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arXiv:2608.17076

Hidden Ergodic Relaxation in the Quench Dynamics of a Bichromatic Mott Lattice

Áttis V. M. Marino, Rhombik Roy, M. A. Caracanhas, N. D. Chavda, A. M. S. Macêdo, Vanderlei Salvador Bagnato, Robin P. Sagar, B. Chakrabarti

Published Aug 17, 2026• 0 citations
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Abstract

We investigate the nonequilibrium dynamics of strongly interacting bosons in a finite bichromatic Mott lattice following a sudden quench of the secondary lattice amplitude. The coefficient entropies and second Rényi entropy exhibit pronounced growth toward their Gaussian Orthogonal Ensemble (GOE) predictions from random-matrix theory, consistent with GOE-like statistical spreading in the employed multiconfigurational representation. In striking contrast, experimentally accessible observables, including the momentum distribution, fragmentation, and Glauber correlation functions, remain nearly unchanged throughout the evolution. For the sampled strong quenches, the coefficient entropies, second Rényi entropy, and the $N$-body coefficient spreading collapse onto a common relaxation trajectory that becomes largely independent of the perturbation strength. Our results reveal an emergent hidden ergodic relaxation beneath the persistent local Mott-like order. An effective embedded random-matrix model captures the qualitative crossover from restricted to extensive Hilbert-space spreading, providing an interpretive framework for the observed relaxation dynamics.

DOI
10.48550/arxiv.2608.17076

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We investigate the nonequilibrium dynamics of strongly interacting bosons in a finite bichromatic Mott lattice following a sudden quench of the secondary lattice amplitude. The coefficient entropies and second Rényi entropy exhibit pronounced growth toward their Gaussian Orthogonal Ensemble (GOE) predictions from random-matrix theory, consistent with GOE-like statistical spreading in the employed multiconfigurational representation. In striking contrast, experimentally accessible observables, including the momentum distribution, fragmentation, and Glauber correlation functions, remain nearly unchanged throughout the evolution. For the sampled strong quenches, the coefficient entropies, second Rényi entropy, and the NNN-body coefficient spreading collapse onto a common relaxation trajectory that becomes largely independent of the perturbation strength. Our results reveal an emergent hidden ergodic relaxation beneath the persistent local Mott-like order. An effective embedded random-matrix model captures the qualitative crossover from restricted to extensive Hilbert-space spreading, providing an interpretive framework for the observed relaxation dynamics.
We study the nonequilibrium dynamics of a bosonic Mott insulator following a sudden quench from a periodic to a quasiperiodic lattice. Using ab initio multiconfigurational (MCTDHB) continuum many-body dynamics, we characterize the evolution through momentum distributions, fragmenta- tion, correlation functions, and information entropy. We find that melting of Mott correlations does not necessarily imply relaxation of the many-body state. In the weakly interacting regime, the initial Mott-like correlation undergo recurrent melting and partial recovery, while the information entropy displays large, intermittent fluctuations within the simulated time window. In contrast, a strongly interacting and fully fragmented Mott insulator retains its characteristic Mott correla- tions, up to partial distortions, while the many-body information entropy approaches a well-defined stationary regime plateau with comparatively small fluctuations. These results indicate that Mott- correlation dynamics and many-body relaxation can be dissociated in this finite system and support the use of information entropy, evaluated in the multiconfigurational representation, as a sensitive complementary diagnostic of nonequilibrium relaxation.
We investigate the time evolution of the second-order R\'enyi entropy (RE) for bosons in a one-dimensional optical lattice following a sudden quench of the hopping amplitude JJJ. Specifically, we examine systems that are quenched into the strongly correlated Mott-insulating (MI) regime with $J/U\ensuremath{\ll}1$ (UUU denotes the strength of the on-site repulsive interaction) from the MI limit with J=0J=0J=0. In this regime, the low-energy excited states can be effectively described by fermionic quasiparticles known as doublons and holons. They are excited in entangled pairs through the quench dynamics. By developing an effective theory, we derive a direct relation between the RE and correlation functions associated with doublons and holons. This relation allows us to analytically calculate the RE and obtain a physical picture for the RE, both in the ground state and during time evolution through the quench dynamics, in terms of doublon-holon pairs. In particular, we show that the RE is proportional to the population of doublon-holon pairs that span the boundary of the subsystem. Our quasiparticle picture introduces some remarkable features that are absent in previous studies on the dynamics of entanglement entropy in free-fermion models. It provides with valuable insights into the dynamics of entanglement entropy in strongly-correlated systems.
We study the out-of-equilibrium dynamics of dipolar bosons and fermions after a sudden change in the interaction strength from zero to a finite repulsive value. We simulate the interaction quench on the initial state which is the ground state of harmonic potential with noninteracting bosons and fermions. We solve the time-dependent many-boson Schrödinger equation exactly using numerical methods. To understand the many-body dynamics we analyze several measures of many-body information entropy, monitoring their time evolution and assessing their dependence on interaction strength. We establish that for weak interaction quench the dynamics is statistics independent, both dipolar bosons and fermions do not relax, whereas it is significantly different for dipolar bosons from that of dipolar fermions in the stronger interaction quench. While dipolar bosons exhibit concurrent signature of relaxation in all entropy measures, dipolar fermions fail to relax, exhibiting modulated oscillation in all entropy dynamics. For dipolar bosons and larger interaction quench, the many-body information entropy measures dynamically approach the value predicted for the Gaussian orthogonal ensemble of random matrices, implying statistical relaxation and ergodicity. The entire relaxation process and signature of ergodicity are established by three unique features: dynamical delocalization in Hilbert space, violent orbital fragmentation, and saturation of all entropy measures to the maximum entropy states in the long-time dynamics. It highlights the importance of many-body effects with a possible exploration in quantum simulation with ultracold atoms.
We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the weakly interacting (Bose-Hubbard) and strongly interacting (sine-Gordon) regimes. While in a higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in one dimension an instability is generated also for shallow lattices with a commensurate periodic potential pinning the atoms to the Mott state through a transition described by the sine-Gordon model. The present work aims at identifying the quench dynamics in both the Bose-Hubbard and sine-Gordon interaction regimes. We numerically exactly solve the time-dependent Schr\"odinger equation for a small number of atoms and obtain dynamical measures of several key quantities. We investigate the correlation dynamics of first and second order; both exhibit rich many-body features in the dynamics. We conclude that in both cases, dynamics exhibits collapse-revival phenomena, though with different timescales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics especially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. Bose-Hubbard dynamics clearly establishes the possible relaxation to the maximum entropy state. In contrast, the sine-Gordon dynamics is so fast that it does not exhibit any signature of relaxation in the present timescale of computation.
We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of N=10N=10N=10 interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schr\"odinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in a way that minimizes the number of significantly contributing ones. It is therefore a nontrivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that mean-field approaches such as the time-dependent Gross-Pitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (R-MCTDHB).
Abstract The relaxation process of a few strongly interacting bosons in a triple well optical lattice is studied from the first principle using the multiconfigurational time-dependent Hartree method for bosons. We report the contrasting response of the system under two independent quench processes: an interaction quench and a lattice depth quench. We analyze the evolution of the reduced one-body density matrix, two-body density and the Shannon information entropy for a wide range of lattice depth and interaction strength parameters. For the strong interaction quench, we observe a very fast relaxation to the steady state. In contrast, for the lattice depth quench, we observe collapse–revival dynamics in all the key measures. We also provide the best fitting formulas for relaxation and revival time which follow power law decay.