Fate of chiral order and impurity self-pinning in flat bands with local symmetry

TL;DR

This paper investigates a chain of flat-band $ ext{pi}$-flux plaquettes with local symmetries, showing the absence of long-range chiral order due to local symmetry constraints, and introduces an impurity self-pinning phenomenon with potential experimental implications.

Contribution

It demonstrates that local symmetries in flat-band $ ext{pi}$-flux chains prevent long-range chiral order and introduces the impurity self-pinning effect, supported by analytical and numerical methods.

Findings

Local symmetries prevent long-range chiral order.

Impurity self-pinning causes non-dispersive density peaks.

Exact diagonalization supports theoretical predictions.

Abstract

Interacting bosons on a single plaquette threaded by a $\pi$-flux can spontaneously break time-reversal symmetry, resulting in a chiral loop current. Connecting such bosonic $\pi$-flux plaquettes in a dispersive configuration was recently shown to lead to long-range chiral order. Here, instead, we design a chain of $\pi$-flux plaquettes that exhibits an all-flat-bands single-particle energy spectrum and an extensive set of local symmetries. Using Elitzur's theorem, we show that these local symmetries prevent the emergence of long-range chiral order. Moreover, projecting the dynamics to a Creutz ladder model with an effective intra-rung interaction allows one to derive simple spin Hamiltonians capturing the ground state degeneracy and the low-energy excitations, and to confirm the absence of chiral order. Nevertheless, we show how to obtain gauge-invariant information from a mean-field approach, which explicitly break gauge-invaraince. Finally, we observe an ``impurity self-pinning'' phenomenon, when an extra boson is added on top of a ground state at integer filling, resulting in a non-dispersive density peak. Exact diagonalization benchmarks are also provided, and experimental perspectives are discussed.