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

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.

14 pages, 9 figures, 1 Table

References in corpus (15)

• "Deconfined" quantum critical points
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Different critical behaviors in cubic to trigonal and tetragonal perovskites
• Magnetocrystalline anisotropy and magnetization reversal in GaMnP synthesized by ion implantation and pulsed-laser melting
• Field-induced Bose-Einstein condensation and supersolid in the two-dimensional Kondo necklace
• Renormalization group analysis of the finite 2DXY model with fourfold anisotropy: Application to the magnetic susceptibility of a ferromagnetic ultrathin film
• The puzzle of bicriticality in the XXZ antiferromagnet
• Variational Tensor Network Operator

Cited by in corpus (2)

• Generating function for projected entangled-pair states
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators