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arXiv:2207.13688 · Physical review. B./Physical review. B

Eigenstate thermalization and disappearance of quantum many-body scar states in weakly interacting fermion systems

Ken K. W., Alexander Volya, Kun Yang

Published Dec 23, 2022• 4 citations
arXivHTMLPDF

Abstract

The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Eigenstates with low entanglement entropy are rare but naturally exist in the integrable system of free fermions. Here, we demonstrate analytically that these atypical states would always be eliminated when an arbitrary weak interaction is introduced between the fermions. In particular, we show that the probability of having a many-body scar state with entanglement entropy satisfying a subvolume scaling law decreases double exponentially as the system size. Thus, our results provide a quantitative argument for the disappearance of scar states in interacting fermion systems.

DOI
10.1103/physrevb.106.214313

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The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Eigenstates with low entanglement entropy are rare but naturally exist in the integrable system of free fermions. Here, we demonstrate analytically that these atypical states would always be eliminated when an arbitrary weak interaction is introduced between the fermions. In particular, we show that the probability of having a many-body scar state with entanglement entropy satisfying a subvolume scaling law decreases double exponentially as the system size. Thus, our results provide a quantitative argument for the disappearance of scar states in interacting fermion systems.
Quantum many-body scars are special eigenstates that violate the eigenstate thermalization hypothesis while residing at finite energy density along with thermalizing eigenstates. The spin-1 XY model is known to host a family of such exceptional states originating from long-lived quasiparticle excitations that exhibit anomalously low entanglement entropy and long-time periodic revivals, resulting in weak ergodicity breaking. We study the stability of these scarred states against typical U(1) symmetry preserving perturbation in the XY chain. While perturbation theory can describe the deformed scar states at small system sizes, finite-size scaling of the perturbation matrix elements indicate that the scars ultimately thermalize in larger chains. Nonetheless, we demonstrate that the long-range order associated with the scars decays under the perturbation, and we estimate the relaxation timescale of oscillatory dynamics in certain local observables to be of order λ−2λ^{-2}λ−2, where λλλ is the perturbation strength.
The eigenstate thermalization hypothesis describes how most isolated many-body quantum systems reach thermal equilibrium. However, the hypothesis is violated by phenomena such as many-body localization and quantum many-body scars. In this work, we study a finite, two-dimensional, disordered model hosting a tower of scar states. This construction is a particular instance of a general framework and we demonstrate its generality by constructing two disordered models hosting a different tower of scar states. At weak disorder, we find numerically that the spectra are nonthermal, and the scar states appear as exact eigenstates with high entropy for certain bipartitions. At strong disorder, the spectra localize and the scar states are identified as inverted scars since the scar states are embedded in a localized background as opposed to a thermal background. We argue that, for the considered type of models, the localization is stronger than what would be naively expected, and we show this explicitly for one of the models. The argument also provides guidelines for obtaining similarly strong localization in other scarred models. We study the transition from the thermal phase to localization by observing the adjacent gap ratio shifting from the Wigner surmise to the Poisson distribution with increasing disorder strength. Moreover, the entanglement entropy transitions from volume-law scaling with system size at weak disorder to area-law scaling at strong disorder. Finally, we demonstrate that localization protects scar revivals for initial states with partial support in the scar subspace.
In generic quantum many-body systems, the exact eigenstates are expected to satisfy the eigenstate thermalization hypothesis: Eigenstates near any given energy are expected to be thermodynamically equivalent. The authors demonstrate that in a system of chiral fermions with generic interaction this expectation is violated by some states. They find a coexistence of fermionic and bosonic types of eigenstates in some regions of the many-body spectrum. This allows for observable density oscillations even at weak coupling.
Quantum many-body scars (QMBSs) appear in a flat-band model with interactions on the sawtooth lattice. The flat-band model includes localized eigenstates within compact support, known as compact localized states (CLSs). Some characteristic many-body states can be constructed from the CLSs at a low filling on the flat band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, the states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with subvolume- or area-law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in nonintegrable systems with the violation of the strong ETH and the QMBS.
Quantum chaos and the eigenstate thermalization hypothesis are based on the assumption of the validity of random matrix theory description on the spectrum and eigenstates. They provide the foundation and descriptions for the typical dynamics and thermalization in generic closed quantum systems. In this thesis, we investigate situations where the systems show atypical dynamics or anomalous thermalization, conflicting with the usual expectations from quantum chaos and eigenstate thermalization hypothesis. We first examine weak thermalization in a nonintegrable spin chain. The system shows long-lived strong oscillations and relaxes to the thermal equilibrium weakly. We identify the dynamics describable by quasiparticles and recognize the oscillation frequency to be the quasiparticle mass gap. We also estimate the damping time for the oscillations. Next, we study prethermalization, a phenomenon where a system relaxes to an intermediate almost-equilibrium stage before reaching the true thermal equilibrium. We study a nonintegrable spin chain in the strong coupling limit, where an almost-conserved quantity emerges and gives rise to the prethermalization. We also study a newly proposed diagnostic for quantum chaos: out-of-time-ordered correlators. Contrasting to the chaotic systems, we inspect their behaviors in various noninteracting integrable models. Finally, we dig into the quantum many-body scar states in the PXP model which describes a Rydberg atom chain. These special states do not satisfy the random matrix theory description nor the eigenstate thermalization hypothesis, therefore defying quantum chaos.
Quantum many-body scars have been put forward as counterexamples to the eigenstate thermalization hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum nonergodicity generally linked to a subextensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic nonequilibrium dynamics in strongly correlated multicomponent quantum systems.