Spectral properties of the three-dimensional Hubbard model

Abstract

We present momentum resolved single-particle spectra for the three-dimensional Hubbard model for the paramagnetic and antiferromagnetically ordered phase obtained within the dynamical cluster approximation. The effective cluster problem is solved by continuous-time Quantum Monte Carlo simulations. The absence of a time discretization error and the ability to perform Monte Carlo measurements directly in Matsubara frequencies enable us to analytically continue the self-energies by maximum entropy, which is essential to obtain momentum resolved spectral functions for the Néel state. We investigate the dependence on temperature and interaction strength and the effect of magnetic frustration introduced by a next-nearest neighbor hopping. One particular question we address here is the influence of the frustrating interaction on the metal insulator transition of the three-dimensional Hubbard model.

Ferromagnetism and nonlocal correlations in the Hubbard model

“…Comparing our results to a recent dynamical cluster approximation 13 (a cluster extension of the DMFT in order to retain a k-dependence) there is good agreement below the MIT (U/W = 0.67 in the mentioned work). The dispersion of the Kondo resonance and the maxima of the lower/upper Hubbard bands show essentially the same behavior as in our calculation.…”

“…This comes at the expense of neglecting certain correlation effects. Most severe in this respect is the missing metal-insulator transition (MIT) at half-filling which should also occur in finite dimensions at roughly U/W ≈ 1 as indicated by DMFT calculations 13 . It is interesting to note, that the (local) MPT, when used as an impurity solver in a DMFT calculation for the infinite dimensional Hubbard model does show a MIT in the correct U/W region, whereas it does not when used as a self-energy for the lattice Hamiltonian 46 .…”

“…So it may be questionable, e.g., whether such a self-energy is sufficient to describe angle-resolved photoemission results. Recent efforts have therefore been focussed on regaining a certain degree of non-locality in the DMFT self-energy [9][10][11][12][13] . There are other approaches to the non-locality of the self-energy at low dimensions d = 2, 3.…”

Charge order and antiferromagnetism in the extended Hubbard model

“…49 and Ref. 30 to study the formation and competition between AFM and CO phases in the half filled 2D extended Hubbard model on a square lattice. The following provides an overview of the formalism, and the interested reader is referred to Ref.…”

“…29 In contrast, a large on-site interaction U will enhance AFM (π, π) correlations. 30 The interplay between inter-cite interaction V , local interaction U , temperature, and doping effects thereby generates the rich phase diagram of the model. The extended Hubbard model has been of interest both as a proxy for the exploration of charge order caused by electron repulsion 24,25,27,29,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] and as a model system for testing the effect of non-local interactions on electron correlations.…”