Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study

Abstract

The interplay between quantum and thermal fluctuations can induce rich phenomena at finite temperatures in strongly correlated fermion systems. Here we report a {\it numerically exact} auxiliary-field quantum Monte Carlo (AFQMC) study for the finite-temperature properties of three-dimensional repulsive Hubbard model at half filling. We concentrate on the complete temperature-interaction strength phase diagram of the model, which contains the low-temperature antiferromagnetic (AFM) long-range ordered phase and metal-insulator crossover (MIC) in the paramagnetic phase. Enabling access to unprecedented system sizes up to $20^3$, we achieve highly accurate results of the Néel transition temperature for representative values of on-site interaction $U$ via finite-size analysis of AFM structure factor. To quantitatively characterize the MIC above the Néel transition, we have developed fully new techniques allowing to compute the thermal entropy versus $U$ at fixed temperature and to directly calculate the $U$-derivative of double occupancy in AFQMC simulations. Then combining variously thermodynamic and dynamical observables, we establish an efficient scheme to precisely determine the boundaries for the MIC by cross-checking different observables. We also demonstrate the temperature dependence of many commonly used observables. Away from half filling, we explore the behavior of the sign problem and AFM spin correlation versus hole doping, and demonstrate the persistance of Néel AFM ordered phase to finite doping with limited results.

arXiv comment32 pages, 24 figures; Accepted by Phys. Rev. B

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• Extended Metal-Insulator Crossover with Strong Antiferromagnetic Spin Correlation in Half-Filled 3D Hubbard Model
• 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
• Finite temperatures and flat bands: the Hubbard model on three-dimensional Lieb lattices
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
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• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory