Exact zero modes in twisted Kitaev chains

@article{Kawabata2017ExactZM,
title={Exact zero modes in twisted Kitaev chains},
author={Kohei Kawabata and Ryohei Kobayashi and Ning Wu and Hosho Katsura},
journal={Physical Review B},
year={2017},
volume={95},
pages={195140}
}
We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of edges'' in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show…

Figures from this paper

Explicit forms of zero modes in symmetric interacting Kitaev chain without and with dimerization
• Physics
Chinese Physics B
• 2018
The fermionic and bosonic zero modes of the 1D interacting Kitaev chain at the symmetric point are unveiled. The many-body structures of the Majorana zero modes in the topological region are given
Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties.
• Physics, Medicine
Journal of physics. Condensed matter : an Institute of Physics journal
• 2020
By means of an exact analytical diagonalization in the real space, the momentum quantization conditions are derived and exact analytical formulae for the resulting energy spectrum and eigenstate wave functions, encompassing boundary and bulk states are presented.
Topological phase transitions in random Kitaev α-chains
• C. Monthus
• Mathematics, Physics
Journal of Physics A: Mathematical and Theoretical
• 2018
The topological phases of random Kitaev $\alpha$-chains are labelled by the number of localized edge Majorana Zero Modes. The critical lines between these phases thus correspond to delocalization
Insensitivity of bulk properties to the twisted boundary condition
The symmetry and the locality are the two major sources of various general theorems in quantum many-body systems. We demonstrate that, in gapped phases of a U(1) symmetric Hamiltonian with
String and conventional order parameters in the solvable modulated quantum chain
• Physics
Physical Review B
• 2019
The phase diagram and the order parameters of the exactly solvable quantum 1D model are analysed. The model in its spin representation is the dimerized XY spin chain in the presence of uniform and
Exact zero modes in a quantum compass chain under inhomogeneous transverse fields
• Physics
Physical Review B
• 2019
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.
Exact ground states for interacting Kitaev chains
• Physics, Mathematics
Physical Review B
• 2018
We introduce a frustration-free, one-dimensional model of spinless fermions with hopping, p-wave superconducting pairing and alternating chemical potentials. The model possesses two exactly
Universal finite-size gap scaling of the quantum Ising chain
I study the universal finite-size scaling function for the lowest gap of the quantum Ising chain with a one-parameter family of defect'' boundary conditions, which includes periodic, open, and
Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• Physics
• 2019
On a ring, a single Jordan-Wigner transformation between the Kitaev model and the spin model suffers redundant degrees of freedom. However, we can establish an exact quaternary Jordan-Wigner mapping
Enhanced localization and protection of topological edge states due to geometric frustration
• Physics
Physical Review B
• 2019
Topologically non-trivial phases are linked to the appearance of localized modes in the boundaries of an open insulator. On the other hand, the existence of geometric frustration gives rise to