Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

TL;DR

This paper demonstrates an exact Jastrow-Slater wave function for the ground state of the one-dimensional Luttinger model, providing a new variational approach that captures excitations and can be generalized to higher dimensions.

Contribution

It introduces an exact Jastrow-Slater wave function for the 1D Luttinger model and explores its potential for describing excitations and extending to higher dimensions.

Findings

Exact wave function for 1D Luttinger model ground state

Representation of one-particle excitations with Jastrow factor

Potential application to photoemission spectra in higher dimensions

Abstract

We show that it is possible to describe the ground state of the Luttinger model in terms of a Jastrow-Slater wave function. Moreover, our findings reveal that one-particle excitations and their corresponding dynamics can be faithfully represented only when a Jastrow factor of a similar form is applied to a coherent superposition of many Slater determinants. We discuss the possible relevance of this approach for the theoretical description of photoemission spectra in higher dimensionality, where the present wave function can be straightforwardly generalized and can be used as a variational ansatz, that is exact for the 1D Luttinger model.