Kitaev chains with long-range pairing

TL;DR

This paper investigates a long-range generalization of the Kitaev chain with power-law decaying p-wave pairing, revealing new phases, symmetry breaking, and entanglement properties relevant for cold atom experiments.

Contribution

It introduces a solvable long-range Kitaev chain model and uncovers novel phases, symmetry breaking, and entanglement behaviors not seen in short-range models.

Findings

Existence of gapped regimes with exponential and algebraic decay of correlations.

Long-range pairing breaks conformal symmetry along critical lines for small lpha.

Violation of the area law for entanglement entropy in certain phases.

Abstract

We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions.