Characterization of Majorana-Ising phase transition in a helical liquid system

JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS

卷:475

Article

Saha, Sudip Kumar¹  Dey, Dayasindhu¹  Roy, Monalisa Singh¹  Sarkar, Sujit²  Kumar, Manoranjan¹ 

[1] SN Bose Natl Ctr Basic Sci, Block JD,Sect 3, Kolkata 700106, India

[2] Poornaprajna Inst Sci Res, 4 Sadashivanagar, Bangalore 560080, Karnataka, India

关键词: Majorana fermion;    DMRG;    Helical liquid;    Spin chain;   

DOI  :  10.1016/j.jmmm.2018.11.088

来源: Elsevier

【 摘 要 】

We map an interacting helical liquid system, coupled to an external magnetic field and s-wave superconductor, to an XYZ spin system, and it undergoes Majorana-Ising transition by tuning of parameters. In the Majorana state lowest excitation gap decays exponentially with system size, and the system has degenerate ground state in the thermodynamic limit. On the contrary, the gap opens in the Ising phase even in the thermodynamic limit. We study various criteria to characterize the transition, such as edge spin correlation with its neighbor C (r = 1), local susceptibility chi(i) superconducting order parameter of edge spin P (r = 1), and longitudinal structure factor S (k). All these criteria lead to the same critical value of parameters for Majorana-Ising phase transition in the thermodynamic limit. We study the entanglement spectrum of the reduced density matrix of the helical liquid system. The system shows finite Schmidt gap and non-degeneracy of the entanglement spectrum in the Ising limit. The Schmidt gap closes in the Majorana state, and all the eigenvalues are either doubly or multiply degenerate.

【 授权许可】

Free