Quantum Phases of the Shraiman-Siggia Model

TL;DR

This paper investigates the phase diagram of the Shraiman-Siggia model for lightly-doped square lattice antiferromagnets, revealing various magnetic and quantum-disordered phases with a focus on their critical behavior and experimental relevance.

Contribution

It provides a self-consistent two-loop analysis of the model, identifying quantum-disordered phases with pseudo-gaps and characterizing the quantum phase transition's critical properties.

Findings

Identification of magnetically-ordered and disordered phases with and without incommensurate correlations

Discovery of pseudo-gap behavior in quantum-disordered phases

Critical behavior similar to the $O(3)$ sigma model transition

Abstract

We examine phases of the Shraiman-Siggia model of lightly-doped, square lattice quantum antiferromagnets in a self-consistent, two-loop, interacting magnon analysis. We find magnetically-ordered and quantum-disordered phases both with and without incommensurate spin correlations. The quantum disordered phases have a pseudo-gap in the spin excitation spectrum. The quantum transition between the magnetically ordered and commensurate quantum-disordered phases is argued to have the dynamic critical exponent $z=1$ and the same leading critical behavior as the disordering transition in the pure $O(3)$ sigma model. The relationship to experiments on the doped cuprates is discussed.