Su-Peng Kou, Gaoyong Sun

Abstract We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.

arXiv:2105.05696•Europhysics Letters (EPL)•Feb 1, 2022•25 citations

Determination of dynamical quantum phase transitions for boson systems using the Loschmidt cumulants method

Pengju Zhao, Jingxin Sun, Shengjie Jin +5 more

We study the dynamical quantum phase transition (DQPT) of the Bose-Hubbard model utilizing the recently developed Loschmidt cumulants method. We determine the complex Loschmidt zeros of the Loschmidt amplitude analogous to the Lee-Yang zeros of the thermal partition function. We obtain the DQPT critical points through identifying the crossing points with the imaginary axis. The critical points show high accuracy when compared to those obtained using the matrix product states method. In addition, we show how the critical points of DQPT can be determined by analyzing the energy fluctuation of the initial state, which makes it a valuable tool for future studies in this area. Finally, DQPT in the extended Bose-Hubbard model is also investigated.

Physical Review A•Jan 8, 2024•2 citations

Determination of dynamical quantum phase transition for boson systems using the Loschmidt cumulants method

Pengju Zhao, Jingxin Sun, Shengjie Jin +4 more

We study the dynamical quantum phase transition(DQPT) of the Bose-Hubbard model utilizing recently developed Loschmidt cumulants method. We determine the complex Loschmidt zeros of the Loschmidt amplitude analogous to the Lee-Yang zeros of the thermal partition function. We obtain the DQPT critical points through identifying the crossing points with the imaginary axis. The critical points show high accuracy when compared to those obtained using the matrix product states method. In addition, we show that how the critical points of DQPT can be determined by analyzing the energy fluctuation of the initial state, making it a valuable tool for future studies in this area. Finally, DQPT in the extended Bose-Hubbaed model is also investigated.

arXiv:2308.00300•Aug 1, 2023•0 citations
Abstract We investigate the spatial and temporal scales of dynamical quantum phase transitions (DQPTs) in the one-dimensional Bose–Hubbard model in the strong interaction limit. Using Jordan–Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo (LE), and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system LE, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical DQPTs using the subsystem LE. It is expected that the present results provide a reliable foundation for further experimental investigations.
We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.
We analytically investigated the dynamical quantum phase transitions in the Bose-Hubbard model using the Loschmidt echo as an observable, revealing that after a quench, the global Loschmidt echo exhibits cusp singularities with a logarithmically divergent rate function near criticality and a critical exponent of zero. Through extensive calculations across various system sizes and initial states, we have demonstrated that in the strongly interacting regime, the critical singularity of dynamical quantum phase transitions exhibits consistency across different model details and initial product states (charge-density wave states). Moreover, we find that modifying the harmonic potential well not only preserves the phase transition but also enables precise control over the transition timing.
In this paper, we revisit collapse and revival oscillations in superfluids suddenly quenched by strong local interactions for the case of a one-dimensional Bose-Hubbard model. As the main result, we identify the inherent nonequilibrium quantum many-body character of these oscillations by revealing that they are controlled by a sequence of underlying dynamical quantum phase transitions in the real-time evolution after the quench, which manifest as temporal nonanalyticities in return probabilities or Loschmidt echos. Specifically, we find that the timescale of the collapse and revival oscillations is, first, set by the frequency at which dynamical quantum phase transitions appear, and is, second, of emergent nonequilibrium nature, since it is not only determined by the final Hamiltonian but also depends on the initial condition.
Abstract We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.
We study the dynamical quantum phase transition (DQPT) of the Bose-Hubbard model utilizing the recently developed Loschmidt cumulants method. We determine the complex Loschmidt zeros of the Loschmidt amplitude analogous to the Lee-Yang zeros of the thermal partition function. We obtain the DQPT critical points through identifying the crossing points with the imaginary axis. The critical points show high accuracy when compared to those obtained using the matrix product states method. In addition, we show how the critical points of DQPT can be determined by analyzing the energy fluctuation of the initial state, which makes it a valuable tool for future studies in this area. Finally, DQPT in the extended Bose-Hubbard model is also investigated.
We study the dynamical quantum phase transition(DQPT) of the Bose-Hubbard model utilizing recently developed Loschmidt cumulants method. We determine the complex Loschmidt zeros of the Loschmidt amplitude analogous to the Lee-Yang zeros of the thermal partition function. We obtain the DQPT critical points through identifying the crossing points with the imaginary axis. The critical points show high accuracy when compared to those obtained using the matrix product states method. In addition, we show that how the critical points of DQPT can be determined by analyzing the energy fluctuation of the initial state, making it a valuable tool for future studies in this area. Finally, DQPT in the extended Bose-Hubbaed model is also investigated.