The XX--model with boundaries. Part I: Diagonalization of the finite chain

Abstract

This is the first of three papers dealing with the XX finite quantum chain with arbitrary, not necessarily hermitian, boundary terms. This extends previous work where the periodic or diagonal boundary terms were considered. In order to find the spectrum and wave-functions an auxiliary quantum chain is examined which is quadratic in fermionic creation and annihilation operators and hence diagonalizable. The secular equation is in general complicated but several cases were found when it can be solved analytically. For these cases the ground-state energies are given. The appearance of boundary states is also discussed and in view to the applications considered in the next papers, the one and two-point functions are expressed in terms of Pfaffians.

56 pages, LaTeX, some minor corrections

References in corpus (2)

• Fractional-Spin Integrals of Motion for the Boundary Sine-Gordon Model at the Free Fermion Point
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics

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