Finite size effects in the Z_2 spin liquid on the kagome lattice

TL;DR

This paper studies finite size effects in the Z_2 spin liquid on the kagome lattice, revealing the necessity of further neighbor interactions to explain the even-odd effect observed in numerical simulations.

Contribution

It introduces a dual analysis mapping the Z_2 gauge theory to a frustrated Ising model and explains the need for second neighbor interactions to capture finite size effects.

Findings

Odd circumference systems show non-zero dimerization decaying exponentially.

Nearest neighbor interactions are insufficient to explain the even-odd effect.

The study provides a symmetry-based analysis of second neighbor interactions.

Abstract

Motivated by the recent discovery of the Z_2 quantum spin liquid state in the nearest neighbor Heisenberg model on the kagome lattice, we investigate the "even-odd" effect occuring when this state is confined to infinitely long cylinders of finite circumference. We pursue a dual analysis, where we map the effective Z_2 gauge theory from the kagome lattice to a frustrated Ising model on the dice lattice. Unexpectedly, we find that the latter theory, if restricted to nearest neighbor interactions, is insufficient to capture this effect. We provide an explanation of why further neighbor interactions are needed via a high-temperature expansion of the effective Hamiltonian. We then carry out projective symmetry group analysis to understand which second neighbor interactions can be introduced while respecting the lattice symmetries. Finally, we qualitatively compare our results to numerics by computing the dimerization operator within our theory. Systems with odd circumferences exhibit a non-vanishing dimerization that decays exponentially with circumference.