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

• URL: http://arxiv.org/abs/2206.09688v2
• Date: Wed, 28 Sep 2022 18:52:51 GMT
• Title: Correlations, long-range entanglement and dynamics in long-range Kitaev chains
• Authors: Gianluca Francica, Luca Dell'Anna
• Abstract summary: We study a one-dimensional fermionic chain with long-range hopping and pairing. We prove that a long-range quantum mutual information exists if the exponent of the decay is not larger than one. We also show that the adiabatic dynamics is dictated by the divergence of a topological length scale at the quantum critical point.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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