Phase diagram of the Hubbard model: Beyond the dynamical mean field

Abstract

The Dynamical Cluster Approximation (DCA) is used to study non-local corrections to the dynamical mean field phase diagram of the two-dimensional Hubbard model. Regions of antiferromagnetic, d-wave superconducting, pseudo-gapped non-Fermi liquid, and Fermi liquid behaviors are found, in rough agreement with the generic phase diagram of the cuprates. The non-local fluctuations beyond the mean field both suppress the antiferromagnetism and mediate the superconductivity.Introduction The rich phenomenology of high-T c superconductors [1] has stimulated strong experimental and theoretical interest in the field of strongly correlated electron systems. Common to all high-T c systems is the presence of antiferromagnetic ordering in undoped samples in proximity to a superconducting phase with a d-wave order parameter and the normal state pseudogap dominating the physics in underdoped samples. A successful theory must describe all these fundamental features at the same time.The 2D Hubbard model in the intermediate coupling regime or closely related models like the t-J model are believed to capture the essential physics of the high-T c cuprates [2]. The antiferromagnetic phase of the cuprates is well understood. In the strong coupling limit U ≫ W , where U is the Coulomb repulsion and W the bare bandwidth, the undoped Hubbard model reduces to the Heisenberg model, which has been proven to describe the low energy spin fluctuations of the cuprate parent compounds. However, off half-filling there is no complete understanding of the superconducting phase or the normal state pseudogap in the intermediate coupling 2D Hubbard model.Finite size quantum Monte Carlo (QMC) calculations for the doped 2D Hubbard model in the intermediate coupling regime with U < ∼ W , support the idea of a spin fluctuation driven interaction mediating d-wave superconductivity [3]. However, the fermion sign problem and the fact that the number of degrees of freedom grows rapidly with the lattice size, limits these calculations to temperatures too high to study a possible transition [3]. These calculations are also restricted to relatively small system sizes making statements for the thermodynamic limit problematic, and inhibiting studies of the low energy physics.These shortcomings do not apply to the Dynamical Mean Field Approximation (DMFA), which is by construction in the thermodynamic limit. Unfortunately,

Failure oft−Jmodels in describing doping evolution of spectral weight in x-ray scattering, optical, and photoemission spectra of cuprates

“…To better understand the failure of QMC calculations with fixed U = 8t to explain the observed ASWT, in Figure 4(a-b) we plot the DOS and the associated electron count calculated in QMC 8,9 . For ω c = 0.4 eV, close to the DOS minimum 38 , W UHB is in good agreement with the exact diagonalization results for the corresponding U = 8t, 39 blue stars in Fig.…”

Strongly correlated superconductivity: A plaquette dynamical mean-field theory study

“…Several studies have already shown that the Hubbard model treated within cluster DMFT on a 2 by 2 plaquette successfully describes many properties of the high temperature superconductors. For example the competition of antiferromagnetism and superconductivity [35][36][37][38][39] , the existence of a pseudogap at low doping [40][41][42][43][44][45][46] , and the formation of Fermi arcs 43,44,47,48 . These phenomena involve short range non local correlations.…”

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

“…(We refer to DCA/CDMFT/VCA collectively as Green's function cluster theories.) These pioneering works have suggested rich phenomenology in the phase diagram including metallic, antiferromagnetic, and d-wave (and other kinds of) superconducting phases, a pseudogap regime, inhomogeneous orders such as stripes, and charge, spin, and pairdensity waves, as well as phase separation [6,19,20,24,25,[27][28][29]32,35,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. However, as different numerical methods have yielded different pictures of the ground-state phase diagram, a precise quantitative picture of the ground-state phase diagram has yet to emerge.…”