Spin-Peierls instability of deconfined quantum critical points

TL;DR

This paper explores how coupling between lattice vibrations and deconfined quantum critical points can induce a spin-Peierls instability, potentially transforming a continuous transition into a first-order one, with quantum effects possibly stabilizing the critical point.

Contribution

It introduces a field-theoretic analysis of spin-lattice coupling effects on DQCPs, revealing conditions under which the transition becomes unstable or remains continuous.

Findings

Classical phonons induce a monopole-phonon interaction leading to lattice distortion.

Quantum phonons can stabilize the DQCP above a critical frequency.

The transition generally becomes first-order due to lattice coupling.

Abstract

Deconfined quantum critical points (DQCPs) are putative phase transitions beyond the Landau paradigm with emergent fractionalized degrees of freedom. The original example of a DQCP is the spin-1/2 quantum antiferromagnet on the square lattice which features a second order transition between valence bond solid (VBS) and N\'eel order. The VBS order breaks a lattice symmetry, and the corresponding VBS order parameter may couple to lattice distortion modes (phonons) at appropriate momenta. We investigate a field-theoretic description of the DQCP in the presence of such a spin-lattice coupling. We show that treating phonons as classical lattice distortions leads to a relevant monopole-phonon interaction inducing an instability towards a distorted lattice by an analogous mechanism to the spin-Peierls instability in one dimension. Consequently, there is a breakdown of the DQCP which generally becomes a strong first-order transition. Taking into account the full quantum nature of the phonons, we argue that the continuous DQCP persists above a critical phonon frequency. Lastly, we comment on the connection to general gapless, deconfined gauge theories.