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arXiv · 1210.7143

Quantum spins on star graphs and the Kondo model

Nicolas Crampe·Andrea Trombettoni
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Abstract

We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y-junction). By performing a Jordan-Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions, in the spin 1 representation of su(2), locally coupled with a magnetic impurity. In the continuum limit our model is shown to be equivalent to the 4-channel Kondo model coupling spin-1/2 fermions with a spin-1/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find a XY model such that - after the Jordan-Wigner transformation - one obtains a quadratic fermionic Hamiltonian directly diagonalizable.

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Nicolas Crampe, Andrea Trombettoni. 2013-03-04. Quantum spins on star graphs and the Kondo model. https://doi.org/10.1016/j.nuclphysb.2013.03.001

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