Chirality and quasi-long-range order in finite-flux Gutzwiller states for magnetized frustrated magnets

TL;DR

This paper investigates Gutzwiller-projected wavefunctions for triangular-lattice U(1) Dirac spin liquids under a magnetic field, revealing finite gauge flux effects, chiral correlations, and novel magnetic behaviors relevant for frustrated magnet materials.

Contribution

It introduces a variational approach with finite gauge flux in Gutzwiller states, uncovering new magnetic and chiral properties in spin liquids under magnetic fields.

Findings

Finite gauge flux states optimize energy at specific magnetizations.

Finite flux induces non-zero scalar spin chirality.

The $|C|=1$ state shows dominant quasi-long-range magnetic correlations.

Abstract

We study Gutzwiller-projected wavefunctions for triangular-lattice U(1) Dirac spin liquids in a Zeeman field, where we allow the U(1) gauge field to develop a gauge flux, resulting in (spin-split) spinon Landau levels. We find that at a given magnetization, the optimal candidate state has a finite flux chosen such that the spinon filling lies in a $|C|=1$ Landau-level gap: it gives the lowest variational energy and the smallest energy variance within our correlation-matrix reconstruction for local Heisenberg-type models. By symmetry, we argue that the finite gauge flux results in a non-zero (staggered) scalar spin chirality, as also numerically observed, and further find that the $|C|=1$ state exhibits dominant quasi-long-ranged $120^\circ$ magnetic correlations. Studying the next-to-optimal wavefunction with a $|C|=2$ Landau-level gap, we observe unusual spin-nematic correlations. Our results may provide guidance for analyzing the magnetic-field response of DSL candidate materials and offer numerical diagnostics that can connect to the underlying theory of spinons coupled to an emergent U(1) gauge field.