Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model

Abstract

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J1 and J2, which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z2 spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J2, we find a Neel phase, a plaquette valence-bond (PVB) phase with a finite spin gap, and a possible spin liquid in a small region of J2 between these two phases. From the finite-size scaling of the magnetic order parameter, we estimate that the Neel order vanishes at J2/J1~0.44. For 0.5<J2/J1<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J2/J1<0.5, spin order, dimer order, and spin gap are small on finite-size systems and appear to scale to zero with increasing system width, which is consistent with a possible gapless SL or a near-critical behavior. We compare and contrast our results with earlier numerical studies.

11 pages, 17 figures, and 1 table

References in corpus (54)

• Anyons in an exactly solved model and beyond
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• "Deconfined" quantum critical points
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• An RVB phase in the triangular lattice quantum dimer model
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Identifying Topological Order by Entanglement Entropy
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• From density-matrix renormalization group to matrix product states
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Neel order in square and triangular lattice Heisenberg models
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• 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
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Dual Order Parameter for the Nodal Liquid
• J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Fractionalization in the cuprates: Detecting the topological order
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Fate of CP(N-1) fixed points with q-monopoles
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Deconfined criticality in the frustrated Heisenberg honeycomb antiferromagnet
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Microscopic models for fractionalized phases in strongly correlated systems
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Schwinger-boson approach to quantum spin systems: Gaussian fluctuactions in the "natural" gauge
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Gapped spin liquid phase in the J1-J2 Heisenberg model by a Bosonic resonating valence-bond ansatz
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Plaquette valence-bond solid in the square lattice J1-J2 antiferromagnet Heisenberg model: a bond operator approach
• Obtaining topological degenerate ground states by the density matrix renormalization group
• Numerical study of fractionalization in an Easy-axis Kagome antiferromagnet
• Microscopic Models of 2D Magnets with Fractionalized Excitations
• Exact Spin Liquid Ground States of the Quantum Dimer Model on the Square and Honeycomb Lattices
• Master equation approach to computing RVB bond amplitudes
• Valence bond spin liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets
• Z4-U(1) crossover of the order parameter symmetry in a two-dimensional valence-bond-solid

Cited by in corpus (199)

• Quantum Spin Liquids
• Quantum Spin Liquid States
• The Hubbard Model
• Quantum criticality with two length scales
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Nematicity and quantum paramagnetism in FeSe
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Quantum phases of Rydberg atoms on a kagome lattice
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by $d^{10}$-$d^0$ cation mixing
• Solving frustrated quantum many-particle models with convolutional neural networks
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Lifshitz transition and frustration of magnetic moments in infinite-layer NdNiO${}_2$ upon hole-doping
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• Neural Gutzwiller-projected variational wave functions
• Exponential Thermal Tensor Network Approach for Quantum Lattice Models
• High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid
• Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method
• 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
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Neural network wave functions and the sign problem
• Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice
• Quantum critical phase with infinite projected entangled paired states
• Empowering deep neural quantum states through efficient optimization
• Proximate deconfined quantum critical point in SrCu2(BO3)2
• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
• Spurious Long-range Entanglement and Replica Correlation Length
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Intertwined Order in a Frustrated 4-leg $t-J$ Cylinder
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Spontaneous formation of a non-uniform chiral spin liquid in moat-band lattices
• Gradient optimization of finite projected entangled pair states
• Magnetic correlations in infinite-layer nickelates: an experimental and theoretical multi-method study
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Intertwined nematic orders in a frustrated ferromagnet
• Ab initio guided minimal model for the "Kitaev" material BaCo${}_2$(AsO${}_4$)${}_2$: Importance of direct hopping, third-neighbor exchange and quantum fluctuations
• Randomness-induced quantum spin liquid behavior in the $s=\frac{1}{2}$ random $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice
• Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice
• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Quantum phase diagram of the spin-$1$ $J_1-J_2$ Heisenberg model on the honeycomb lattice
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Novel phases in a square-lattice frustrated ferromagnet : 1/3-magnetisation plateau, helicoidal spin-liquid and vortex crystal
• Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons
• Accurate simulation for finite projected entangled pair states in two dimensions
• Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet
• Ground-State Ordering of the $J_1$--$J_2$ Model on the Simple Cubic and Body-Centered Cubic Lattices
• Multiple-$q$ states of the $J_1$-$J_2$ classical honeycomb-lattice Heisenberg antiferromagnet under magnetic fields
• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Field-enhanced quantum fuctuation in S=1/2 frustrated square lattice
• Ultrafast ab-initio Quantum Chemistry Using Matrix Product States
• Plaquette Valence Bond Theory of High-Temperature Superconductivity
• Spin Ferroquadrupolar Order in the Nematic Phase of FeSe
• Schwinger boson spin liquid states on square lattice
• Frustrated Heisenberg antiferromagnet on the honeycomb lattice: Spin gap and low-energy parameters
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• Quantum spin liquid phase in the Shastry-Sutherland model detected by an improved level spectroscopic method
• Investigating Topological Order using Recurrent Neural Networks
• Effect of epitaxial strain on the electronic structure and magnetic correlations in infinite-layer (Nd,Sr)NiO${}_2$
• Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems
• Quantum Anomalous Hall Insulator Stabilized By Competing Interactions
• Possible Nematic Spin Liquid in Spin-$1$ Antiferromagnetic System on the Square Lattice: Implication for the Nematic Paramagnetic State of FeSe
• Block product density matrix embedding theory for strongly correlated spin systems
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
• Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders
• Interaction-driven fractional quantum Hall state of hard-core bosons on kagome lattice at one-third filling
• 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
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• $J_1-J_2$ Square-Lattice Heisenberg Antiferromagnets with 4$d^1$ spins: AMoOPO${}_4$Cl (A = K, Rb)
• Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
• Quantum Phases in the Honeycomb-Lattice $J_1$--$J_3$ Ferro-Antiferromagnetic Model
• Extended degeneracy and order by disorder in the square lattice J${}_1$-J${}_2$-J${}_3$ model
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Lee-Yang theory of criticality in interacting quantum many-body systems
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Neural Network Evolution Strategy for Solving Quantum Sign Structures
• Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
• Gapless spin liquids in disguise
• Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study
• Magnetization Process of the Spin-1/2 Triangular-Lattice Heisenberg Antiferromagnet with Next-Nearest-Neighbor Interactions -- Plateau or Nonplateau
• Emergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
• Cluster functional renormalization group and absence of a bilinear spin liquid in the $J_1$-$J_2$-Heisenberg model
• Antiferroquadrupolar order and rotational symmetry breaking in a generalized bilinear-biquadratic model on a square lattice
• Renormalization group analysis of dipolar Heisenberg model on square lattice
• Vanishing Wilson ratio as the hallmark of quantum spin-liquid models
• Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State
• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
• High-temperature expansion for frustrated magnets: Application to the J1-J2 model on the BCC lattice
• Nematic Spin Liquid Phase in a Frustrated Spin-1 System on the Square Lattice
• Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Effects of spin-phonon coupling in frustrated Heisenberg models
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Multiple Magnetization Plateaus and the Magnetic Structures in $S=1/2$ Heisenberg Model on the Checkerboard Lattice
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• The phase diagram of a frustrated Heisenberg model: from disorder to order and back again
• Chern-Simons superconductors and their instabilities
• 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
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction
• Symmetry-projected cluster mean-field theory applied to spin systems
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Certifying ground-state properties of quantum many-body systems
• Field Induced Quantum Phase Transitions in $S=1/2$ $J_1$-$J_2$ Heisenberg Model on the Square Lattice
• Deformed spin-$\frac{1}{2}$ square lattice in antiferromagnetic NaZnVOPO${}_4$(HPO${}_4$)
• Elementary excitations in the ordered phase of spin-1/2 J1-J2 model on square lattice
• Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model
• Odd Fracton Theories, Proximate Orders, and Parton Constructions
• Quantum Transitions of Nematic Phases in a Spin-$1$ Bilinear-Biquadratic Model and Their Implications for FeSe
• Randomness and Frustration in a S = 1/2 Square-Lattice Heisenberg Antiferromagnet
• Optimal inhomogeneity for pairing in Hubbard systems with next-nearest-neighbor hopping
• Non-abelian bosonization in two and three spatial dimensions and applications
• Quantum magnetism in the frustrated square lattice oxyhalides YbBi2IO4 and YbBi2ClO4
• Entanglement Hamiltonian of the quantum Néel state
• Nature of continuous phase transitions in interacting topological insulators
• Spin dynamics and continuum spectra of the honeycomb J1-J2 antiferromagnetic Heisenberg model
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Contrasting Magnetic Structures in SrLaCuSbO${}_6$ and SrLaCuNbO${}_6$: Spin-1/2 Quasi-Square-Lattice $J_1-J_2$ Heisenberg Antiferromagnets
• Strain-Tuned Magnetic Frustration in a Square Lattice $J_1$-$J_2$ Material
• Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach
• Lanczos steps to improve variational wave functions
• Fine-tuning Neural Network Quantum States
• Are queries and keys always relevant? A case study on Transformer wave functions
• Diagnosing order by disorder in quantum spin systems
• Characterizing Random-singlet State in Two-dimensional Frustrated Quantum Magnets and Implications for the Double Perovskite Sr${}_2$CuTe${}_{1-x}$W${}_x$O${}_6$
• Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice
• Variational Quantum Eigensolver Ansatz for the $J_1$-$J_2$-model
• Translation constraints on quantum phases with twisted boundary conditions
• Comment on "Gapless spin liquid ground state of the spin-$\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on square lattices"
• Equivariant Variational Quantum Eigensolver to detect Phase Transitions through Energy Level Crossings
• Gapless Spin Liquid and Non-local Corner Excitation in the Spin-1/2 Heisenberg Antiferromagnet on Fractal
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• Magnetism and field-induced effects in the S = 5/2 honeycomb lattice antiferromagnet FeP3SiO11
• Combination of Tensor Network States and Green's function Monte Carlo
• Pressure-induced phase transition in the $J_1$-$J_2$ square lattice antiferromagnet RbMoOPO${}_4$Cl
• Defining a universal sign to strictly probe a phase transition
• Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice
• Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Linear combinations of cluster mean-field states applied to spin systems
• Phase Diagram of the Frustrated Square-Lattice Hubbard Model: Variational Cluster Approach
• Non-stabilizerness of Neural Quantum States
• 2D excitation information by MPS method on infinite helixes
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• Boltzmann machines and quantum many-body problems
• Finite-Temperature Signatures of Spin Liquids in Frustrated Hubbard Model
• Low-energy singlet sector in spin-$\frac{1}{2}$ $J_1$--$J_2$ Heisenberg model on square lattice
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Field induced non-BEC transitions in frustrated magnets
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• Variational Quantum Simulation of Valence-Bond Solids
• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain
• Plaquette valence bond state in spin-1/2 J1-J2 XY model on square lattice
• General Formula for the Green's Function Approach to the Spin-1/2 Antiferromagnetic Heisenberg Model
• Gapped paramagnetic state in a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the cross-striped square lattice
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model
• Competing orders, the Wess-Zumino-Witten term, and spin liquids
• Quantum phase transitions: The mean-field perspective
• Phases of frustrated quantum antiferromagnets on the square and triangular lattices
• Improving neural network performance for solving quantum sign structure
• Magnetic phases of orbital bipartite optical lattices
• PEPS++: Towards Extreme-scale Simulations of Strongly Correlated Quantum Many-particle Models on Sunway TainhuLight
• Hidden $SU(2)$ Symmetries, the Symmetry Hierarchy and the Emergent Eight-Fold Way in Spin-1 Quantum Magnets
• Unified Spin Model for Magnetic Excitations in Iron Chalcogenides
• Spin dynamics in the square-lattice cupola system Ba(TiO)Cu${}_4$(PO${}_4$)${}_4$
• Reply to comments on "Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices"
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• Reentrant phase transitions involving glassy and superfluid orders in the random hopping Bose-Hubbard model
• Diagnosing energy gap in quantum spin liquids via polarization amplitude
• Field-induced states and thermodynamics of the frustrated Heisenberg antiferromagnet on a square lattice
• Higher-order topological quantum paramagnets
• Crystal field splittings and magnetic ground state of the square-lattice antiferromagnets YbBi2ClO4 and YbBi2IO4 with Jeff = 1/2
• Generalized Lanczos method for systematic optimization of neural-network quantum states
• Quantum effects in the magnon spectrum of 2D altermagnets via continuous similarity transformations