Spectral functions of two-band spinless fermion and single-band spin-1/2 fermion models

TL;DR

This paper derives analytical expressions for the spectral functions of one-dimensional two-band spinless and single-band spin-1/2 fermion models, revealing the crossover from spin-charge separation to decoupled fermions.

Contribution

It provides exact spectral function formulas using hypergeometric functions for two-band spinless fermions and explores the crossover to spin-charge separation in spin-1/2 fermions.

Findings

Spectral functions expressed in hypergeometric functions.

Recovery of spin-charge separation in identical fermions.

Crossover from spin-charge separation to decoupled fermions.

Abstract

We examine zero-temperature one-particle spectral functions for the one-dimensional two-band spinless fermions with different velocities and general forward-scattering interactions. By using the bosonization technique and diagonalizing the model to two Tomonaga-Luttinger-liquid Hamiltonians, we obtain general expressions for the spectral functions which are given in terms of the Appell hypergeometric functions. For the case of identical two-band fermions, corresponding to the SU(2) symmetric spin-1/2 fermions with repulsive interactions,the spectral functions can be expressed in terms of the Gauss hypergeometric functions and are shown to recover the double-peak structure suggesting the well-known "spin-charge" separation. By tuning the difference in velocities for the two-band fermions, we clarify the crossover in spectral functions from the "spin-charge" separation to the decoupled fermions. We discuss the relevance of our results to the spin-1/2 Hubbard model under a magnetic field which can be mapped onto two-band spinless fermions.