We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-$3/2$ Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasi-regular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasi-regular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.
We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-3/2 Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasi-regular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasi-regular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.
Additional quantum many-body scars of the spin-1XY model with Fock-space cages and commutant algebras
Quantum many-body scars (QMBS) represent a mechanism for weak ergodicity breaking, characterized by the coexistence of atypical non-thermal eigenstates within an otherwise thermalizing many-body spectrum. In this work, we revisit the spin-1XY model on a periodic chain and construct several new families of exact scar eigenstates embedded within its extensively degenerate manifolds that owe their origins to an interplay of U(1) magnetization conservation and chiral symmetries. We go beyond previously studied towers of states and first identify a novel set of interference-protected eigenstates resembling Fock space cage states, where destructive interference confines the wave function to sparse subgraphs of the Fock space. These states exhibit subextensive entanglement entropy, and when subjected to a transverse magnetic field, form equally spaced ladders whose coherent superpositions display long-lived fidelity oscillations. We further reveal a simpler organizing principle behind these nonthermal states by using the commutant algebra framework, in particular by showing that they are simultaneous eigenstates of non-commuting local operators. Moreover, in doing so, we uncover two more novel families of exact scars: a tower of volume-entangled states, and a set of mirror-dimer states with some free local degrees of freedom. Our results illustrate the power and interplay of interference-based and algebraic mechanisms of non-ergodicity, offering systematic routes to identifying and classifying QMBS in generic many-body quantum systems.
The typical mechanisms of ergodicity breaking in isolated interacting quantum systems, such as many-body localization and quantum many-body scars, originate from the nonthermal nature of the underlying eigenstates. Here, in the absence of nonthermal eigenstates, we identify a mechanism for collective revivals of multiparticle Wannier states (MWSs) associated with nearly linear bands in a spatially modulated Bose-Hubbard lattice. The MWSs, as superpositions of multiparticle Bloch states within individual energy bands, give rise to band-resolved Wannier-sector fragmentation. The key idea is that spatially periodic modulation folds and separates energy bands of a simple lattice into several sub-bands, among which nearly linear sub-bands inherit the linear segments of the original bands. Although multiparticle Bloch states satisfy the eigenstate thermalization hypothesis (ETH), the MWSs in the nearly linear band still exhibit long-lived collective revivals, due to emergent equally spaced energy levels. Our work provides a route to weak ergodicity breaking in which long-lived revivals arise from spectral phase coherence among ETH-satisfying eigenstates rather than from scar-like nonthermal eigenstates.
Quantum many-body scars consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum, and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of quantum many-body scars follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit. A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system's rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the eigenstate thermalization hypothesis, and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical unstable periodic orbits, while satisfying the eigenstate thermalization hypothesis. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates.
The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.
Universal Dynamics of a Spin-3/2 Fermi Gas in Traps with Distinct Spectra
Universal power-law decay of spin-mixing oscillations has been observed in a harmonically trapped spin-3/2 Fermi gas, whose exactly equally spaced spectrum represents a highly special case. To gain insight into the origin of this behavior, we investigate the dynamics in traps with increasing and decreasing level spacings, represented by the infinite square well and the Pöschl--Teller potential, respectively. Despite pronounced differences in their single-particle spectra, all systems exhibit power-law decay of coherent oscillations, described by A(t)=A0−γtα. The exponent α remains insensitive to particle number, interaction strength, and the overall energy scale, but exhibits systematic differences among traps with distinct spectral structures. In contrast, the decay parameter γ is strongly influenced by both the spectral structure and the overall energy scale. These findings demonstrate that power-law decay is not restricted to the harmonic trap but persists across qualitatively distinct spectral structures. The observed variation of α among different traps further suggests that the underlying single-particle spectrum plays an important role in shaping the decay dynamics.
Generic quantum many-body systems are expected to thermalize, scrambling initial coherence while local observables relax to equilibrium values. Weak ergodicity breaking, often associated with quantum many-body scarring of homogeneous states, provides rare exceptions with long-lived coherence. We introduce a family of local spin-1/2 chains with a structured subspace that hosts a much broader range of nonthermal phenomena, such as scars, chirally propagating quasiparticles or approximate topological edge modes. These nonthermal phenomena happening at high energy densities can be understood via structured subspaces that are protected by destructive interference. We develop a quantitative leakage theory predicting which states retain coherence and suggest ways to improve the stability by inducing fast oscillations in the complement subspace. Our framework connects asymptotic scars, quantum cages, and parent-Hamiltonian constructions, and shows that weak ergodicity breaking in chaotic systems extends well beyond revivals of homogeneous initial states.