Phase diagrams of the S=1/2 quantum antiferromagnetic XY model on the triangular lattice in magnetic fields

TL;DR

This study investigates the phase diagrams of the S=1/2 quantum antiferromagnetic XY model on a triangular lattice under magnetic fields, revealing complex phase transitions and orderings through numerical methods.

Contribution

It provides the first detailed phase diagrams of the quantum XY model on a triangular lattice in magnetic fields, highlighting the emergence of various ordered phases.

Findings

Presence of a finite chiral order parameter at low temperatures in longitudinal fields.

Observation of a 1/3 magnetization plateau at low temperatures in transverse fields.

Sequential appearance of chiral-ordered, ferrimagnetic, and spin flop phases with increasing magnetic field.

Abstract

We study the S=1/2 quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins $N \leq 27$, and those at finite temperatures using a quantum transfer Monte Carlo method for $N \leq 24$. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3-plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.