Topological bosonic Bogoliubov excitations with sublattice symmetry

TL;DR

This paper explores the topological classification of bosonic Bogoliubov excitations with sublattice symmetry, revealing an enriched topological framework and proposing methods to characterize and measure topological invariants in such systems.

Contribution

It uncovers a hidden sublattice symmetry in bosonic Bogoliubov systems, leading to an expanded topological classification including a new class AIII, and demonstrates this with a 1D model.

Findings

Identification of sublattice symmetry in bosonic Bogoliubov systems

Introduction of a topological invariant via winding number or symplectic polarization

Edge states exhibit robustness to symmetry-preserving disorder

Abstract

Here we investigate the internal sublattice symmetry, and thus the enriched topological classification of bosonic Bogoliubov excitations of thermodynamically stable free-boson systems with non-vanishing particle-number-nonconserving terms. Specifically, we show that such systems well described by the bosonic Bogoliubov-de Gennes Hamiltonian can be in general reduced to particle-number-conserving (single-particle) ones. Building upon this observation, the sublattice symmetry is uncovered with respect to an excitation energy, which is usually hidden in the bosonic Bogoliubov-de Gennes Hamiltonian. Thus, we obtain an additional topological class, i.e., class AIII, which enriches the framework for the topological threefold way of free-boson systems. Moreover, a construction is proposed to show a category of systems respecting such a symmetry. For illustration, we resort to a one-dimensional (1D) prototypical model to demonstrate the topological excitation characterized by a winding number or symplectic polarization. By introducing the correlation function, we present an approach to measure the topological invariant. In addition, the edge excitation together with its robustness to symmetry-preserving disorders is also discussed.