Spin-Peierls instability of the U(1) Dirac spin liquid

Abstract

A complicating factor in the realization and observation of quantum spin liquids in materials is the ubiquitous presence of other degrees of freedom, in particular lattice distortion modes (phonons). These provide additional routes for relieving magnetic frustration, thereby possibly destabilizing spin-liquid ground states. In this work, we focus on triangular-lattice Heisenberg antiferromagnets, where recent numerical evidence suggests the presence of an extended U(1) Dirac spin liquid phase which is described by compact quantum electrodynamics in 2+1 dimensions (QED${}_3$), featuring gapless spinons and monopoles as gauge excitations, and believed to flow to a strongly-coupled fixed point with conformal symmetry. Using complementary perturbation theory and scaling arguments, we show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) 12-site valence-bond solid state. We support our theoretical analysis with state-of-the-art density matrix renormalization group simulations. Away from the limit of static distortions, we demonstrate that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable, and show that the monopole-lattice coupling leads to softening of the phonon in analogy to the Kohn anomaly. We discuss the applicability of our results to similar systems, in particular the Dirac spin liquid on the Kagome lattice.

26 pages, 14 figures

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Cited by in corpus (14)

• Spectral evidence for Dirac spinons in a kagome lattice antiferromagnet
• Spin-Peierls instability of the U(1) Dirac spin liquid
• Monopole excitations in the $U(1)$ Dirac spin liquid on the triangular lattice
• Revealing spinons by proximity effect
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Spin-Peierls instability of deconfined quantum critical points
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Topological characterization of magnon-polaron bands and thermal Hall conductivity in a frustrated kagome antiferromagnet
• Spin excitations arising from anisotropic Dirac spinons in YCu${}_3$(OD)${}_6$Br${}_2$[Br${}_{0.33}$(OD)${}_{0.67}$]
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• Stability of algebraic spin liquids coupled to quantum phonons
• The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality
• An integrated theoretical and numerical approach to understand modern experiments on quantum magnetism