# Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States

## TL;DR

This paper investigates the microscopic properties of the interface between Laughlin and Halperin 332 topological phases using matrix product state wavefunctions, revealing detailed low-energy physics and excitations.

## Contribution

It introduces a novel matrix product state framework to model and analyze topological interfaces, validated by comparisons with exact diagonalization.

## Key findings

- Characterization of the gapless interface mode
- Identification of spin and charge excitations
- Validation of the wavefunction approach against exact methods

## Abstract

Interfaces between topologically distinct phases of matter reveal a remarkably rich phenomenology. We study the experimentally relevant interface between a Laughlin phase at filling factor $\nu=1/3$ and a Halperin 332 phase at filling factor $\nu=2/5$. Based on our recent construction of chiral topological interfaces in [Nat. Commun. 10, 1860 (2019)], we study a family of model wavefunctions that captures both the bulk and interface properties. These model wavefunctions are built within the matrix product state framework. The validity of our approach is substantiated through extensive comparisons with exact diagonalization studies. We probe previously unreachable features of the low energy physics of the transition. We provide, amongst other things, the characterization of the interface gapless mode and the identification of the spin and charge excitations in the many-body spectrum. The methods and tools presented are applicable to a broad range of topological interfaces.