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

Abstract

The exact solution of the Schrödinger 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.

arXiv comment4 pages

References in corpus (8)

• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• The Quantum Spin Hall Effect: Theory and Experiment
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Valley separation in graphene by polarized light
• Moving zero-gap Wannier-Mott excitons in graphene
• Linearity of the edge states energy spectrum in the 2D topological insulator
• Edge capacitance of a 2D topological insulator

Cited by in corpus (1)

• Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of $p$- and $n$-domains