Frustrated RVB states in 2D: classifications and short-range correlations

TL;DR

This paper classifies short-range bosonic RVB states in 2D, demonstrating they are gapped $Z_2$ quantum spin liquids with only short-range correlations, using flux pattern analysis and Monte Carlo simulations.

Contribution

It provides a systematic classification of 2D short-range bosonic RVB states and maps them into projected BCS wave functions for large-scale simulations.

Findings

All studied short-range frustrated bosonic RVB states exhibit exponential decay of correlations.

These states are identified as gapped $Z_2$ quantum spin liquids.

Short-range frustrated bosonic RVB states generally have only short-range correlations.

Abstract

Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (non-bipartite or $Z_2$) bosonic RVB states we studied, indicating that they are gapped $Z_2$ quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.