Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
Abstract
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that completely characterizes the solutions, and allow to identify an indicator of bulk-boundary correspondence. As an illustration, we show how our method correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave superconductor in a Josephson ring configuration, and predicts that a fractional 4 pi Josephson effect can only be observed in phases hosting an odd number of Majorana pairs.
Keywords
Cite
@article{arxiv.1601.05486,
title = {Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions},
author = {Abhijeet Alase and Emilio Cobanera and Gerardo Ortiz and Lorenza Viola},
journal= {arXiv preprint arXiv:1601.05486},
year = {2016}
}
Comments
8 pages (including supplementary material), 1 figure. Minor revisions for consistency with published version