Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays

TL;DR

This paper explores the dualities and symmetries of quantum orbital compass models, revealing their connection to p+ip superconducting arrays and implications for phase transitions.

Contribution

It introduces new duality transformations and symmetry analyses for orbital compass models, linking them to superconducting array models in a novel way.

Findings

Models exhibit self-dualities and discrete sliding symmetries.

Dualities relate orbital compass models to p+ip superconducting arrays.

Implications for order parameters and phase transitions are discussed.

Abstract

We study the spin- 1/2 two and three dimensional Orbital Compass Models relevant to the problem of orbital ordering in transition metal oxides. We show that these systems display self-dualities and novel (gauge-like) discrete sliding symmetries. An important and surprising consequence is that these models are dual to (seemingly unrelated) recently studied models of p+ip superconducting arrays. The duality transformations are constructed by means of a path-integral representation in discretized imaginary time and considering its Z_{2} spatial reflection symmetries and space-time discrete rotations, we obtain, in a transparent unified geometrical way, several dualities. We also introduce an alternative construction of the duality transformations using operator identities. We discuss the consequences of these dualities for the order parameters and phase transitions of the orbital compass model and its generalizations, and apply these ideas to a number of related systems.