All Majorana Models with Translation Symmetry are Supersymmetric

作者：Hsieh Timothy H; Halasz Gabor B; Grover Tarun

来源：Physical Review Letters, 2016, 117(16): 166802.

DOI：10.1103/PhysRevLett.117.166802

We establish results similar to Kramers and Lieb-Schultz-Mattis theorems but involving only translation symmetry and for Majorana modes. In particular, we show that all states are at least doubly degenerate in any one-and two-dimensional array of Majorana modes with translation symmetry, periodic boundary conditions, and an odd number of modes per unit cell. Moreover, we show that all such systems have an underlying N = 2 supersymmetry and explicitly construct the generator of the supersymmetry. Furthermore, we establish that there cannot be a unique gapped ground state in such one-dimensional systems with antiperiodic boundary conditions. These general results are fundamentally a consequence of the fact that translations for Majorana modes are represented projectively, which in turn stems from the anomalous nature of a single Majorana mode. An experimental signature of the degeneracy arising from supersymmetry is a zero-bias peak in tunneling conductance.

• 出版日期2016-10-11
• 单位中国科学院理论物理研究所