Density Matrix Renormalization Group Study of Nematicity in Two Dimensions: Application to a Spin-$1$ Bilinear-Biquadratic Model on the Square Lattice

Abstract

Nematic order is an exotic property observed in several strongly correlated systems, such as the iron-based superconductors. Using large-scale density matrix renormalization group (DMRG) techniques, we study at zero-temperature the nematic spin liquid that competes with spin dipolar and quadrupolar orders. We use these nematic orders to characterize different quantum phases and quantum phase transitions. More specifically, we study a spin-$1$ bilinear-biquadratic Heisenberg model on the square lattice with couplings beyond nearest neighbors. We focus on parameter regions around the highly symmetric $SU(3)$ point where the bilinear and biquadratic interactions are equal. With growing further-neighbor biquadratic interactions, we identify different spin dipolar and quadrupolar orders. We find that the DMRG results on cylindrical geometries correctly detect nematicity in different quantum states and accurately characterize the quantum phase transitions among them. Therefore, spin-driven nematicity -- here defined as the spontaneous breaking of the lattice invariance under a 90${}^o$ rotation -- is an order parameter which can be studied directly in DMRG calculations in two dimensions in different quantum states.

8 pages, 6 figures

References in corpus (47)

• Nematic order in iron superconductors - who is in the driver's seat?
• Evidence for an electron nematic phase transition in underdoped iron pnictide superconductors
• Lieb-Schultz-Mattis in Higher Dimensions
• Theory of Electron Nematic Order in LaOFeAs
• Incommensurate magnetic order in the alpha-Fe(Te,Se) superconductor systems
• First-order magnetic and structural phase transitions in Fe${}_{1+y}$Se${}_x$Te${}_{1-x}$
• Magnetism and its microscopic origin in iron-based high-temperature superconductors
• Ising and Spin orders in Iron-based Superconductors
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Nematic spin correlations in the tetragonal state of uniaxial strained BaFe2-xNixAs2
• Iron pnictides as a new setting for quantum criticality
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Spin nematics in the bilinear-biquadratic S=1 spin chain
• High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S=1$ quantum spin-liquids based on Ni^{2+}
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• Antiferroquadrupolar and Ising-Nematic Orders of a Frustrated Bilinear-Biquadratic Heisenberg Model and Implications for the Magnetism of FeSe
• Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Nematic State of the Pnictides Stabilized by the Interplay Between Spin, Orbital, and Lattice Degrees of Freedom
• Bimetric Theory of Fractional Quantum Hall States
• Field theory of the quantum Hall nematic transition
• Theory of Nematic Fractional Quantum Hall State
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
• Competition between two- and three-sublattice ordering for S=1 spins on the square lattice
• An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State
• Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice
• Evidence for a $\nu =5/2$ Fractional Quantum Hall Nematic State in Parallel Magnetic Fields
• Evidence for a spinon Fermi surface in the triangular S=1 quantum spin liquid Ba${}_3$NiSb${}_2$O${}_9$
• Effective Field Theory of Fractional Quantized Hall Nematics
• Spin Dynamics of a J1-J2-K Model for the Paramagnetic Phase of Iron Pnictides
• Broken rotation symmetry in the fractional quantum Hall system
• Emergent Haldane phase in the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice
• Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state
• A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
• Spontaneous trimerization in a bilinear-biquadratic S=1 zig-zag chain
• Spatially Ordered Fractional Quantum Hall States
• Spin Ferroquadrupolar Order in the Nematic Phase of FeSe
• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
• Possible Nematic Spin Liquid in Spin-$1$ Antiferromagnetic System on the Square Lattice: Implication for the Nematic Paramagnetic State of FeSe
• Bicollinear Antiferromagnetic Order, Monoclinic Distortion, and Reversed Resistivity Anisotropy in FeTe as a Result of Spin-Lattice Coupling
• Antiferroquadrupolar order and rotational symmetry breaking in a generalized bilinear-biquadratic model on a square lattice
• Broken mirror symmetry, incommensurate spin correlations, and $B_{2g}$ nematic order in iron pnictides
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Possible Bicollinear Nematic State with Monoclinic Lattice Distortions in Iron Telluride Compounds

Cited by in corpus (8)

• Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice
• Range of biquadratic and triquadratic Heisenberg effective couplings deduced from multiorbital Hubbard models
• Quantum Transitions of Nematic Phases in a Spin-$1$ Bilinear-Biquadratic Model and Their Implications for FeSe
• Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Quantum criticality and emergent orders in the spin-1 bilinear-biquadratic-Kitaev chain
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model