Trapping Hard-Core Bosons in Flatband Lattices

TL;DR

This paper analytically constructs exact groundstates of hard-core bosons in flatband lattices, revealing macroscopic degeneracy, Hilbert space fragmentation, and connections to spin models with quantum scars.

Contribution

It introduces a method to construct exact groundstates in flatband lattices with hard-core bosons, highlighting macroscopic degeneracy and novel many-body phenomena.

Findings

Groundstates constructed up to half-filling with macroscopic degeneracy.

At half-filling, the groundstate forms a Wigner crystal.

Occupied localized states act as barriers, causing Hilbert space fragmentation.

Abstract

We investigate 1D and 2D cross-stitch lattices with hard-core bosons and analytically construct exact groundstates that feature macroscopic degeneracy. The construction relies on the presence of a flatband in the single particle spectrum and the orthogonality of the associated compact localized states (CLS). Up to filling fraction $\nu=1/2$, the groundstate is constructed by occupying the CLS. Exactly at $\nu=1/2$, the groundstate becomes a Wigner crystal. For higher filling fractions, the groundstate is constructed by filling the CLS sites completely one by one. Macroscopic degeneracy arises from the multiple choices available when occupying or filling the CLS sites. An occupied CLS acts as an impenetrable barrier for bosons both in 1D and 2D, leading to Hilbert space fragmentation. A similar phenomenology also holds for hard-core bosons on the diamond chain and its higher dimensional generalizations. We also discuss the mapping of these hard-core models onto spin models with quantum many-body scars.