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arXiv:2110.15365 · Physical review. B./Physical review. B

Exact quantum scars in the chiral nonlinear Luttinger liquid

Frank Schindler, Nicolas Regnault, Bogdan Andrei Bernevig

Published Jan 26, 2022• 37 citations
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Abstract

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.

DOI
10.1103/physrevb.105.035146

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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.
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 chiral Luttinger liquid develops quantum chaos as soon as a—however slight—nonlinear dispersion is introduced for the microscopic electronic degrees of freedom. For this nonlinear version of the model, we identify an infinite family of translation-invariant interaction potentials with corresponding modulated symmetries. These symmetries are highly unconventional: they are modulated in momentum space (and do not seem to have an easy physical interpretation). We develop a systematic understanding of these symmetries and study the resulting blocks in the Hamiltonian. In particular, this approach allows us to predict the analytic Hamiltonian block sizes and derive asymptotic scaling laws in the limit of large total momentum. These blocks are reminiscent of Hilbert space fragmentation in that, even though they are labeled by a symmetry, this symmetry is highly nonlocal and does not have a simple interpretation. We corroborate this result by studying entanglement entropy and level statistics.
Quantum many-body scars are atypical nonthermal states embedded in the chaotic spectrum that evade conventional ergodicity. We propose the asymptotically AdS mini-boson star as a holographic candidate for scar-like states. Their spectrum exhibits random-matrix signatures of chaos while supporting embedded integrable spectral branches. The whole holographic system, including black holes, is generically chaotic with most eigenstates satisfying the eigenstate thermalization hypothesis; in contrast, the boson star macrostate probes a near-integrable subsector within this chaotic spectrum, signaling scarred spectral structures. Boson stars further display anomalously low entanglement relative to black holes at the same energy density, and also robust revivals in Krylov complexity, revealing nonergodic dynamics. These spectral, entanglement, and dynamical diagnostics provide unified evidence for holographic quantum scars in a self-gravitating system. Our work suggests a new connection between many-body scar physics, quantum chaos, and horizonless gravitational dynamics.
Here, the authors develop a general formalism to analytically compute the entanglement spectra of exact excited states and use it to obtain the entanglement spectra of the infinite tower of states of the spin-SSS AKLT models, which are the first analytical examples of what are now called quantum many-body scars. Located in the bulk of the spectrum, these states have a subthermal entanglement entropy, showing for the first time the violation of the strong eigenstate thermalization hypothesis (ETH) in a well-known translation-invariant nonintegrable model.
We construct few-body, interacting, nonlocal Hamiltonians with a quantum scar state in an otherwise thermalizing many-body spectrum. In one dimension, the embedded state is a critical state, and in two dimensions, the embedded state is a chiral topologically ordered state. The models are defined on slightly disordered lattices, and the scar state appears to be independent of the precise realization of the disorder. A parameter allows the scar state to be placed at any position in the spectrum. We show that the level spacing distributions are Wigner-Dyson and that the entanglement entropies of the states in the middle of the spectrum are close to the Page value. Finally, we confirm the topological order in the scar state by showing that one can insert anyons into the state.
Abstract Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a “hard” kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a “soft” constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure.