T−t′−J model in one dimension using extremely correlated Fermi-liquid theory and time-dependent density matrix renormalization group

Peizhi Mai,Steven R White,B Sriram Shastry

doi:10.1103/physrevb.98.035108

Abstract

We study the one dimensional t-t'-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.

Highlights

In varying dimensions the t-Jmodel continues to attract attention owing to its relevance in cuprates and other important strongly interacting electronic systems
For large U several non-perturbative methods have been devised to study the t-Jmodel for general dimensions, including the study of finite clusters[6,7] and large-N based slave particle mean-field theories[8]
In 1-d we have exact results using Bethe’s ansatz[9,10,11,12,13,14] at special values of the parameters of the model, and for longranged versions[15] of the t-Jmodel, using techniques developed in the Haldane-Shastry models

Summary

INTRODUCTION

In varying dimensions the t-Jmodel continues to attract attention owing to its relevance in cuprates and other important strongly interacting electronic systems. The other technique used is the extremely correlated Fermi liquid (ECFL) theory[21] This analytical theory, which can treat a large class of large U problems, including the t-Jmodel, uses Schwinger’s functional differential equations for the electron Green’s function. The O(λ2) theory leads to a closed set of coupled equations[21,22] for the Green’s function This treatment has been benchmarked in high dimensions and in 2-d. Dynamical mean field theory (DMFT)[23] provides a solution to the Hubbard model, and ECFL has been benchmarked recently[24,25] against exact results from the single impurity Anderson model, and DMFT in d = ∞26,27. Understanding the extent of momentum dependence of the Dysonian self-energy Σ in various dimensions is one of the goals of the present work. In contrast we focus on unraveling the (k, ω) dependence of the Dysonian self-energy in 1-d and comparing with its higher dimensional counterparts

MODEL AND PARAMETERS USED

MOMENTUM DISTRIBUTION FUNCTION

SELF-ENERGY

SPECTRAL FUNCTION

DISPERSION RELATION OF SPINONS AND HOLONS

VIII. CONCLUSION AND DISCUSSION