Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices

Abstract

We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We present studies of thermodynamic observables for spin models on square, triangular, and kagome lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLC, are presented. We also include a comparison of NLC results with those obtained from exact analytical expressions (where available), high-temperature expansions (HTE), exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo simulations.For many models and properties NLC results are substantially more accurate than HTE and ED.

14 pages, 16 figures, as published

References in corpus (17)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Stochastic series expansion method with operator-loop update
• Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Spin-1/2 Heisenberg-Antiferromagnet on the Kagome Lattice: High Temperature Expansion and Exact Diagonalisation Studies
• Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet
• Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet
• Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Universal Magnetic Properties of Frustrated Quantum Antiferromagnets in Two Dimensions
• Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets
• Temperature Dependence of the Magnetic Susceptibility for Triangular-Lattice Antiferromagnets with spatially anisotropic exchange constants
• Flat spin wave dispersion in a triangular antiferromagnet
• Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions
• Bose-Einstein Quantum Phase Transition in an Optical Lattice Model
• Exact Study of the 1D Boson Hubbard Model with a Superlattice Potential
• Quantum Phase Transitions of Hard-Core Bosons in Background Potentials

Cited by in corpus (91)

• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Probing quench dynamics across a quantum phase transition into a 2D Ising antiferromagnet
• Imaging magnetic polarons in the doped Fermi-Hubbard model
• Prethermalization and Thermalization in Isolated Quantum Systems
• Quantum Quenches in the Thermodynamic Limit
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• A Short Introduction to Numerical Linked-Cluster Expansions
• Magnetism of the N=42 kagome lattice antiferromagnet
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• Thermodynamics of strongly interacting fermions in two-dimensional optical lattices
• Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
• Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions
• Kagome lattice antiferromagnets and Dzyaloshinsky-Moriya interactions
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Finite temperature spin-dynamics and phase transitions in spin-orbital models
• Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian
• Heating Rates in Periodically Driven Strongly Interacting Quantum Many-Body Systems
• Linked cluster expansions for open quantum systems on a lattice
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Quantum quenches and many-body localization in the thermodynamic limit
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Bold Diagrammatic Monte Carlo technique for frustrated spin systems
• Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores
• Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet
• Signatures of quantum phase transitions after quenches in quantum chaotic one-dimensional systems
• Finite-temperature crossover phenomenon in the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice
• Perturbative quantum simulation
• Unravelling competing microscopic interactions at a phase boundary: a single crystal study of the metastable antiferromagnetic pyrochlore Yb${}_2$Ge${}_2$O${}_7$
• Matrix product state techniques for two-dimensional systems at finite temperature
• Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
• Effect of particle statistics in strongly correlated two-dimensional Hubbard models
• Quantum quenches in the thermodynamic limit. II. Initial ground states
• Three-dimensional Hubbard model in the thermodynamic limit
• Optimization of finite-size errors in finite-temperature calculations of unordered phases
• Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
• Finite-temperature superconducting correlations of the Hubbard model
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Prethermalization, thermalization, and Fermi's golden rule in quantum many-body systems
• Thermodynamics of two-dimensional spin models with bimodal random-bond disorder
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
• Numerical study of the thermodynamics of clinoatacamite
• Finite-temperature properties of strongly correlated fermions in the honeycomb lattice
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Short-Range Correlations and Cooling of Ultracold Fermions in the Honeycomb Lattice
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Vanishing Wilson ratio as the hallmark of quantum spin-liquid models
• Valence Bond Solid Phases on Deformed Kagome Lattices: Application to Rb2Cu3SnF12
• Numerical linked cluster expansions for inhomogeneous systems
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• A generalized perspective on non-perturbative linked cluster expansions
• Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin $S$
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets
• Exotic pairing symmetry of interacting Dirac fermions on a $\pi$ flux lattice
• Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model
• Cubic trihedral corner entanglement for a free scalar
• Strong-coupling diagrammatic Monte Carlo technique for correlated fermions and frustrated spins
• Nuclear relaxation rates in the Herbertsmithite Kagome antiferromagnets ZnCu3(OH)6Cl2
• Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models
• Numerical linked-cluster expansions for disordered lattice models
• High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
• Projective cluster-additive transformation for quantum lattice models
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Similarity of thermodynamic properties of Heisenberg model on triangular and kagome lattices
• Probing trihedral corner entanglement for Dirac fermions
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems
• Griffiths-McCoy Singularities in the Dilute Transverse-Field Ising Model: A Numerical Linked Cluster Expansion Study
• Thermodynamic Properties of Kagome Antiferromagnets with different Perturbations
• Extracting critical exponents for sequences of numerical data via series extrapolation techniques
• Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$: No Apparent Octupolar Correlations Above $T=0.05$ K
• Magnetism of competing high-spin/low-spin states in Ba${}_2$NiO${}_2$(AgSe)${}_2$ and related two-orbital two-electron systems
• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
• L-based numerical linked cluster expansion for square lattice models
• Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions
• Enhanced Convergence of Quantum Typicality using a Randomized Low-Rank Approximation
• Auxiliary-Field Monte Carlo for lattice bosons: tackling strong interactions and frustration
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
• Density-Matrix Mean-Field Theory
• Sample complexity of matrix product states at finite temperature
• Gibbs state sampling via cluster expansions
• Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices
• Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
• Site-resolved observables in the doped spin-imbalanced triangular Hubbard model
• Extracting quantum-critical properties from directly evaluated enhanced perturbative continuous unitary transformations