Abstract
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 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.
Highlights
Thermalization in quantum many-body systems is encoded in individual eigenstates of a generic Hamiltonian, and such a mechanism is hypothesized under the name eigenstate thermalization [1,2]
An experiment in a Rydberg atomic chain witnessed a weak ergodicity breaking where long-time oscillations of local observables persisted when the system was initialized in a specific quantum many-body state [6], and such periodic revivals were termed “quantum many-body scars” [7,8,9] in analogy to the quantum scars in chaotic singleparticle systems [10]
Quantum many-body scars are defined as instances of one or more states in the spectrum of a nonintegrable Hamiltonian that violate the strong sense of eigenstate thermalization, and several interesting models have been studied and constructed that support these nontrivial states in the sea of thermal states [11,12,13,14,15,16,17,18,19]
Summary
Thermalization in quantum many-body systems is encoded in individual eigenstates of a generic Hamiltonian, and such a mechanism is hypothesized under the name eigenstate thermalization [1,2]. We construct a few-body Hamiltonian on twodimensional (2D) lattices, which has a scar state with chiral topological order in the middle of the spectrum. We construct a few-body Hamiltonian on one-dimensional (1D) lattices with a critical scar state For both models, a parameter allows us to place the scar state at any desired position in the spectrum. For the special case γ = 0, we observe that | scar is the ground state We expect this approach to work quite generally to construct scar models, the thermal properties of the spectrum need to be checked in each case. We compute the energy level spacing distributions and entanglement entropies to show that the spectra are thermal.
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