Quantum criticality of dipolar spin chains

TL;DR

This paper investigates the quantum critical behavior of a dipolar Heisenberg spin chain in a magnetic field, revealing a transition in the 2D Ising universality class and analyzing fluctuation effects near the critical point.

Contribution

It demonstrates the existence of a quantum critical point in dipolar spin chains and characterizes its universality class using advanced theoretical methods.

Findings

Quantum critical point belongs to 2D Ising universality class

Magnon dispersion exhibits a gap closing at critical field

Ginzburg regime width varies significantly across transition

Abstract

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.