Condensation of Anyons in Frustrated Quantum Magnets

TL;DR

This paper derives the exact ground states of a family of spin-1/2 Heisenberg chains with anisotropy and extended interactions, revealing a condensation of anyons with a specific statistical phase.

Contribution

It introduces a generalized Jordan-Wigner transformation mapping spins to anyons and provides explicit matrix-product state representations of the ground states.

Findings

Exact ground states are characterized as anyon condensates.

Ground states depend on a parameter Q, with anyon statistics phase phi=-4Q.

Matrix-product states enable efficient correlation function calculations.

Abstract

We derive the exact ground space of a family of spin-1/2 Heisenberg chains with uniaxial exchange anisotropy (XXZ) and interactions between nearest and next-nearest-neighbor spins. The Hamiltonian family, H(Q), is parametrized by a single variable Q. By using a generalized Jordan-Wigner transformation that maps spins into anyons, we show that the exact ground states of H(Q) correspond to a condensation of anyons with statistical phase phi=-4Q. We also provide matrix-product state representations of some ground states that allow for the efficient computation of spin-spin correlation functions.