Strongly interacting Majorana fermions

Bo-Hai Li, Shao-Kai Jian, Hong Yao

Mobin Shakeri

Majorana fermions have been an important subject of research for the past few years in the field of condensed matter physics. After the realization of Majorana zero mode (MZM) in a Kitaev-chain, studies on the systems of many-body MZMs have been increased. Throughout the previous research, It was found that a few of the Majorana zero mode 1-dimensional chain models possess a Tricritical Ising model conformal field theory as a critical point in their phase diagram. These critical points are supersymmetric and the supersymmetric behaviour remains at a near vicinity of them in their neighbouring gapped phase. This particular behaviour of these 1D strongly-interacting MZMs is believed to be interesting since the system possesses a supersymmetric phase whilst having a nite correlation length in the gapped phase. In this thesis, we are going to investigate the supersymmetric realization of these models in their gapped phase, try to understand their excitation levels with the concept of soliton/antisoliton states and try to find traces of supersymmetry in this system of a condensed matter.

Marcel Franz, Armin Rahmani, Xiaoyu Zhu +1 more

Sujit Sarkar

The physics of Majorana fermion occurs at the edge and interface of many one-dimensional quantum many body system with gapped excitation spectrum. We present the renormalization group equations for strongly interacting helical liquid. We present the results of both Majorana- Ising topological quantum phase transition and also Berezinskii-Kosterlitz-Thouless topological phase transition. We show that the Majorana-Ising topological quantum phase transition for non-interacting case is an exactly solvable line but in presence of interaction the system has no exactly solvable line. We study the effect of umklapp scattering on the renormalization group flow diagrams and also the condition for the appearence of Majorana fermion modes.

Fei Lin, V. W. Scarola

Pairing between spinless fermions can generate Majorana fermion excitations that exhibit intriguing properties arising from nonlocal correlations. But, simple models indicate that nonlocal correlation between Majorana fermions becomes unstable at nonzero temperatures. We address this issue by showing that anisotropic interactions between dipolar fermions in optical lattices can be used to significantly enhance thermal stability. We construct a model of oriented dipolar fermions in a square optical lattice. We find that domains established by strong interactions exhibit enhanced correlation between Majorana fermions over large distances and long times even at finite temperatures, suitable for stable redundancy encoding of quantum information. Our approach can be generalized to a variety of configurations and other systems, such as quantum wire arrays.

Dirk K. Morr