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arXiv:2109.06220 · Physical review. B./Physical review. B

Scar states in a system of interacting chiral fermions

Ivar Martin, К. А. Матвеев

Published Jan 14, 2022• 12 citations
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Abstract

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.

DOI
10.1103/physrevb.105.045119

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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.
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 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 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.
We investigate eigenstate thermalization from the point of view of vanishing particle and heat currents between a few-body fermionic Hamiltonian prepared in one of its eigenstates and an external, weakly coupled Fermi-Dirac gas. The latter acts as a thermometric probe, with its temperature and chemical potential set so that there is neither particle nor heat current between the two subsystems. We argue that the probe temperature can be attributed to the few-fermion eigenstate in the sense that (i) it varies smoothly with energy from eigenstate to eigenstate, (ii) it is equal to the temperature obtained from a thermodynamic relation in a wide energy range, (iii) it is independent of details of the coupling between the two systems in a finite parameter range, (iv) it satisfies the transitivity condition underlying the zeroth law of thermodynamics, and (v) it is consistent with Carnot's theorem. For the spinless fermion model considered here, these conditions are essentially independent of the interaction strength. When the latter is weak, however, orbital occupancies in the few-fermion system differ from the Fermi-Dirac distribution so that partial currents from or to the probe will eventually change its state. We find that (vi) above a certain critical interaction strength, orbital occupancies become close to the Fermi-Dirac distribution, leading to a true equilibrium between the few-fermion system and the probe. In that case, the coupling between the Fermi-Dirac gas and few-fermion system does not modify the state of the latter, which justifies our approach a posteriori. From these results, we conjecture that for few-body systems with sufficiently strong interaction, the eigenstate thermalization hypothesis is complemented by ensemble equivalence: individual many-body eigenstates define a microcanonical ensemble that is equivalent to a canonical ensemble with grand canonical orbital occupancies.
While the chiral linear Luttinger liquid is integrable via bosonization, its nonlinear counterpart does not admit of an analytic solution. Nonetheless, the authors find a number of exact eigenstates for a large family of density-density interaction terms. These quantum many-body scar states are embedded in a continuum of strongly correlated excited states. They exhibit identically zero momentum-space entanglement. Among other properties, this sets them apart from many previous examples of quantum many-body scars.
An explanation of the thermalization of closed quantum systems is the eigenstate thermalization hypothesis, which states that all eigenstates are thermal. Quantum many-body scars are a relatively newly discovered phenomenon, which describe a band of nonthermal eigenstates that have high overlap with the initial state. These states impede the thermalization of systems. This paper looks at a system of ultracold Rubidium Rydberg atoms that interact via dipole-dipole interactions. This system has apparently normal thermalization when the dipole interactions are primarily two-body interactions, however when they are primarily three-body interaction the system thermalizes slower than expected. Simulations results are presented which suggest that scars states affect the time evolution of the system.