Ward identity and optical-conductivity sum rule in the d-density wave state

TL;DR

This paper investigates the impact of the Ward identity on the optical-conductivity sum rule in a d-density wave state, providing a controlled approximation for current correlations and exploring implications for cuprate superconductors.

Contribution

It introduces a novel low-energy sum rule for the d-density wave state using the Ward identity and analyzes vertex functions for better understanding of transport properties.

Findings

Proposes a non-standard low-energy sum rule for the d-density wave state.

Provides an analytical approach to current-current correlation functions.

Discusses potential relevance to cuprate pseudogap regime.

Abstract

We consider the role of the Ward identity in dealing with the transport properties of an interacting system forming a d-wave modulated charge-density wave or staggered flux phase. In particular, we address this issue from the point of view of the restricted optical-conductivity sum rule. Our aim is to provide a controlled approximation for the current-current correlation function which allows us also to determine analytically the corresponding sum rule. By analyzing the role of the vertex functions in both the microscopic interacting model and in the effective mean-field Hamiltonian, we propose a non-standard low-energy sum-rule for this system. We also discuss the possible applicability of these results for the description of cuprate superconductors in the pseudogap regime.