Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature

TL;DR

This paper investigates the topological properties of a 1D Kitaev chain with long-range superconducting pairings at finite temperature, using geometric phases to identify topological features in mixed states.

Contribution

It compares Uhlmann and interferometric phase approaches to detect topological signatures at finite temperature in long-range Kitaev chains, revealing limitations of the Uhlmann phase.

Findings

Uhlmann phase fails to capture topology in the pure state limit when long-range effects dominate

Interferometric phase remains consistent with pure state topology regardless of temperature

Long-range effects significantly influence the topological signatures at finite temperature

Abstract

We study the 1D Kitaev chain with long range superconductive pairing terms at a finite temperature where the system is prepared in a mixed state in equilibrium with a heat reservoir maintained at a constant temperature $T$. In order to probe the footprint of the ground state topological behavior of the model at finite temperature, we look at two global quantities extracted out of two geometrical constructions: the Uhlmann and the interferometric phase. Interestingly, when the long-range effect dominates, the Uhlmann phase approach fails to reproduce the topological aspects of the model in the pure state limit; on the other hand, the interferometric phase, though has a proper pure state reduction, shows a behaviour independent of the ambient temperature.