Correlations, long-range entanglement and dynamics in long-range Kitaev chains

TL;DR

This paper investigates the effects of long-range interactions in a one-dimensional fermionic chain, revealing unique entanglement properties, correlation decay behaviors, and dynamical phase transitions that differ from short-range systems.

Contribution

It provides a comprehensive analysis of long-range entanglement, correlation decay, and dynamical phase transitions in long-range Kitaev chains, highlighting novel phenomena and mechanisms.

Findings

Long-range quantum mutual information exists if decay exponent ≤ 1.

Dynamical quantum phase transitions occur without crossing phase boundaries.

Adiabatic dynamics involve divergence of a topological length scale at criticality.

Abstract

Long-range interactions exhibit surprising features which have been less explored so far. Here, studying a one-dimensional fermionic chain with long-range hopping and pairing, we discuss some general features associated to the presence of long-range entanglement. In particular, after determining the algebraic decays of the correlation functions, we prove that a long-range quantum mutual information exists if the exponent of the decay is not larger than one. Moreover, we show that the time evolution triggered by a quantum quench between short-range and long-range regions, can be characterized by dynamical quantum phase transitions without crossing any phase boundary. We show, also, that the adiabatic dynamics is dictated by the divergence of a topological length scale at the quantum critical point, clarifying the violation of the Kibble-Zurek mechanism for long-range systems.