Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models

TL;DR

This paper investigates PT-symmetric Su-Schrieffer-Heeger models within pseudo-Hermitian quantum mechanics, constructing explicit pseudometrics to define physical inner products and analyze their properties.

Contribution

It provides explicit closed-form pseudometrics for specific PT-symmetric SSH models, advancing the understanding of their inner product structures.

Findings

Complete set of pseudometrics constructed for two cases

Pseudometrics determine all physical inner products under positivity

Enhances understanding of PT-symmetric topological models

Abstract

A Su-Schrieffer-Heeger model with added PT-symmetric boundary term is studied in the framework of pseudo-hermitian quantum mechanics. For two special cases, a complete set of pseudometrics is constructed in closed form. When complemented with a condition of positivity, the pseudometrics determine all the physical inner products of the considered model.