Vector Chiral Phases in the Frustrated 2D XY Model and Quantum Spin Chains

TL;DR

This paper analytically explores the phase diagram of frustrated 2D classical and 1D quantum XY models, revealing multiple phase transitions, including vortex unbinding and chiral transitions with unique critical behavior, relevant to quantum spin chains and multiferroics.

Contribution

It provides an analytical calculation of the phase diagram, identifying four distinct transitions and characterizing their nature and critical exponents in frustrated XY models.

Findings

Four phase transitions identified, including vortex unbinding and chiral transitions.

Vortex interactions are short-range at small scales and logarithmic at large scales.

Chiral transition exhibits nonlocal interactions with Ising universality class but different critical exponents.

Abstract

The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.