A Tale of Two Quantum Compass Models

TL;DR

This paper explores two quantum compass models, revealing quantum phase transitions, topological phases, and temperature-dependent dimensional crossovers, with implications for simulating exotic quantum phases in cold-atom and Josephson junction systems.

Contribution

It introduces new insights into quantum phase transitions and topological phases in two variants of quantum compass models, including potential realizations in cold-atom systems.

Findings

Identified a quantum phase transition in honeycomb QCM in the 3d-Ising universality class.

Discovered a temperature-driven dimensional crossover in the fermionic QCM.

Proposed methods to simulate exotic quantum phases using cold-atom and Josephson junction platforms.

Abstract

We investigate two variants of quantum compass models (QCMs). The first, an orbital-only honeycomb QCM, is shown to exhibit a quantum phase transition (QPT) from a $XX$- to $ZZ$-ordered phase in the $3d$-Ising universality class, in accord with earlier studies. In a fractionalized parton construction, this describes a ``superfluid-Mott insulator'' transition between a higher-order topological superfluid and the toric code, the latter described as a $p$-wave resonating valence bond state of the partons. The second variant, the spinless fermion QCM on a square lattice, is of interest in the context of cold-atom lattices with higher-angular momentum states on each atom. We explore finite-temperature orbital order-disorder transitions in the itinerant and localized limits using complementary methods. In the itinerant limit, we uncover an intricate temperature ($T$)-dependent dimensional crossover from a high-$T$ quasi-$1d$ insulator-like state, via an incoherent bad-metal-like state at intermediate $T$, to a $2d$ symmetry-broken insulator at low $T$, well below the ``orbital'' ordering scale. Finally, we discuss how engineering specific, tunable, and realistic perturbations in both these variants can act as a playground for simulating a variety of exotic QPTs between topologically ordered and trivial phases. In the cold-atom context, we propose a novel way to engineer a possible realisation of the exotic exciton Bose liquid phase at a QPT between a Bose superfluid and a charge density wave insulator. We argue that advances in the design of Josephson junction arrays and manipulating cold-atom lattices offer the hope of simulating such novel phases of matter in the foreseeable future.