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.

First-order metal-insulator transitions in the extended Hubbard model due to self-consistent screening of the effective interaction

“…This is in line with the finding that the second-order correlation energies in d = 3 and d = ∞ do not differ strongly 63 . Finally, results in the thermodynamic limit for the U -dependent double occupancy using the numerical linked-cluster expansion show a kink in the double occupation in line with our DMFT results 64 .…”

Machine Learning Phases of Strongly Correlated Fermions

“…This leads to a magnetic phase diagram in the more physical temperature-density space that very much depends on whether or not the sign has been properly taken into account. Our results suggest that, at T = 0.32 and the critical µ = −2, the density is less than 0.95, consistent with recent results from a more conventional method [21].…”

“…Grey pentagons, hexagons, and circles for weak-, intermediate-, and strongcoupling regimes are taken from Refs. [18,19,21], respectively. The solid line is a guide to the eye.…”

“…One can omit configurations from the training data for an arbitrary temperature range in the proximity of the estimated critical value, e.g., the temperature at which the correlations reach the linear size of the cluster, at the expense of losing some predicting accuracy by the network after the training. Here, we take advantage of the fact that finite-size errors are small in the strongcoupling regime and use T N = 0.23 for U = 16, obtained for the thermodynamic limit [21], for both cluster sizes. For U = 5, however, we use the approximate critical temperatures T N = 0.24 and 0.25 for N = 4 3 and 8 3 , respectively, from the analysis of the Binder ratio for the order parameter [19].…”

Thermodynamics and magnetism in the 2D-3D crossover of the Hubbard model

“…4 have a simple explanation. In a 3D cubic lattice, S π is maximized around U/t ∼ 10 [63]. One effect of anisotropy is to change the average tunneling to be somewhere between t and the smaller t ⊥ , and thus one would expect anisotropy to decrease the effective tunneling, t eff , and increase the effective U/t eff compared to U/t.…”