Fermi surface evolution of the 2D Hubbard model within a novel four-pole approximation

Andrea Di Ciolo,Adolfo Avella

doi:10.1063/1.5042831

Abstract

We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of its evolution with doping.

Highlights

Correlated electron systems (SCES) exhibit a very rich phenomenology due to the interplay between different types of interactions and to the closeness of the related energy scales.[1,2,3,4] For instance, we have metal-insulator transitions (MIT) driven by charge, spin and/or orbital ordering,[5] or solely by the competition of kinetic energy and Hubbard repulsion (Mott-Hubbard insulators).[6]
In order to assess the quality of the 4p solution, we compare its internal energy per site E with data from advanced numerical methods
We have introduced a novel four-pole solution for the 2D Hubbard model within the Composite Operator Method: we have chosen a basis given by two Hubbard operators and two operators describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations

Summary

INTRODUCTION

The AC can be used to determine unknown correlation functions and parameters in a self-consistent way.[10,27,28,29] We apply the COM to the 2D Hubbard model, designing a novel four-pole (4p) approximation, performing very well with respect to numerical methods from the weak-to the strong-coupling regime, thanks to a careful treatment of nearest-neighbor spin fluctuations. The paper is organized as follows: in Sec. II, we apply the COM to the Hubbard model and devise a novel 4p approximation; in Sec. III, we show the accuracy of the related 4p solution comparing its results with numerical data and explore the doping evolution of its Fermi surface for a sizable value of the Coulomb repulsion.

MODEL AND METHOD

RESULTS

CONCLUSIONS