SciPost Physics

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

Ido Niesen, Philippe Corboz

SciPost Phys. 3, 030 (2017) · published 28 October 2017

• doi: 10.21468/SciPostPhys.3.4.030
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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.

• Huang et al., Indirect K-edge bimagnon resonant inelastic x-ray scattering spectrum ofα-FeTe
  J. Phys.: Condens. Matter 29, 505802 (2017) [Crossref]
• Hu et al., Density matrix renormalization group study of nematicity in two dimensions: Application to a spin-1 bilinear-biquadratic model on the square lattice
  Phys. Rev. B 101, 014421 (2020) [Crossref]
• Vlaar et al., Simulation of three-dimensional quantum systems with projected entangled-pair states
  Phys. Rev. B 103, 205137 (2021) [Crossref]
• Lee et al., Spin-one bilinear-biquadratic model on a star lattice
  Phys. Rev. B 97, 205123 (2018) [Crossref]
• Emonts et al., Finding the ground state of a lattice gauge theory with fermionic tensor networks: A 2+1D Z2 demonstration
  Phys. Rev. D 107, 014505 (2023) [Crossref]
• Pohle et al., Spin nematics meet spin liquids: Exotic quantum phases in the spin-1 bilinear-biquadratic model with Kitaev interactions
  Phys. Rev. B 107, L140403 (2023) [Crossref]
• Tilloy et al., Continuous Tensor Network States for Quantum Fields
  Phys. Rev. X 9, 021040 (2019) [Crossref]
• Remund et al., Semi-classical simulation of spin-1 magnets
  Phys. Rev. Research 4, 033106 (2022) [Crossref]
• Yokoyama et al., Spin nematics next to spin singlets
  Phys. Rev. B 97, 180404 (2018) [Crossref]
• Tanaka et al., Multiple quadrupolar or nematic phases driven by the Heisenberg interactions in a spin-1 dimer system forming a bilayer
  Phys. Rev. B 101, 094422 (2020) [Crossref]
• Schmoll et al., Benchmarking global SU(2) symmetry in two-dimensional tensor network algorithms
  Phys. Rev. B 102, 241101 (2020) [Crossref]
• Niesen et al., Ground-state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
  Phys. Rev. B 97, 245146 (2018) [Crossref]
• Karanikolaou et al., Gaussian continuous tensor network states for simple bosonic field theories
  Phys. Rev. Research 3, 023059 (2021) [Crossref]
• Motoyama et al., TeNeS: Tensor network solver for quantum lattice systems
  Computer Physics Communications 279, 108437 108437 (2022) [Crossref]
• Zohar et al., Combining tensor networks with Monte Carlo methods for lattice gauge theories
  Phys. Rev. D 97, 034510 (2018) [Crossref]
• Zhang et al., Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model
  Phys. Rev. B 104, 195135 (2021) [Crossref]
• Ruiz et al., Frustrated magnetism from local moments in FeSe
  Phys. Rev. B 99, 125130 (2019) [Crossref]
• Gauthé et al., SU(4) topological resonating valence bond spin liquid on the square lattice
  Phys. Rev. B 99, 241112 (2019) [Crossref]
• Szasz et al., Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
  Phys. Rev. B 106, 115103 (2022) [Crossref]
• Boos et al., Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
  Phys. Rev. Research 2, 023098 (2020) [Crossref]
• Seifert et al., Phase diagrams and excitations of anisotropic S=1 quantum magnets on the triangular lattice
  Phys. Rev. B 106, 195147 (2022) [Crossref]
• Patil et al., Weakly first-order quantum phase transition between spin-nematic and valence-bond crystal order in a square-lattice SU(4) fermionic model
  Phys. Rev. B 105, L140403 (2022) [Crossref]
• Camacho et al., Dynamically generated quadrupole polarization using Floquet adiabatic evolution
  Phys. Rev. Research 5, 023015 (2023) [Crossref]
• Haferkamp et al., Contracting projected entangled pair states is average-case hard
  Phys. Rev. Research 2, 013010 (2020) [Crossref]