SU(N) Quantum Antiferromagnets and the Phase Structure of QED in the Strong Coupling Limit

TL;DR

This paper establishes a precise equivalence between SU(N) antiferromagnets and the strong coupling limit of lattice QED, revealing how chiral symmetry breaking depends on N and spacetime dimensions.

Contribution

It demonstrates an exact mapping between SU(N) antiferromagnets and lattice QED in the strong coupling limit, elucidating symmetry breaking patterns across different N and dimensions.

Findings

Chiral symmetry breaks for odd N in all dimensions.

For even N, symmetry breaks when D ≥ 2 and N is small.

Exact ground states of lattice Coulomb gas and related systems identified.

Abstract

We examine the strong coupling limit of both compact and non compact QED on a lattice with staggered fermions. We show that every SU(N) antiferromagnet with spins in a particular fundamental representation of the SU(N) Lie Algebra and with nearest neighbor couplings on a bipartite lattice is exactly equivalent to the infinite coupling limit of lattice QED with the numbers of flavors of electrons related to N and the dimension of spacetime D+1. We find that,for both compact and noncompact QED,when N is odd the ground state of the strong coupling limit breaks chiral symmetry in any dimensions and for any N and the condensate is an isoscalar mass operator. When N is even,chiral symmetry is broken if D is bigger or equal to 2 and N is small enough and the order parameter is an isovector mass operator. We also find the exact ground state of the lattice Coulomb gas as well as a variety of related lattice statistical systems with long ranged interactions.