Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary

TL;DR

This paper investigates a 2D cubic ferromagnet model, revealing an emergent continuous U(1) symmetry at the phase boundary through tensor network methods, highlighting the effectiveness of iPEPS near critical points.

Contribution

It demonstrates the emergence of U(1) symmetry at the phase boundary using iPEPS, providing a concrete example of tensor network methods capturing critical phenomena.

Findings

iPEPS yields more accurate transition points than mean-field

Easy-axis softening indicates emergent U(1) symmetry

Emergent symmetry captured with small bond dimension

Abstract

We study the simplest quantum lattice spin model for the two-dimensional (2D) cubic ferromagnet by means of mean-field analysis and tensor network calculation. While both methods give rise to similar results in detecting related phases, the 2D infinite projected entangled-pair state (iPEPS) calculation provides more accurate values of transition points. Near the phase boundary, moreover, our iPEPS results indicate that it is more difficult to pin down the orientation of magnetic easy axes, and we interpret it as the easy-axis softening. This phenomenon implies an emergence of continuous $U(1)$ symmetry, which is indicated by the low-energy effective model and has been analytically shown by the field theory. Our model and study provide a concrete example for utilizing iPEPS near the critical region, showing that the emergent phenomenon living on the critical points can already be captured by iPEPS with a rather small bond dimension.