Topological quantum phase transitions and criticality in a longer-range Kitaev chain

TL;DR

This paper investigates topological quantum phase transitions in a Kitaev chain with both finite and infinite-range couplings, revealing how longer-range interactions influence topological invariants, critical lines, and phase stability.

Contribution

It provides a comprehensive topological analysis of long-range Kitaev chains, deriving critical lines, examining winding number stability, and offering exact solutions with experimental implications.

Findings

Higher order winding numbers decrease with shorter-range couplings.

Topological quantum critical lines can superimpose, affecting phase stability.

Exact solutions facilitate understanding of long-range topological phases.

Abstract

In an attempt to theoretically investigate the quantum phase transition and criticality in topological models, we study Kitaev chain with longer-range couplings (finite number of neighbors) as well as truly long-range couplings (infinite number of neighbors). We carry out an extensive topological characterization of the momentum space to explore the possibility of obtaining higher order winding numbers and analyze the nature of their stability in the model. The occurrences of phase transitions from even-to-even and odd-to-odd winding numbers are observed with decreasing longer-rangeness in the system. We derive topological quantum critical lines and study them to understand the behavior of criticality. A suppression of higher order winding numbers is observed with decreasing longer-rangeness in the model. We show that the mechanism behind such phenomena is due to the superposition and vanishing of the topological quantum critical lines associated with the higher winding number. Through the study of Berry connection we show the possible different behaviors of critical lines when they undergo superposition along with the corresponding critical exponents. We analyze the behavior of the long-range models through the momentum space characterization. We also provide exact solution for the problem and discuss the experimental aspects of the work.