Exotic phase transitions in spin ladders with discrete symmetries that emulate spin-1/2 bosons in two dimensions

TL;DR

This paper introduces a spin ladder model with discrete symmetries that mimics two-dimensional spin-1/2 boson systems, revealing exotic quantum critical points and connecting to gauge theories.

Contribution

It constructs an exactly solvable spin ladder model emulating 2D boson systems, establishing dualities, and analyzing symmetry-breaking phase transitions.

Findings

Identifies exotic deconfined quantum critical points.

Maps the spin ladder to a $ ext{Z}_2$ gauge theory of partons.

Constructs exactly solvable models for symmetry-breaking phases.

Abstract

We introduce a spin ladder with discrete symmetries designed to emulate a two-dimensional spin-1/2 boson system at half-filling. Using global properties, such as the structure of topological defects, we establish a correspondence between the two systems and construct a dictionary of symmetries and operators. In particular, translation invariance leads to Lieb-Schultz-Mattis constraints for both systems, resulting in exotic deconfined quantum critical points. Subsequently, we study the spin ladder in detail. An exact duality transformation maps it onto a $\mathbb{Z}_2$ gauge theory of three partons, analogous to the U(1) gauge theory of chargons and spinons in two-dimensional spin-1/2 boson systems. With the mapping between spins and partons, we construct exactly solvable models for all pertinent symmetry-breaking phases and analyze their transitions. We further make connections between our exact analysis and conventional parton gauge theories.