Simplex solid states of SU(N) quantum antiferromagnets

TL;DR

This paper introduces simplex solid states for SU(N) antiferromagnets, providing exact ground states, analyzing their correlations via classical models, and exploring symmetry-breaking and edge phenomena.

Contribution

It defines a new class of wavefunctions extending AKLT states to SU(N), with exact solvability and classical correlation mappings, and studies their phase transitions and boundary properties.

Findings

SS states are exact ground states of local Hamiltonians.

Quantum correlations map to classical N-spin models.

In higher dimensions, SS states exhibit spontaneous SU(N) symmetry breaking.

Abstract

I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT), in which the singlets are extended over N-site simplices. As with the valence bond solids, the new simplex solid (SS) states are extinguished by certain local projection operators, allowing us to construct Hamiltonians with local interactions which render the SS states exact ground states. Using a coherent state representation, we show that the quantum correlations in each SS state are calculable as the finite temperature correlations of an associated classical model, with N-spin interactions, on the same lattice. In three and higher dimensions, the SS states can spontaneously break SU(N) and exhibit N-sublattice long-ranged order, as a function of a discrete parameter which fixes the local representation of SU(N). I analyze this transition using a classical mean field approach. For N>2 the ordered state is selected via an "order by disorder" mechanism. As in the AKLT case, the bulk representations fractionalize at an edge, and the ground state entropy is proportional to the volume of the boundary.