Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Density matrix renormalization group study of nematicity in two dimensions: Application to a spin-1 bilinear-biquadratic model on the square lattice

Journal Article · · Physical Review B
 [1];  [2];  [3];  [3];  [4]
  1. Univ. of Tennessee, Knoxville, TN (United States)
  2. Beihang Univ., Beijing (China). Dept. of Physics
  3. Rice Univ., Houston, TX (United States)
  4. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
+ Show Author Affiliations
Nematic order is an exotic property observed in several strongly correlated systems, such as 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 for 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° rotation, is an order parameter which can be studied directly in DMRG calculations in two dimensions in different quantum states.
Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1606682
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 1 Vol. 101; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (81)

Rigorous Results on Valence-Bond Ground States in Antiferromagnets book January 2004
Two soluble models of an antiferromagnetic chain journal December 1961
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model journal February 1983
Unusual phases in quantum spin-1 systems journal November 1988
Magnetism and its microscopic origin in iron-based high-temperature superconductors journal October 2012
What drives nematic order in iron-based superconductors? journal January 2014
Biquadratic Exchange and Quadrupolar Ordering journal March 1969
Iron pnictides as a new setting for quantum criticality journal March 2009
Broken rotation symmetry in the fractional quantum Hall system journal February 1996
Broken mirror symmetry, incommensurate spin correlations, and B 2 g nematic order in iron pnictides journal September 2019
Nematic spin liquid phase in a frustrated spin-1 system on the square lattice journal October 2019
Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S =1 Heisenberg chain journal August 1993
Onset of incommensurability at the valence-bond-solid point in the S =1 quantum spin chain journal February 1996
Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains journal April 1996
Lieb-Schultz-Mattis in higher dimensions journal March 2004
Spin nematics correlations in bilinear-biquadratic S = 1 spin chains journal October 2006
Spontaneous trimerization in a bilinear-biquadratic S = 1 zig-zag chain journal December 2007
Theory of electron nematic order in LaFeAsO journal June 2008
Ising and spin orders in the iron-based superconductors journal July 2008
First-order magnetic and structural phase transitions in Fe 1 + y Se x Te 1 − x journal February 2009
Isotropic to anisotropic transition in a fractional quantum Hall state journal August 2010
Effective field theory of fractional quantized Hall nematics journal November 2011
Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice journal March 2012
Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice journal April 2012
Competition between two- and three-sublattice ordering for S = 1 spins on the square lattice journal April 2012
Simplex solids in SU( N ) Heisenberg models on the kagome and checkerboard lattices journal July 2012
Spin dynamics of a J 1 - J 2 - K model for the paramagnetic phase of iron pnictides journal August 2012
Competing states in the SU(3) Heisenberg model on the honeycomb lattice: Plaquette valence-bond crystal versus dimerized color-ordered state journal May 2013
Evidence for a ν = 5 / 2 fractional quantum Hall nematic state in parallel magnetic fields journal July 2013
Field theory of the quantum Hall nematic transition journal September 2013
Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice journal March 2015
Gapless quantum spin liquid ground state in the spin-1 antiferromagnet 6HB- Ba 3 NiSb 2 O 9 journal June 2016
Evidence for a spinon Fermi surface in the triangular S = 1 quantum spin liquid Ba 3 NiSb 2 O 9 journal February 2017
Emergent Haldane phase in the S = 1 bilinear-biquadratic Heisenberg model on the square lattice journal May 2017
Possible nematic spin liquid in spin-1 antiferromagnetic system on the square lattice: Implications for the nematic paramagnetic state of FeSe journal May 2017
Possible bicollinear nematic state with monoclinic lattice distortions in iron telluride compounds journal July 2017
Ground-state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks journal June 2018
Tunable ( δ π , δ π )-Type Antiferromagnetic Order in α -Fe(Te,Se) Superconductors journal June 2009
Three-Sublattice Ordering of the SU(3) Heisenberg Model of Three-Flavor Fermions on the Square and Cubic Lattices journal December 2010
High-Pressure Sequence of Ba 3 NiSb 2 O 9 Structural Phases: New S = 1 Quantum Spin Liquids Based on Ni 2 + journal November 2011
Nematic State of Pnictides Stabilized by Interplay between Spin, Orbital, and Lattice Degrees of Freedom journal July 2013
Antiferroquadrupolar and Ising-Nematic Orders of a Frustrated Bilinear-Biquadratic Heisenberg Model and Implications for the Magnetism of FeSe journal September 2015
Spin Ferroquadrupolar Order in the Nematic Phase of FeSe journal June 2016
Bicollinear Antiferromagnetic Order, Monoclinic Distortion, and Reversed Resistivity Anisotropy in FeTe as a Result of Spin-Lattice Coupling journal September 2016
Antiferroquadrupolar Order and Rotational Symmetry Breaking in a Generalized Bilinear-Biquadratic Model on a Square Lattice journal April 2017
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State journal April 1983
Rigorous results on valence-bond ground states in antiferromagnets journal August 1987
Magnetization process of an S=1 linear-chain Heisenberg antiferromagnet journal July 1989
Ising transition in frustrated Heisenberg models journal January 1990
Observation of S =1/2 degrees of freedom in an S =1 linear-chain Heisenberg antiferromagnet journal December 1990
Density matrix formulation for quantum renormalization groups journal November 1992
Quadrupolar Phases of the S = 1 Bilinear-Biquadratic Heisenberg Model on the Triangular Lattice journal August 2006
Theory of Nematic Fractional Quantum Hall States journal December 2014
Bimetric Theory of Fractional Quantum Hall States journal November 2017
Observation of new plasmons in the fractional quantum Hall effect: Interplay of topological and nematic orders journal March 2019
Spin Disorder on a Triangular Lattice journal September 2005
In-Plane Resistivity Anisotropy in an Underdoped Iron Arsenide Superconductor journal August 2010
Nematic spin correlations in the tetragonal state of uniaxial-strained BaFe2-xNixAs2 journal July 2014
Spatially ordered fractional quantum Hall states journal February 1996
The non-Abelian density matrix renormalization group algorithm journal March 2002
A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice journal January 2017
An Isotropic to Anisotropic Transition in a Fractional Quantum Hall State text January 2010
Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices text January 2010
Effective Field Theory of Fractional Quantized Hall Nematics text January 2011
Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice text January 2011
High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S = 1$ quantum spin-liquids based on Ni^{2+} text January 2011
Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices text January 2012
Magnetism and its microscopic origin in iron-based high-temperature superconductors text January 2012
Nematic State of the Pnictides Stabilized by the Interplay Between Spin, Orbital, and Lattice Degrees of Freedom text January 2013
Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagome lattice text January 2014
Antiferroquadrupolar and Ising-Nematic Orders of a Frustrated Bilinear-Biquadratic Heisenberg Model and Implications for the Magnetism of FeSe text January 2015
Bicollinear Antiferromagnetic Order, Monoclinic Distortion, and Reversed Resistivity Anisotropy in FeTe as a Result of Spin-Lattice Coupling text January 2016
Possible Bicollinear Nematic State with Monoclinic Lattice Distortions in Iron Telluride Compounds text January 2017
Bimetric Theory of Fractional Quantum Hall States text January 2017
A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice text January 2017
Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice text January 2017
A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks text January 2018
The Non-Abelian Density Matrix Renormalization Group Algorithm text January 2000
Spatially Ordered Fractional Quantum Hall States text January 1995
Broken rotation symmetry in the fractional quantum Hall system text January 1995
Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains text January 1995

Similar Records

Nematic spin liquid phase in a frustrated spin-1 system on the square lattice
Journal Article · Mon Oct 28 00:00:00 EDT 2019 · Physical Review. B · OSTI ID:1803293
Fragility of the nematic spin liquid induced by diagonal couplings in the square-lattice SU(3) model
Journal Article · Thu Nov 18 23:00:00 EST 2021 · Physical Review B · OSTI ID:1836413

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Antiferromagnetism
Density matrix renormalization group
Frustrated magnetism
Magnetism
Quantum spin liquid
Spin state transition