Renormalization group approach to a $p$-wave superconducting model

Abstract

We present in this work an exact renormalization group (RG) treatment of a one-dimensional $p$-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a $p$-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining $p$-wave superconductivity in a one-dimensional system without spin-orbit interaction.

14 pages and 4 figures, to appear in Physics Letters A

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Cited by in corpus (8)

• Universality classes of topological phase transitions with higher-order band crossing
• Effective Theory and Breakdown of Conformal Symmetry in a Long-Range Quantum Chain
• Multi-critical Behavior in Topological Phase Transitions
• Topological states in normal and superconducting $p$-wave chains
• Mechanism for enhancement of superconductivity in multi-band systems with odd parity hybridization
• Multicriticality in a one-dimensional topological band insulator
• Scaling behavior in a multicritical one-dimensional topological insulator
• From Ising model to Kitaev Chain -- An introduction to topological phase transitions