Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions

Abstract

We have performed a numerical investigation of the ground state properties of the frustrated quantum Heisenberg antiferromagnet on the square lattice (``$J_1-J_2$ model''), using exact diagonalization of finite clusters with 16, 20, 32, and 36 sites. Using a finite-size scaling analysis we obtain results for a number of physical properties: magnetic order parameters, ground state energy, and magnetic susceptibility (at $q=0$). For the unfrustrated case these results agree with series expansions and quantum Monte Carlo calculations to within a percent or better. In order to assess the reliability of our calculations, we also investigate regions of parameter space with well-established magnetic order, in particular the non-frustrated case $J_2<0$. We find that in many cases, in particular for the intermediate region $0.3<J_2/J_1<0.7$, the 16 site cluster shows anomalous finite size effects. Omitting this cluster from the analysis, our principal result is that there is Néel type order for $J_2/J_1<0.34$ and collinear magnetic order (wavevector $\bbox{Q}=(0,π)$) for $J_2/J_1>0.68$. There thus is a region in parameter space without any form of magnetic order. Including the 16 site cluster, or analyzing the independently calculated magnetic susceptibility we arrive at the same conclusion, but with modified values for the range of existence of the nonmagnetic region. We also find numerical values for the spin-wave velocity and the spin stiffness. The spin-wave velocity remains finite at the magnetic-nonmagnetic transition, as expected from the nonlinear sigma

34 pages, RevTeX 3.0, figures appended in uuencoded form

Cited by in corpus (154)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Green Function Monte Carlo with Stochastic Reconfiguration
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Density matrix quantum Monte Carlo
• Quantum phases of SrCu2(BO3)2 from high-pressure thermodynamics
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Frustrated two dimensional quantum magnets
• Phase diagram of a frustrated Heisenberg antiferromagnet on the honeycomb lattice: the $J_1$--$J_2$--$J_3$ model
• Neural Gutzwiller-projected variational wave functions
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Quantum critical phase with infinite projected entangled paired states
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3
• The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz
• The quantum $J_1$--$J_1^{\prime }$--$J_2$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Intertwined nematic orders in a frustrated ferromagnet
• Phase diagram of the frustrated, spatially anisotropic S=1 antiferromagnet on a square lattice
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• Quantum magnetism on the Cairo pentagonal lattice
• Very low-frequency excitations in frustrated two-dimensional $S=1/2$ Heisenberg antiferromagnets
• Random-exchange quantum Heisenberg antiferromagnets on the square lattice
• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• Spin-Charge Separation in Two-dimensional Frustrated Quantum Magnets
• The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond
• Master equation approach to computing RVB bond amplitudes
• Simulations of pure and doped low-dimensional spin-1/2 gapped systems
• Variational ground states of 2D antiferromagnets in the valence bond basis
• Anisotropy-induced ordering in the quantum J1-J2 antiferromagnet
• Thermodynamics of a two-dimensional frustrated spin-1/2 Heisenberg ferromagnet
• Spin correlations and exchange in square lattice frustrated ferromagnets
• Finite-Size Scaling in the transverse Ising Model on a Square Lattice
• Modified spin-wave theory with ordering vector optimization II: Spatially anisotropic triangular lattice and $J_1{J}_2{J}_3$ model with Heisenberg interactions
• Simulating two- and three-dimensional frustrated quantum systems with string-bond states
• Projective studies of spin nematics in a quantum frustrated ferromagnet
• Magnetic order in coupled spin-half and spin-one Heisenberg chains in anisotropic triangular-lattice geometry
• Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice
• Theory of two magnon Raman scattering in antiferromagnetic iron pnictides
• Magnetic order on a frustrated spin-1/2 Heisenberg antiferromagnet on the Union Jack lattice
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Spin waves and local magnetizations on the Penrose tiling
• Ground-state phases of the frustrated spin-1/2 $J_1$--$J_2$--$J_3$ Heisenberg ferromagnet ($J_1<0$) on the honeycomb lattice with $J_3=J_2>0$
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
• Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems
• Ground-state phase diagram and magnetic properties of a tetramerized spin-1/2 J_1-J_2 model: BEC of bound magnons and absence of the transverse magnetization
• Plaquette Order in the J1-J2-J3 model: a series expansion analysis
• Spinon deconfinement in doped frustrated quantum antiferromagnets
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Correlation-Enhanced Neural Networks as Interpretable Variational Quantum States
• Magnon Dispersion and Anisotropies in SrCu${}_2$(BO${}_3$)${}_2$
• Combined use of translational and spin-rotational invariance for spin systems
• Extended degeneracy and order by disorder in the square lattice J${}_1$-J${}_2$-J${}_3$ model
• The Ising phase in the J1-J2 Heisenberg Model
• Spin Dilution in Frustrated Two-Dimensional s=1/2 Antiferromagnets on a Square Lattice
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Fractional spin excitations in the infinite-layer cuprate CaCuO${}_2$
• Magnetic properties and Mott transition in the square-lattice Hubbard model with frustration
• Thermal valence-bond-solid transition of quantum spins in two dimensions
• Cluster functional renormalization group and absence of a bilinear spin liquid in the $J_1$-$J_2$-Heisenberg model
• Impurity-induced frustration in correlated oxides
• Thermodynamics of the two-dimensional frustrated J1-J2 Heisenberg ferromagnet in the collinear stripe regime: Susceptibility and correlation length
• Two-dimensional randomly-frustrated spin 1/2 Heisenberg model
• Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
• Theory of the Reentrant Charge-Order Transition in the Manganites
• Ordered moment in the anisotropic and frustrated square lattice Heisenberg model
• Ferromagnetic frustrated spin systems on the square lattice: a Schwinger boson study
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure
• Spin correlations near the edge as probe of Dimer order in square-lattice Heisenberg models
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Thermodynamics of frustrated ferromagnetic spin-$1/2$ Heisenberg chains: The role of inter-chain coupling
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Role of Frustration and Dimensionality in the Hubbard Model on the Stacked Square Lattice: Variational Cluster Approach
• Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
• A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$
• A 2D quantum antiferromagnet with a four-fold degenerate valence-bond-solid ground state
• Theoretical studies of the phase transition in the anisotropic 2-D square spin lattice
• Certifying ground-state properties of quantum many-body systems
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• Symmetry-projected cluster mean-field theory applied to spin systems
• Emergent topological excitations in a two-dimensional quantum spin system
• Entanglement Hamiltonian of the quantum Néel state
• The ground-state magnetic ordering of the spin-1/2 frustrated J1-J2 XXZ model on the square lattice
• Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach
• Spin polaron in the J1-J2 Heisenberg model
• Evidence of spin liquid with hard-core bosons in a square lattice
• Divide and conquer the Hilbert space of translation-symmetric spin systems
• Impurity-induced frustration: low-energy model of diluted oxides
• Are queries and keys always relevant? A case study on Transformer wave functions
• Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems
• Impact of conditional modelling for a universal autoregressive quantum state
• Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model
• Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice
• Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems
• Z4-U(1) crossover of the order parameter symmetry in a two-dimensional valence-bond-solid
• Linear combinations of cluster mean-field states applied to spin systems
• An Equilibrium for Frustrated Quantum Spin Systems in the Stochastic State Selection Method
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• 2D excitation information by MPS method on infinite helixes
• Finite-size spin-wave theory of a collinear antiferromagnet
• Bootstrap Approximations in Contractor Renormalization
• Bose-Einstein condensation of deconfined spinons in two dimensions
• Triplon mean-field analysis of an antiferromagnet with degenerate Shastry-Sutherland ground states
• Phase diagram of a frustrated asymmetric ferromagnetic spin ladder
• Gapped paramagnetic state in a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the cross-striped square lattice
• Exact staggered dimer ground state and its stability in a two-dimensional magnet
• Improving neural network performance for solving quantum sign structure
• Exotic phenomena in doped quantum magnets
• The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study
• Two-orbital quantum spin model of magnetism in the iron pnictides
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• The two dimensional Antiferromagnetic Heisenberg model with next nearest neighbour Ising exchange
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model
• Fractal Path Strategies for Efficient 2D DMRG Simulations
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice