Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires

TL;DR

This paper constructs a local Hamiltonian on a triangular lattice that stabilizes a chiral spin liquid phase, using coupled-wire methods and tensor network simulations to confirm its properties and topological order.

Contribution

It introduces a new lattice Hamiltonian for the Kalmeyer-Laughlin CSL that does not require fine-tuning, employing coupled-wire constructions and duality techniques.

Findings

Ground states exhibit fourfold periodicity in circumference.

Tensor network simulations confirm fractional quasiparticles.

Long-range entanglement and topological order are demonstrated.

Abstract

Chiral spin liquids (CSLs) are exotic phases of interacting spins in two dimensions, characterized by long-range entanglement and fractional excitations. We construct a local Hamiltonian on the triangular lattice that stabilizes the Kalmeyer-Laughlin CSL without requiring fine-tuning. Our approach employs coupled-wire constructions and introduces a lattice duality to construct a solvable chiral sliding Luttinger liquid, which is driven toward the CSL phase by generic perturbations. By combining symmetry analysis and bosonization, we make sharp predictions for the ground states on quasi-one-dimensional cylinders and tori, which exhibit a fourfold periodicity in the circumference. Extensive tensor network simulations demonstrating ground-state degeneracies, fractional quasiparticles, nonvanishing long-range order parameters, and entanglement signatures confirm the emergence of the CSL in the lattice Hamiltonian.