Three-dimensional Hubbard model in the thermodynamic limit

Abstract

We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the Néel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.

8 pages, 6 figures

References in corpus (18)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Criticality in Heavy Fermion Metals
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Early breakdown of area-law entanglement at many-body delocalization transition
• A Short Introduction to Numerical Linked-Cluster Expansions
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Thermodynamics of the 3D Hubbard model on approach to the Neel transition
• Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model
• 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
• Néel transition of lattice fermions in a harmonic trap: a real-space DMFT study
• Discerning Incompressible and Compressible Phases of Cold Atoms in Optical Lattices
• Thermodynamics of the three-dimensional Hubbard model: Implications for cooling cold atomic gases in optical lattices
• Thermodynamics of the Quantum Critical Point at Finite Doping in the 2D Hubbard Model: A Dynamical Cluster Approximation Study
• Effect of particle statistics in strongly correlated two-dimensional Hubbard models
• Unusual Corrections to Scaling and Convergence of Universal Renyi Properties at Quantum Critical Points

Cited by in corpus (19)

• Machine Learning Phases of Strongly Correlated Fermions
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model
• First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction
• Phase transitions in partial summation methods: Results from the 3D Hubbard model
• Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
• Numerical linked cluster expansions for inhomogeneous systems
• Extended Metal-Insulator Crossover with Strong Antiferromagnetic Spin Correlation in Half-Filled 3D Hubbard Model
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Dynamical resilience to disorder: the dilute Hubbard model on the Lieb lattice
• Magnetic phase diagram of the three-dimensional doped Hubbard model
• Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models
• Thermodynamics of the disordered Hubbard model studied via numerical linked-cluster expansions
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Thermodynamics of the Hubbard Model on the Bethe Lattice
• Thermal Entropy, Density Disorder and Antiferromagnetism of Repulsive Fermions in 3D Optical Lattice
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Evolution of magnetic correlation in an inhomogeneous square lattice
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory