Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model

TL;DR

This paper constructs lattice wave functions from the SU(n)_1 Wess-Zumino-Witten model, deriving parent Hamiltonians, and explores their properties in 1D and 2D, revealing connections to quantum Hall states and chiral spin liquids.

Contribution

It introduces new lattice wave functions based on SU(n)_1 WZW models and derives their parent Hamiltonians, linking them to known quantum Hall and spin liquid states.

Findings

1D wave functions exhibit quantum criticality or deviations from SU(n)_1 WZW predictions.

2D wave functions converge to Halperin's multilayer fractional quantum Hall states.

The models reveal hidden SU(n) symmetry in certain quantum states.

Abstract

We propose 1D and 2D lattice wave functions constructed from the SU(n)_1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)_1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)_1 WZW model.