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

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.

This article is an extended and more polished version of the original supplementary material of arxiv:1806.06858

References in corpus (18)

• Fractional Quantum Hall States and Jack Polynomials
• Topological boundary conditions in abelian Chern-Simons theory
• Applying matrix product operators to model systems with long-range interactions
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• A theory of topological edges and domain walls
• Half-Filled Lowest Landau Level on a Thin Torus
• Composite Fermions and Broken Symmetries in Graphene
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Topological Phase Transitions in the Golden String-Net Model
• One-Dimensional Theory of the Quantum Hall System
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Atypical Fractional Quantum Hall Effect in Graphene at Filling Factor 1/3
• Theoretical expectations for a fractional quantum Hall effect in graphene
• Matrix product state representation of non-Abelian quasiholes