Optical Conductivity in Symmetric Mass Generation Insulators

TL;DR

This paper investigates the optical conductivity of symmetric mass generation insulators, revealing that proper regularization shows these insulators have zero optical conductivity below the charge gap, resolving previous paradoxes.

Contribution

It introduces a lattice regularization of the current operator for SMG insulators and demonstrates, through analytical and numerical methods, that these insulators lack low-energy optical conductivity.

Findings

SMG insulators have no optical conductivity below the charge gap.

A well-behaved lattice current operator is derived.

The paradox of negative optical conductivity is resolved.

Abstract

Symmetric mass generation (SMG) insulators are interaction-driven, featureless Mott insulating states in quantum many-body fermionic systems. Recent advancements suggest that zeros in the fermion Green's function could lead to non-vanishing negative optical conductivity in SMG insulators, even below the charge excitation gap. This study explores the origin of this unusual behavior through the lens of pole-zero duality, highlighting a critical issue where the current operator becomes unbounded, rendering the response function unphysical. By employing a lattice model, we derive a well-behaved lattice regularization of the current operator, enabling a detailed study of optical conductivity in SMG insulators. Utilizing both analytical and numerical methods, including strong-coupling expansions, we confirm that SMG insulators exhibit no optical conductivity at low energies below the charge gap, effectively resolving the paradox. This work not only deepens our understanding of quantum many-body phenomena but also lays a robust theoretical groundwork for future experimental explorations of SMG materials.