Stability of algebraic spin liquids coupled to quantum phonons

TL;DR

This paper investigates the stability of algebraic spin liquids, specifically the U(1) Dirac spin liquid, when coupled to quantum phonons, revealing conditions under which a stable spin liquid phase can exist despite tendencies towards valence bond order.

Contribution

The study provides a detailed variational Monte Carlo analysis of the $J_1$-$J_2$ Heisenberg model on the triangular lattice, identifying parameter regimes for stable algebraic spin liquids under spin-phonon coupling.

Findings

Identifies a low-temperature transition from U(1) DSL to valence bond order.

Predicts parameter regimes where the DSL remains stable.

Shows monopole operators drive the instability.

Abstract

Algebraic spin liquids are quantum disordered phases of insulating magnets which exhibit fractionalized gapless excitations and power-law correlations. Quantum spin liquids in this category include the experimentally established 1D Luttinger liquid, as well as the U(1) Dirac spin liquid (DSL) which has been a focus of recent candidate materials searches. Most notably, several exchange-frustrated Heisenberg materials on the triangular lattice have shown evidence of the U(1) DSL. In this work, we measure the algebraic correlations of spin-singlet excitations in the $J_1$-$J_2$ antiferromagnetic Heisenberg model on the triangular lattice, prompting a detailed investigation of this model's stability under spin-phonon coupling using variational Monte Carlo. As seen before in 1D spin chains, we observe a low-temperature transition from a U(1) DSL to valence bond order and predict the parameter regime where the model realizes a stable DSL ground state. To achieve this, we employ a series of finite-size scaling Ans\"atze inspired by the low-energy DSL's conformal description in terms of quantum electrodynamics, and show that emergent monopole operators drive the instability. We compare the physics of this transition to the 1D Luttinger liquid throughout our analysis. We derive the regime of stability against spin-Peierls ordering and argue that the DSL ground state might still be achievable in candidate materials, despite its tendency to valence bond solid ordering.