Gapless spin liquids in disguise

TL;DR

This paper demonstrates that gapless spin liquids, often considered as ground states of frustrated 2D Heisenberg models, appear as trivial insulators on cylindrical geometries, complicating their detection in such setups.

Contribution

It reveals how boundary conditions and geometry influence the nature of spin liquids, showing that gapless states can become gapped insulators on cylinders, which is a novel insight.

Findings

Gapless spin liquids become trivial insulators on cylinders with even legs.

Boundary conditions can realize both gapless and gapped states with different energies.

Detecting true gapless spin liquids in cylindrical geometries is challenging.

Abstract

We show that gapless spin liquids, which are potential candidates to describe the ground state of frustrated Heisenberg models in two dimensions, become trivial insulators on cylindrical geometries with an even number of legs. In particular, we report calculations for Gutzwiller-projected fermionic states on strips of square and kagome lattices. By choosing different boundary conditions for the fermionic degrees of freedom, both gapless and gapped states may be realized, the latter ones having a lower variational energy. The direct evaluation of static and dynamical correlation functions, as well as overlaps between different states, allows us to demonstrate the sharp difference between the ground-state properties obtained within cylinders or directly in the two-dimensional lattice. Our results shed light on the difficulty to detect bona fide gapless spin liquids in such cylindrical geometries.