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arXiv:1212.3027 · Physical Review B

Néel temperature and thermodynamics of the half-filled three-dimensional Hubbard model by diagrammatic determinant Monte Carlo

Evgeny Kozik, Evgeni Burovski, V. W. Scarola, Matthias Troyer

Published May 3, 2013• 75 citations
arXivHTMLPDF

Abstract

We study the thermodynamics of the three-dimensional Hubbard model at half filling on approach to the N\'eel transition by means of large-scale unbiased diagrammatic determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as the temperature dependence of the energy, entropy, double occupancy, and nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.

DOI
10.1103/physrevb.87.205102

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We study the thermodynamics of the three-dimensional Hubbard model at half filling on approach to the N'eel transition by means of large-scale unbiased diagrammatic determinant Monte Carlo simulations. We obtain the transition temperature in the strongly correlated regime, as well as the temperature dependence of the energy, entropy, double occupancy, and nearest-neighbor spin correlation function. Our results improve the accuracy of previous unbiased studies and present accurate benchmarks in the ongoing effort to realize the antiferromagnetic state of matter with ultracold atoms in optical lattices.
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The authors present here a comprehensive and numerically unbiased study for finite-temperature properties of the 3D fermionic Hubbard model. At half-filling, a complete temperature-interaction strength phase diagram of the model is established, including the highly accurate results of the N\'eel transition temperature and a multimessenger characterization of the metal-insulator crossover in the paramagnetic phase. The temperature dependence of various thermodynamic quantities and their underlying physics are thoroughly explored. The persistence of N\'eel AFM ordered phase to finite doping is further revealed.
We have systematically studied the thermodynamic properties of a two-dimensional half-filled SU(2N)\mathrm{SU}(2N)SU(2N) Hubbard model on a square lattice by using the determinant quantum Monte Carlo method. The entropy-temperature relation, the isoentropy curve, and the probability distribution of the on-site occupation number are calculated in both SU(4) and SU(6) cases, which exhibit prominent features of the Pomeranchuk effect. We analyze these thermodynamic behaviors based on energy scales in the density and spin channels. In the density channel, the interaction strength that marks the crossover from the weak to strong interaction regimes increases with the number of fermion components. In the spin channel, increasing the number of fermion components enhances quantum spin fluctuations, which is shown in the simulations of uniform spin susceptibilities and antiferromagnetic structure factors.
We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.
We study the phase diagram of the two-dimensional repulsive Hubbard model with spin-dependent anisotropic hopping at half filling. The system develops Ising antiferromagnetic long-range order already at infinitesimal repulsive interaction strength in the ground state. Outside the perturbative regime, unbiased predictions for the critical temperatures of the Ising antiferromagnet are made for representative interaction values by a variety of state-of-the-art quantum Monte Carlo methods, including the diagrammatic Monte Carlo, continuous-time determinantal Monte Carlo, and path-integral Monte Carlo methods. Our findings are relevant to ultracold atom experiments in the ppp orbital or with spin-dependent optical lattices.