Exactly Solvable Models of Interacting Chiral Bosons and Fermions on a Lattice

TL;DR

This paper presents exactly solvable lattice models of chiral fermions and bosons, revealing their properties and impurity effects, and providing insights into topological edge states in condensed matter physics.

Contribution

It introduces exactly solvable lattice models for interacting chiral fermions and bosons, and analyzes impurity effects and continuum limits with exact solutions.

Findings

Hard core bosons behave like free fermions

Exact solution of impurity effects in fermions

Orthogonality catastrophe demonstrated in continuum limit

Abstract

We consider one-dimensional theories of chiral fermions and bosons on a lattice, which arise as edge states of two-dimensional topological matter breaking time-reversal invariance. We show that hard core bosons or their spin chain equivalent exhibit properties that are similar to free fermions, solving the many-body problem exactly. For fermions, we study the effect of a static impurity exactly and show the orthogonality catastrophe in the continuum limit via bosonization. The interacting many-fermion problem in the continuum limit is solved exactly using simple momentum conservation arguments.