A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice

Abstract

Using infinite projected entangled pair states, we study the ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice directly in the thermodynamic limit. We find an unexpected partially nematic partially magnetic phase in between the antiferroquadrupolar and ferromagnetic regions. Furthermore, we describe all observed phases and discuss the nature of the phase transitions involved.

arXiv comment27 pages, 15 figures; v3: adjusted sections 1 and 3, and added a paragraph to section 5.2.2

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• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Combining Tensor Networks with Monte Carlo Methods for Lattice Gauge Theories
• A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
• Spin Nematics Meet Spin Liquids: Exotic Quantum Phases in the Spin-$1$ Bilinear-Biquadratic Model with Kitaev Interactions
• Continuous Tensor Network States for Quantum Fields
• Semi-classical simulation of spin-1 magnets
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• TeNeS: Tensor Network Solver for Quantum Lattice Systems
• Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
• Phase diagrams and excitations of anisotropic $S=1$ quantum magnets on the triangular lattice
• Spin-one bilinear-biquadratic model on a star lattice
• Frustrated Magnetism from Local Moments in FeSe
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Benchmarking global $SU(2)$ symmetry in 2d tensor network algorithms
• Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice
• Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories
• Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
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• Abundant quadrupolar or nematic phases driven by the Heisenberg interactions in a spin-1 dimer system forming a bilayer
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• SU(4) topological RVB spin liquid on the square lattice
• Indirect K-edge bimagnon resonant inelastic X-ray scattering spectrum of $\alpha$-FeTe
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Dynamically generated quadrupole polarization using Floquet adiabatic evolution
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model