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arXiv · 1505.03966

Phase Diagram of the Interacting Majorana Chain Model

Armin Rahmani·Xiaoyu Zhu·Marcel Franz·Ian Affleck
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Abstract

The Hubbard chain and spinless fermion chain are paradigms of strongly correlated systems, very well understood using Bethe ansatz, Density Matrix Renormalization Group (DMRG) and field theory/renormalization group (RG) methods. They have been applied to one-dimensional materials and have provided important insights for understanding higher dimensional cases. Recently, a new interacting fermion model has been introduced, with possible applications to topological materials. It has a single Majorana fermion operator on each lattice site and interactions with the shortest possible range that involve 4 sites. We present a thorough analysis of the phase diagram of this model in one dimension using field theory/RG and DMRG methods. It includes a gapped supersymmetric region and a novel gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. In addition to a first order transition, three critical points occur: tricritical Ising, Lifshitz and a novel generalization of the commensurate-incommensurate transition. We also survey various gapped phases of the system that arise when the translation symmetry is broken by dimerization and find both trivial and topological phases with 0, 1 and 2 Majorana zero modes bound to the edges of the chain with open boundary conditions.

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Armin Rahmani, Xiaoyu Zhu, Marcel Franz, Ian Affleck. 2015-12-17. Phase Diagram of the Interacting Majorana Chain Model. https://doi.org/10.1103/physrevb.92.235123

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