# Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves

## TL;DR

This paper introduces an SU(2) gauge theory that links topological order with broken symmetries, explaining the pseudogap phase in hole-doped cuprates through quantum fluctuations of magnetic states.

## Contribution

It develops a unified SU(2) gauge framework connecting topological order and broken symmetries in cuprates, advancing understanding of the pseudogap phase.

## Key findings

- Metals with an antinodal gap emerge from the theory.
- Topological order intertwines with observed broken symmetries.
- The theory applies to various models including Hubbard and spinon theories.

## Abstract

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the `anti-nodal' region of the square lattice Brillouin zone, and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin density wave mean field theory of the square lattice Hubbard model, and in a CP$^1$ theory of spinons. This theory leads to metals with an antinodal gap, and topological order which intertwines with precisely the observed broken symmetries.