Hydrodynamic Edge Modes and Fragile Surface States of Symmetry Protected Integer Quantum Hall Effect of Bosons

TL;DR

This paper models the edge modes and fragile surface states of bosonic integer quantum Hall phases using hydrodynamics, revealing boundary conditions that influence edge state behavior and their distinction from traditional topological theories.

Contribution

It introduces a hydrodynamical framework to analyze boundary modes and fragile surface states in bosonic SPT phases, extending understanding beyond conventional topological field theories.

Findings

Boundary conditions produce counter-propagating edge modes.

Hydro boundary conditions can gap or isolate edge states.

Identification of fragile surface states requiring bulk dynamics.

Abstract

We adapt the fluid description of Fractional Quantum Hall (FQH) states, as seen in (arXiv:2203.06516), to model a system of interacting two-component bosons. This system represents the simplest physical realization of an interacting bosonic Symmetry-Protected Topological (SPT) phase, also known as the integer quantum Hall effect (IQHE) of bosons. In particular, we demonstrate how the fluid dynamical boundary conditions of no-penetration and no-stress at a hard wall naturally give rise to the two counter-propagating boundary modes expected in these SPT phases. Moreover, we identify energy-conserving hydro boundary conditions that can either create a gap in these edge modes or completely isolate the edge states from the bulk, as described in (Physical Review X 14, 011057 (2024)), where they are termed fragile surface states. These fragile surface states are typically absent in K-matrix edge theories and require bulk dynamics to manifest. By leveraging insights from hydrodynamical boundary dynamics, we can further elucidate the intricate surface properties of SPTs beyond the usual topological quantum field theory based approaches.