Translational symmetry breaking in two-dimensional antiferromagnets and superconductors

TL;DR

This paper reviews translational symmetry breaking in two-dimensional antiferromagnets and superconductors, discussing spin-Peierls order, stripe states, and transitions to deconfined phases, with implications for experimental observations.

Contribution

It provides a comprehensive review of symmetry-breaking phenomena in antiferromagnets and their relation to superconductivity, including detailed derivations of the Ising model used to describe phase transitions.

Findings

Translational symmetry breaking is fundamental in quantum paramagnetic states.

Deconfined antiferromagnetic states can occur without lattice symmetry breaking.

The Ising model in a transverse field describes transitions between different magnetic phases.

Abstract

It was argued many years ago that translational symmetry breaking due to the appearance of spin-Peierls ordering (or bond-charge stripe order) is a fundamental property of the quantum paramagnetic states of a large class of square lattice antiferromagnets. Recently, such states were shown to be a convenient point of departure for studying translational symmetry breaking in doped antiferromagnets: these results are briefly reviewed here with an emphasis on experimental implications. In the presence of stronger frustration, it was also argued that the insulating antiferromagnet can undergo a transition to a deconfined state with no lattice symmetry breaking. This transition is described by a fully-frustrated Ising model in a transverse field: details of this earlier derivation of the Ising model are provided here--this is motivated by the reappearance of the same Ising model in a recent study of the competition between antiferromagnetism and d-wave superconductivity by Senthil and Fisher (cond-mat/9910224).