[Paper Review] Spin-Peierls instability of the U(1) Dirac spin liquid

Urban F. P. Seifert, Josef Willsher+3 more|arXiv (Cornell University)|Jul 23, 2023

Advanced Condensed Matter Physics116 references4 citations

TL;DR

This paper investigates the stability of the U(1) Dirac spin liquid (DSL) on the triangular lattice against spin-lattice coupling, showing that symmetry-allowed coupling between finite-wavevector lattice distortions and monopole operators induces a spin-Peierls instability toward a 12-site valence-bond solid (VBS) state. Using perturbation theory, scaling arguments, and state-of-the-art DMRG simulations, it demonstrates that phonon modes soften due to monopole-lattice coupling, resembling a Kohn anomaly, and identifies a parameter regime—determined by the phonon energy gap—where the DSL remains stable despite coupling to lattice degrees of freedom.

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.

Motivation & Objective

• To understand the stability of the U(1) Dirac spin liquid (DSL) in triangular-lattice Heisenberg antiferromagnets against spin-lattice coupling.
• To determine whether symmetry-allowed lattice distortions can drive a spin-Peierls transition in a gapless, strongly correlated spin liquid.
• To clarify the role of quantum fluctuations in phonons and monopoles in stabilizing or destabilizing the DSL phase.
• To identify parameter regimes—particularly involving phonon energy gaps—where the DSL remains stable despite coupling to lattice distortions.

Proposed method

• Employing perturbation theory and scaling arguments to analyze the relevance of monopole-lattice coupling in the U(1) DSL described by compact QED3.
• Using state-of-the-art density matrix renormalization group (DMRG) simulations to study finite-size systems with various lattice distortion patterns (K, M, and K/2 points).
• Implementing a self-consistent perturbative analysis of the phonon self-energy to evaluate the spectral function and renormalized phonon dispersion.
• Integrating out VBS-monopole fluctuations to derive the dressed phonon propagator, including the effect of the spinon susceptibility at finite and zero temperature.
• Using a heuristic finite-temperature scaling form for the spin-VBS channel susceptibility, assuming a universal scaling function consistent with Sachdev-Ye-type expansions.
• Analyzing the phonon spectral function numerically to observe Kohn-anomaly-like softening and mode divergence near the spin-Peierls transition.

Experimental results

Research questions

• RQ1 Does a symmetry-allowed coupling between finite-wavevector lattice distortions and monopole operators in the U(1) Dirac spin liquid lead to a spin-Peierls instability?
• RQ2 What is the role of phonon energy gap in stabilizing the U(1) DSL against lattice-driven instabilities?
• RQ3 How does the coupling between monopoles and lattice distortions affect the phonon spectrum, and does it lead to Kohn-anomaly-like softening?
• RQ4 Can DMRG simulations reliably detect the formation of a 12-site valence-bond solid (VBS) state due to monopole-lattice coupling in the DSL?
• RQ5 What is the finite-temperature behavior of the phonon spectral function, and how does it signal the onset of a spin-Peierls transition?

Key findings

• The coupling between lattice distortions and monopole operators in the U(1) DSL induces a spin-Peierls instability, driving the system toward a 12-site valence-bond solid (VBS) state.
• Phonon modes soften due to monopole-lattice coupling, exhibiting a Kohn-anomaly-like dip in the spectral function, with the mode approaching zero frequency at the spin-Peierls transition.
• A finite phonon energy gap stabilizes the DSL in a parameter regime where the instability is suppressed, even in the presence of strong monopole fluctuations.
• DMRG simulations confirm the instability for small distortion strengths (δ = 0.002) and converge for bond dimensions up to χ = 7000, particularly for K-point patterns.
• The phonon spectral function shows a divergent continuum of excitations at low energies at zero temperature, which blurs into a sharp mode at finite temperature, consistent with a soft mode near the transition.
• The finite-temperature susceptibility of the spin-VBS channel scales as T^{2ΔΦ−3}Φ(ω/T, c|k−ka|/T), suggesting universal scaling behavior near the critical point.