Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the 2D Hubbard model

TL;DR

This study investigates how next-nearest-neighbor electron hopping ($t'$) affects the static and dynamic properties of the 2D Hubbard model, revealing its renormalization with interaction strength and implications for Fermi surface features.

Contribution

It provides a numerical analysis of how $t'$ is renormalized in the 2D Hubbard model as electron interactions increase, including effects on magnetic correlations and spectral functions.

Findings

Negative $t'$ can induce hole pockets at $(rac{ ext{pi}}{2},rac{ ext{pi}}{2})$

Positive $t'$ affects features at $( ext{pi},0)$ and $(0, ext{pi})$

Negative $t'$ may be dynamically generated from the model

Abstract

Comparing experimental data for high temperature cuprate superconductors with numerical results for electronic models, it is becoming apparent that a hopping along the plaquette diagonals has to be included to obtain a quantitative agreement. According to recent estimations the value of the diagonal hopping $t'$ appears to be material dependent. However, the values for $t'$ discussed in the literature were obtained comparing theoretical results in the weak coupling limit with experimental photoemission data and band structure calculations. The goal of this paper is to study how $t'$ gets renormalized as the interaction between electrons, $U$, increases. For this purpose, the effect of adding a bare diagonal hopping $t'$ to the fully interacting two dimensional Hubbard model Hamiltonian is investigated using numerical techniques. Positive and negative values of $t'$ are analyzed. Spin-spin correlations, $n(\bf{k})$, $\langle n\rangle$ vs $\mu$, and local magnetic moments are studied for values of $U/t$ ranging from 0 to 6, and as a function of the electronic density. The influence of the diagonal hopping in the spectral function $A(\bf{k},\omega)$ is also discussed, and the changes in the gap present in the density of states at half-filling are studied. We introduce a new criterion to determine probable locations of Fermi surfaces at zero temperature from $n(\bf{k})$ data obtained at finite temperature. It appears that hole pockets at ${\bf{k}}=(\pi/2,\pi/2)$ may be induced for negative $t'$ while a positive $t'$ produces similar features at ${\bf{k}}=(\pi,0)$ and $(0,\pi)$. Comparisons with the standard 2D Hubbard ($t'=0$) model indicate that a negative $t'$ hopping amplitude appears to be dynamically generated. In general, we conclude that it is very dangerous to extract a bare parameter of the Hamiltonian $(t')$ from PES data where