The 1D t-J model with next-nearest neighbor hopping - breakdown of the Luttinger liquid?

TL;DR

This study explores how adding next-nearest neighbor hopping t' to the 1D t-J model significantly alters its dynamical properties and Fermi surface, leading to a breakdown of traditional Luttinger liquid behavior.

Contribution

It demonstrates that moderate t' values cause a phase transition in the 1D t-J model, challenging the applicability of Luttinger liquid theory at high doping levels.

Findings

Holon becomes diffuse and overdamped with t'

Fermi surface transitions from hole pocket to high doping phase

Neither phase conforms to standard Luttinger liquid predictions

Abstract

We investigate the effect of a next-nearest neighbor hopping integral t' in the 1D t-J model, using Lanczos diagonalization of finite chains. Surprisingly, even moderate values of t' have a quite dramatic effect on the dynamical correlation functions and Fermi surface volume. The `holon' becomes diffuse and overdamped, the band structure near the Fermi energy is dominated by t'. Most importantly, however, with increasing hole concentration the system undergoes a phase transition from a `hole pocket' Fermi surface, where k_F corresponds to the number of holes rather than electrons, to a high doping phase where the doped holes correspond to spinless Fermions. Neither phase thus has a Fermi momentum compatible with the `standard' Luttinger liquid.