1D Hubbard model elementary objects scattering

TL;DR

This paper develops a scattering theory for elementary objects in the 1D Hubbard model, simplifying the analysis of its dynamical properties by leveraging integrability and zero-momentum forward scattering.

Contribution

It introduces a novel scattering framework for elementary objects in the 1D Hubbard model, revealing a commutative factorization of the S matrix and momentum-dependent exponents.

Findings

Elementary objects undergo only zero-momentum forward scattering.

The dressed S matrix factorizes into a product of two-object scattering matrices.

Momentum-dependent power-law exponents are controlled by phase shifts.

Abstract

In terms of electron processes, the 1D Hubbard model is a nonperturbative problem. That renders the description in terms of electron scattering of the microscopic processes that control the model properties a very difficult task. In this paper we study the corresponding scattering processes of the elementary objects whose occupancy configurations generate the energy eigenstates from the electron vacuum. Due to the related occurrence of an infinite set of conservation laws associated with the model integrability, such objects are found to undergo only zero-momentum forward-scattering collisions. The description of the model dynamical properties in terms of such elementary objects scattering events then drastically simplifies. The corresponding 1D Hubbard model scattering theory refers to arbitrary values of the densities and finite repulsive interaction U>0. Each ground-state - excited-state transition is associated with a well defined set of elementary zero-momentum forward-scattering events. The elementary-object scatterers dressed S matrix is expressed as a commutative product of S matrices, each corresponding to a two-object scattering event. This commutative factorization is stronger than the factorization associated with Yang-Baxter equation for the original spin-1/2 electron bare S matrix. The power-law singularities exponents in the finite-energy correlation-functions of the metallic phases of a wide class of 1D integrable and non-integrable systems are momentum dependent. In the present exactly solvable model such an exponent momentum dependence is controlled by the phase shifts and corresponding dressed S matrix considered in this paper.