Exact solution for many-body Hamiltonian of interacting particles with linear spectrum

TL;DR

This paper presents an exact analytical solution for a one-dimensional many-body quantum system with linear dispersion, applicable to edge states in 2D topological insulators, revealing particle dynamics in external fields.

Contribution

It provides the first exact solution for interacting particles with linear spectra in arbitrary external fields, simplifying the complex many-body problem.

Findings

Exact solution reduces to two groups of particles with constant velocities.

Solution applies to edge states of 2D topological insulators.

Provides insights into particle interactions under external fields.

Abstract

The exact solution of the Schr\"odinger equation for the one-dimensional system of interacting particles with the linear dispersion law in an arbitrary external field is found. The solution is reduced to two groups of particles moving with constant velocities in the opposite directions with a fixed distance between the particles in each group. The problem is applied to the edge states of the 2D topological insulator.