Anyonic Liquids in Nearly Saturated Spin Chains

TL;DR

This paper predicts and demonstrates the emergence of an exotic anyonic-liquid fixed point in nearly saturated XXZ spin chains with two minima in the dispersion relation, using analytical and numerical methods.

Contribution

It introduces a new type of fixed point characterized by mutual anyonic statistics in spin chains with specific dispersion features.

Findings

Existence of an anyonic-liquid fixed point in XXZ chains with two minima.

Identification of parameter ranges supporting the phase.

Validation through bosonization, exact calculations, and DMRG simulations.

Abstract

Most Heisenberg-like spin chains flow to a universal free-fermion fixed point near the magnetic-field induced saturation point. Here we show that an exotic fixed point, characterized by two species of low-energy excitations with mutual anyonic statistics, may also emerge in such spin chains if the dispersion relation has two minima. By using bosonization, two-magnon exact calculations, and numerical density-matrix-renormalization-group, we demonstrate the existence of this anyonic-liquid fixed point in an XXZ spin chain with up to second neighbor interactions. We also identify a range of microscopic parameters, which support this phase.