Quantum many-body scars in the Bose-Hubbard model with a three-body constraint

TL;DR

This paper identifies exact quantum many-body scar states in a constrained Bose-Hubbard model, linking them to known states in the $S=1$ $XY$ model, and discusses their potential experimental realization.

Contribution

It constructs and characterizes QMBS states in the constrained Bose-Hubbard model, revealing their equivalence to states in the $S=1$ $XY$ model and their existence as low-energy eigenstates.

Findings

Exact QMBS states are generated by an SU(2) ladder operator.

QMBS states are equivalent to those in the $S=1$ $XY$ model.

Potential for adiabatic preparation and observation in ultracold-atom experiments.

Abstract

We uncover the exact athermal eigenstates in the Bose-Hubbard (BH) model with a three-body constraint, motivated by the exact construction of quantum many-body scar (QMBS) states in the $S=1$ $XY$ model. These states are generated by applying an $\rm SU(2)$ ladder operator consisting of a linear combination of two-particle annihilation operators to the fully occupied state. By using the improved Holstein-Primakoff expansion, we clarify that the QMBS states in the $S=1$ $XY$ model are equivalent to those in the constrained BH model with additional correlated hopping terms. We also find that, in the strong-coupling limit of the constrained BH model, the QMBS state exists as the lowest-energy eigenstate of the effective model in the highest-energy sector. This fact enables us to prepare the QMBS states in a certain adiabatic process and opens up the possibility of observing them in ultracold-atom experiments.