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.

arXiv comment14 pages, 9 figures, 1 Table

References in corpus (53)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Ferromagnetism in semiconductors and oxides: prospects from a ten years' perspective
• "Deconfined" quantum critical points
• Entanglement renormalization
• Dilute ferromagnetic semiconductors: Physics and spintronic structures
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor networks for complex quantum systems
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Corner Transfer Matrix Renormalization Group Method
• Ising models of quantum frustration
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Quantum criticality with two length scales
• Differentiable Programming Tensor Networks
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Gradient methods for variational optimization of projected entangled-pair states
• The N-component Ginzburg-Landau Hamiltonian with cubic anisotropy: a six-loop study
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Anisotropic perturbations in three-dimensional O(N)-symmetric vector models
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Recent Developments of World-Line Monte Carlo Methods
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Finite correlation length scaling with infinite projected entangled-pair states
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• A tensor network annealing algorithm for two-dimensional thermal states
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Critical properties of the two-dimensional $q$-state clock model
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• 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
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Metallic and Deconfined Quantum Criticality in Dirac Systems
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• A scaling hypothesis for projected entangled-pair states
• Multicritical crossovers near the dilute Bose gas quantum critical point
• Competing quantum phases of hard-core boson with tilted dipole-dipole interaction
• Magnetocrystalline anisotropy and magnetization reversal in GaMnP synthesized by ion implantation and pulsed-laser melting
• Different critical behaviors in cubic to trigonal and tetragonal perovskites
• Cubic anisotropy in high homogeneity thin (Ga,Mn)As layers
• Theory of ferromagnetism driven by superexchange in dilute magnetic semiconductors
• 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
• Magnetic and quadrupolar order in a one-dimensional ferromagnet with cubic crystal-field anisotropy
• The puzzle of bicriticality in the XXZ antiferromagnet
• Variational Tensor Network Operator

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