Exact zero modes in a quantum compass chain under inhomogeneous transverse fields

Abstract

We study the emergence of exact Majorana zero modes (EMZMs) in a one-dimensional quantum transverse compass model with both the nearest-neighbor interactions and transverse fields varying over space. By transforming the spin system into a quadratic Majorana-fermion model, we derive an exact formula for the number of the emergent EMZMs, which is found to depend on the partition nature of the lattice sites on which the magnetic fields vanish. We also derive explicit expressions for the wavefunctions of these EMZMs and show that they indeed depend on fine features of the foregoing partition of site indices. Based on the above rigorous results about the EMZMs, we provide an interpretation for the interesting dependence of the eigenstate-degeneracy on the transverse fields observed in prior literatures. As a special case, we employ a plane-wave ansatz to exactly solve an open compass chain with alternating nearest-neighbor interactions and staggered magnetic fields. Explicit forms of the canonical Majorana modes diagonalizing the model are given even for finite chains. We show that besides the possibly existing EMZMs, no almost Majorana zero modes exist unless the fields on both the two sublattices are turned off. Our results might shed light on the control of ground-state degeneracies by solely tuning the external fields in related systems.

17 pages, 4 figures; to appear in Physical Review B

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Cited by in corpus (12)

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• Unveiling the phase diagram of a bond-alternating spin-$\frac{1}{2}$ $K$-$\Gamma$ chain
• Lifshitz phase transitions in one-dimensional Gamma model
• Entanglements and correlations of one-dimensional quantum spin-1/2 chain with anisotropic power-law long range interactions
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Spin dynamics of the generalized quantum spin compass chain
• Field Induced Chiral Soliton Phase in the Kitaev Spin Chain
• Effects of anisotropic correlations in fermionic zero-energy bound states of topological phases
• Field-Induced Ordered Phases in Anisotropic Spin-1/2 Kitaev Chains
• Evolution of two-magnon bound states in a higher-spin ferromagnetic chain with single-ion anisotropy: A complete solution
• Few-magnon excitations in a frustrated spin-$S$ ferromagnetic chain with single-ion anisotropy
• Exact solution of the two-magnon problem in the $k=-\pi /2$ sector of a finite-size anisotropic spin-1/2 frustrated ferromagnetic chain