Majorana-Hubbard model on the square lattice

We study a one-dimensional (1D) chain of 2N Majorana bound states, which interact through a local quartic interaction. This model describes for example the edge physics of a quasi 1D stack of 2N Kitaev chains with modified time-reversal symmetry T γiT −1 = γi, which precludes the presence of quadratic coupling. The ground state of our 1D Majorana chain displays a four-fold periodicity in N , corresponding to the four distinct topological classes of the stacked Kitaev chains. We analyze the transport properties of the 1D Majorana chain, when probed by local conductors located at its ends. We find that for finite but large N , the scattering matrix partially reflects the four-fold periodicity, and the chain exhibits strikingly different transport properties for different chain lengths. In the thermodynamic limit, the 1D Majorana chain hosts a robust many-body zero mode, which indicates that the corresponding stacked two-dimensional bulk system realizes a weak topological phase.

Section: Introductionmentioning

confidence: 99%

Interacting Majorana chain: Transport properties and signatures of an emergent two-dimensional weak topological phase

Liu¹,

Bergholtz²,

Romito³

et al. 2017

“…These definitions of γ e/o are slightly different than those of [8], and are chosen to simplify the form of the U(1) breaking operators. To derive a low energy field theory, we start with the dispersion relation of the non-interacting model,…”

Section: Low Energy Field Theorymentioning

confidence: 99%

“…3 The interactions between the Majorana modes are predicted to drop off exponentially with the superconducting coherence length. 4 The simplest model for this system, the "Majorana-Hubbard model", has nearest neighbor hopping and the shortest possible range interaction, which must occur on 4 sites; [4][5][6][7][8][9] for the square lattice, these are plaquettes: H = it m,n γ m,n [(−1) n γ m+1,n + γ m,n+1 ] + g m,n γ m,n γ m+1,n γ m+1,n+1 γ m,n+1…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Renormalization group analysis of phase transitions in the two-dimensional Majorana-Hubbard model

Wamer

Affleck

2018

Self Cite

A lattice of interacting Majorana modes can occur in a superconducting film on a topological insulator in a magnetic field. The phase diagram as a function of interaction strength for the square lattice was analyzed recently using a combination of mean field theory and renormalization group methods, and was found to include second order phase transitions. One of these corresponds to spontaneous breaking of an emergent U(1) symmetry, for attractive interactions. Despite the fact that the U(1) symmetry is not exact, this transition was claimed to be in a supersymmetric universality class when time reversal symmetry is present and in the conventional XY universality class otherwise. Another second order transition was predicted for repulsive interactions with time reversal symmetry to be in the same universality class as the transition occurring in the Gross-Neveu model, despite the fact that the U(1) symmetry is not exact in the Majorana model. We analyze these phase transitions using a modified -expansion, confirming the previous conclusions.

“…Here, we present an extension of these ideas to 2D systems of interacting Majorana fermions [29,30], which were recently studied (in a different context) on the square [31][32][33] and honeycomb [34,35] lattices. We construct a supersymmetric model of interacting Majorana fermions on the kagome lattice, Fig.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetry in an interacting Majorana model on the kagome lattice

Lantagne-Hurtubise

Franz

2019

We construct a supersymmetric model of interacting Majorana fermions on the kagome lattice. In the infinite-coupling limit, the model exhibits an extensively degenerate ground state manifold separated in two topological sectors, in addition to two parity supersectors. An exact solution for thin-torus geometries allows us to analytically construct the entire zero-energy ground state manifold. Upon inclusion of hopping terms with energy scale g, the supersymmetry is spontaneously broken with the ground state energy density scaling as g 4 . We also briefly discuss the non-interacting limit of the model, which exhibits a zero-energy flat band and Majorana Chern bands. arXiv:1811.06104v2 [cond-mat.str-el]