PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields - Mathematical PhysicsReport as inadecuate




PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: The XX spin-chain with non-Hermitian diagonal boundary conditions is shown tobe quasi-Hermitian for special values of the boundary parameters. This isproved by explicit construction of a new inner product employing a-quasi-fermion- algebra in momentum space where creation and annihilationoperators are not related via Hermitian conjugation. For a special example,when the boundary fields lie on the imaginary axis, we show the spectralequivalence of the quasi-Hermitian XX spin-chain with a non-local fermionmodel, where long range hopping of the particles occurs as the non-Hermitianboundary fields increase in strength. The corresponding Hamiltonianinterpolates between the open XX and the quantum group invariant XXZ model atthe free fermion point. For an even number of sites the former is known to berelated to a CFT with central charge c=1, while the latter has been connectedto a logarithmic CFT with central charge c=-2. We discuss the underlyingalgebraic structures and show that for an odd number of sites the superalgebrasymmetry Ugl1|1 can be extended from the unit circle along the imaginaryaxis. We relate the vanishing of one of its central elements to the appearanceof Jordan blocks in the Hamiltonian.



Author: Christian Korff

Source: https://arxiv.org/







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