Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion

TL;DR

This paper identifies special parameter values where the nonlinear dispersion Tomonaga-Luttinger model simplifies to noninteracting fermions, enabling exact solutions and perturbative expansions for more general cases.

Contribution

It introduces a class of exactly solvable one-dimensional spinless fermion models and applies this to analyze the nonlinear dispersion Tomonaga-Luttinger Hamiltonian.

Findings

Exact density-density propagator for special parameters

Unitary equivalence to noninteracting fermions at specific values

Framework for perturbative expansion around exact solutions

Abstract

It is shown that for some special values of Hamiltonian parameters the Tomonaga-Luttinger model with nonlinear dispersion is unitary equivalent to the system of noninteracting fermions. For such parameter values the density-density propagator of the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion can be found exactly. In a generic situation the exact solution can be used as a reference point around which a perturbative expansion in orders of certain irrelevant operators may be constructed.