Strong Disorder Real-Space Renormalization for the Many-Body-Localized phase of random Majorana models

TL;DR

This paper details a Strong Disorder Real-Space Renormalization approach for the Many-Body-Localized phase in random Majorana models, emphasizing the advantages of the Majorana framework over spin models for constructing excited states.

Contribution

It extends the RSRG-X method to arbitrary quadratic Hamiltonians and the Kitaev chain, highlighting the benefits of Majorana representation.

Findings

Explicit RG rules derived for free-fermion models

RG rules formulated for the Kitaev chain with local interactions

Majorana language offers advantages over spin language in RSRG-X

Abstract

For the Many-Body-Localized phase of random Majorana models, a general Strong Disorder Real-Space Renormalization procedure known as RSRG-X [D. Pekker, G. Refael, E. Altman, E. Demler and V. Oganesyan, Phys. Rev. X 4, 011052 (2014)] is described to produce the whole set of excited states, via the iterative construction of the Local Integrals of Motion (LIOMs). The RG rules are then explicitly derived for arbitrary quadratic Hamiltonians (free-fermions models) and for the Kitaev chain with local interactions involving even numbers of consecutive Majorana fermions. The emphasis is put on the advantages of the Majorana language over the usual quantum spin language to formulate unified RSRG-X rules.