A chiral spin liquid wave function and the Lieb-Schulz-Mattis theorem

TL;DR

This paper investigates a chiral spin liquid wave function using a projected BCS state, demonstrating its properties align with the Lieb-Schultz-Mattis theorem and supporting the existence of a gapped spin liquid ground state in two dimensions.

Contribution

It introduces a specific chiral spin liquid wave function and analyzes its dimerization behavior across different chain configurations, linking it to the Lieb-Schultz-Mattis theorem.

Findings

Dimerization occurs for odd chains, not for even chains.

Dimer order parameter vanishes in the 2D thermodynamic limit.

Supports the existence of a gapped spin liquid ground state in 2D.

Abstract

We study a chiral spin liquid wave function defined as a Gutwziller projected BCS state with a complex pairing function. After projection, spontaneous dimerization is found for any odd but finite number of chains, thus satisfying the Lieb-Schultz-Mattis theorem, whereas for even number of chains there is no dimerization. The two-dimensional thermodynamic limit is consistently reached for large number of chains since the dimer order parameter vanishes in this limit. This property clearly supports the possibility of a spin liquid ground state in two dimensions with a gap to all {\em physical} excitations and with no broken translation symmetry.