Magnetic phases in the $J_{1}$-$J_{2}$ antiferromagnetic XY model on the honeycomb lattice

TL;DR

This paper investigates the ground-state phases of the $J_{1}$-$J_{2}$ antiferromagnetic XY model on a honeycomb lattice, identifying multiple magnetic phases and phase transitions using advanced tensor network algorithms.

Contribution

It introduces a combined use of corner transfer matrix renormalization group and infinite spiral PEPS to map the phase diagram of this model.

Findings

Identified Neel, Ising, collinear, and incommensurate spiral phases.

Found that dimerized states have higher energy than collinear states.

Discovered a second-order transition from collinear to spiral phase as $J_2/J_1$ increases.

Abstract

We study ground-state properties and phase diagram of the $J_{1}$-$J_{2}$ antiferromagnetic XY model on the honeycomb lattice by means of the developed corner transfer matrix renormalization group algorithm with the two-site unit cell and the infinite spiral projected entangled pair states ansatz. We identify the main phases: N\'{e}el, Ising, collinear, and incommensurate spiral phases, as well as the transitions between them, as functions of the ratio $J_{2}/J_{1}$. In the regime of competing types of ordering, we show that the energies of the dimerized states are systematically higher than the energies in the collinear phase. This collinear phase transforms to the incommensurate spiral phase through the second-order phase transition upon a further increase of $J_2/J_1$.