Composite Operator Method Analysis of the Underdoped Cuprates Puzzle

Abstract

The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the composite operator method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable of describing the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical algebras. In this case (underdoped cuprates—2D Hubbard model), the residual interactions—beyond a 2-pole approximation—between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the noncrossing approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large versus small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal versus antinodal physics, pseudogap(s), and kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the antinodal dynamics in the underdoped regime.

The composite operator method route to the 2D Hubbard model and the cuprates

“…The tale of strongly correlated electronic systems (SCES) [1][2][3][4][5][6] is deeply intertwined to that of cuprate high-T c superconductors (HTcS) [7][8][9][10][11][12][13][14][15][16][17][18][19] simply because the prototypical model for the former is exactly the same as the very minimal model to describe the latter [20]: the 2D Hubbard model [21][22][23]. This very fact has enormously increased the number of studies performed in the last thirty years, that is since the discovery of HTcS, on this model and its extensions (the Emery or p-d model among all others [24][25][26]) and derivatives (the t-J model [27,28], the spin-fermion model [29], .…”

“…Among these methods, several approaches employ multi-electron operators, generated by a set of equations of motion, and the high-order Green's function (GF) projection. In particular, in the class of operatorial approaches (the Hubbard approximations [21][22][23], an early high-order GF approach [30], the projection operator method [31,32], the works of Mori [33], Rowe [34], and Roth [35], the spectral density approach [36], the works of Barabanov [37], Val'kov [38], and Plakida [39][40][41][42][43], and the cluster perturbation theory in the Hubbard-operator representation [44]), we have been developing the composite operator method [4,15,45,46].…”

“…According to the physical properties under analysis and the range of temperatures, dopings, and interactions that we want to explore, we have to choose an approximation to compute the residual self-energy. In the last years, we have been using the n−pole approximation , the asymptotic field approach [72][73][74] and the non-crossing approximation (NCA) [15,[75][76][77][78].…”

“…In the last twenty years, the COM has been applied to several models and materials: Hubbard [46-55, 79, 80], p-d [59][60][61][62], t-J [81], t-t -U [56][57][58], extended Hubbard (t-U-V) [63,64], Kondo [72], Anderson [73,74], two-orbital Hubbard [65,82,83], Ising [66,67], J 1 − J 2 [84][85][86][87][88][89], Hubbard-Kondo [90], cuprates [15,68,69,[75][76][77][78], etc. In this review, we will focus just on the 2D Hubbard model (section 2) and on the best COM solutions available at the time within the n-pole (section 3) and the NCA to the residual self-energy (section 4) approximation frameworks.…”

Single-particle properties of the Hubbard model in a novel three-pole approximation

“…The COM, which is based on the equations of motion and Green's function formalisms, is highly tunable and expressly devised for the characterization of strongly correlated electronic states and the exploration of novel emergent phases. Motivated by the long-standing experimental challenge posed by the puzzling single-particle properties of the underdoped cuprates [13,14] (Fermi arcs, pseudogap, non-Fermi liquid behavior, extreme momentum dependence of spectral properties, . .…”