Field-control of symmetry-broken and quantum disordered phases in frustrated moir\'e bilayers with population imbalance

TL;DR

This paper investigates the ground states and excitations of a four-flavor Heisenberg model on a triangular lattice under population imbalance, revealing symmetry-broken phases and a fluctuating regime connecting spin liquids of different symmetries.

Contribution

It introduces a comprehensive analysis of the imbalanced four-flavor Heisenberg model, combining multiple theoretical methods to uncover novel phases and fluctuation regimes.

Findings

Identification of symmetry-broken phases with spin and excitonic order

Discovery of a strongly fluctuating regime without long-range order

Observation of a robust 1/3 polarisation polarisability

Abstract

We determine the ground states and excitation spectra of the paradigmatic four-flavour Heisenberg model with nearest- and next-nearest-neighbor exchange couplings on the triangular lattice in a field controlling the population imbalance of flavor pairs. Such a system arises in the strongly correlated limit of moir\'e bilayers of transition metal dichalcogenides in an electric displacement field or in-plane magnetic field, and can be simulated via ultracold alkaline-earth atoms. We argue that the field tunes between effective SU(4) and SU(2) symmetries in the balanced and fully polarised limits and employ a combination of mean-field calculations, flavour-wave theory, and exact diagonalisation to analyse the intermediate, imbalanced regime. We find different symmetry-broken phases with simultaneous spin and excitonic order depending on the field and next-nearest-neighbor coupling. Furthermore, we demonstrate that there is a strongly fluctuating regime without long-range order that connects candidate spin liquids of the SU(2) and SU(4) limit. The strong fluctuations are facilitated by an extensive classical degeneracy of the model, and we argue that they are also responsible for a strong polarisability at 1/3 polarisation that survives from the mean-field level to the exact spectrum.