A Short Introduction to Numerical Linked-Cluster Expansions

Abstract

We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques that can be used to accelerate the convergence of the series.

11 pages, 6 figures, 2 tables

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• Thermodynamics of strongly interacting fermions in two-dimensional optical lattices
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Cited by in corpus (96)

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• Probing quench dynamics across a quantum phase transition into a 2D Ising antiferromagnet
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• Quantum Quenches in the Thermodynamic Limit
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
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• Correlations and diagonal entropy after quantum quenches in XXZ chains
• The case for a U(1)${}_{\pi }$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
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• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Equation of State of the Fermionic 2D Hubbard Model
• 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
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• Selected applications of typicality to real-time dynamics of quantum many-body systems
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• Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores
• Parafermionic clock models and quantum resonance
• Equation of State and Thermometry of the 2D SU($N$) Fermi-Hubbard Model
• Unravelling competing microscopic interactions at a phase boundary: a single crystal study of the metastable antiferromagnetic pyrochlore Yb${}_2$Ge${}_2$O${}_7$
• Many-Body Open Quantum Systems
• Quantum quenches in the thermodynamic limit. II. Initial ground states
• Analysis of continuous and discrete Wigner approximations for spin dynamics
• Three-dimensional Hubbard model in the thermodynamic limit
• Metal-insulator transition and magnetism of SU(3) fermions in the square lattice
• Optimization of finite-size errors in finite-temperature calculations of unordered phases
• Exponential damping induced by random and realistic perturbations
• Dipolar spin ice regime proximate to an all-in-all-out Néel ground state in the dipolar-octupolar pyrochlore Ce${}_2$Sn${}_2$O${}_7$
• Finite-temperature superconducting correlations of the Hubbard model
• Anisotropic exchange Hamiltonian, magnetic phase diagram and domain inversion of Nd${}_2$Zr${}_2$O${}_7$
• Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
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• Limitations of optimization algorithms on noisy quantum devices
• Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points
• Finite-temperature properties of strongly correlated fermions in the honeycomb lattice
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model
• Two-dimensional coherent spectrum of interacting spinons from matrix-product states
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• Numerical linked cluster expansions for inhomogeneous systems
• A generalized perspective on non-perturbative linked cluster expansions
• Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model
• Exotic pairing symmetry of interacting Dirac fermions on a $\pi$ flux lattice
• Cubic trihedral corner entanglement for a free scalar
• Magnon heat transport in a two-dimensional Mott insulator
• Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interactions
• $\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$
• Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models
• Magnetic properties and temperature variation of spectra in the Hubbard model
• 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
• Probing trihedral corner entanglement for Dirac fermions
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems
• Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps
• Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model
• Griffiths-McCoy Singularities in the Dilute Transverse-Field Ising Model: A Numerical Linked Cluster Expansion Study
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• 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
• Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
• Magnetic Field Response of Dipolar-Octupolar Quantum Spin Ice
• L-based numerical linked cluster expansion for square lattice models
• Numerical linked-cluster expansions for two-dimensional spin models with continuous disorder distributions
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Gibbs state sampling via cluster expansions
• Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
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• Towards a global phase diagram of Ce-based dipolar-octupolar pyrochlore magnets under magnetic fields
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