Normal and abnormal thermalization indicators in a one-dimensional low-density Jaynes-Cummings Hubbard model with and without dipole-dipole interaction
In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.
In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.
In one-dimensional low-density Jaynes-Cummings Hubbard (JCH) models [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107], we proved that the eigenstate thermalization hypothesis (ETH) is valid when the tunneling strength and coupling strength are of the same order. Surprisingly, at the weak tunneling limit, we observed that the entanglement entropy and scaling law of kinetic energy operators also exhibit obvious quantum chaotic properties, this is an unexpected result. To substantiate these findings, we further discuss their nonequilibrium dynamics in this paper. Our analysis reveals that when the model is a weak tunneling limit after the quench and the initial state is an equilibrium state of chaos, the system reaches an equilibrium state. This observation supports the conclusion that the low-density JCH model at the weak tunneling limit is nonintegrable, corroborating our previous results [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107]. Additionally, by discussing the validity of the fluctuation-dissipation theorem (FDT) and the evolution behavior of entanglement entropy and fidelity, we numerically demonstrate the differences between the one-dimensional low-density JCH model and general nonintegrable systems. Specifically, in the low-density JCH model, when the Hamiltonian after the quench is integrable, the validity of FDT depends on the thermal behavior of the initial Hamiltonian, and a metastable state is observed during the evolution of entanglement entropy. Our research presents an an intriguing and unique nonintegrable model, enriching the current understanding of nonintegrable systems.
Disorder in one-dimensional (1D) many-body systems emerges abundant phases such as many-body localization (MBL), and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, as known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder comparing to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of MBL phase in the JCH model that strongly violate eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in weak disorder or weak coupling regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.
Abstract The eigenstate thermalization hypothesis (ETH) is a mechanism for the thermalization of quantum chaotic systems. Most researches on quantum chaotic systems involve the two-body interaction between spins, fermions, and bosons, but for the JCH model, the emergence of quantum-chaotic properties comes from the competition between the hopping strength of the photon and the photon-atom coupling strength. We use exact diagonalization to prove that the JCH system has the property of the quantum chaotic system and verify the validity of ETH ansatz both for diagonal and off-diagonal matrix elements of the photon observables with reasonable experimental parameters.
Disorder in one-dimensional (1D) many-body systems facilitates abundant phases such as many-body localization (MBL) and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder compared to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of a MBL phase in the JCH model that strongly violates the eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in the weak disorder regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.
Motivated by the nonequilibrium dynamics experiment, we study the quantum quench dynamics of the JCH model with weak nearest-neighbor hopping strength by exact diagonalization. One of the crucial insights is to focus on the comparison between the time-averaged density matrix and the canonical ensemble in a wide range of values for the coupling strength between the cavity and the atom, and significant differences are found. Thus, this phenomenon can be used to infer that the system with weak nearest-neighbor hopping strength may be integrable. In order to verify our prediction, we perform the level spacing distribution of the system and find that they conform with the characteristics of the integrable system. Further, a nearly integrable system is presented by removing the degenerate energy level and fitting Brody distribution. Besides, the evolution of the momentum distribution functions of the photon and the equilibrium value predicted by the canonical ensemble are followed, which demonstrates that the system cannot be thermalized. Finally, the way how the system avoids thermalization is also discussed by the finite-size scaling of the fluctuations of the diagonal and the off-diagonal matrix elements.
We study how the proximity to an integrable point or to localization as one approaches the atomic limit, as well as the mixing of symmetries in the chaotic domain, may affect the onset of thermalization in finite one-dimensional systems. We consider systems of hard-core bosons at half-filling with nearest-neighbor hopping and interaction, and next-nearest-neighbor interaction. The latter breaks integrability and induces a ground-state superfluid to insulator transition. By full exact diagonalization, we study chaos indicators and few-body observables. We show that when different symmetry sectors are mixed, chaos indicators associated with the eigenvectors, contrary to those related to the eigenvalues, capture the onset of chaos. The results for the complexity of the eigenvectors and for the expectation values of few-body observables confirm the validity of the eigenstate thermalization hypothesis in the chaotic regime, and therefore the occurrence of thermalization. We also study the properties of the off-diagonal matrix elements of few-body observables in relation to the transition from integrability to chaos and from chaos to localization.