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-l/2 fermions with a spin-l/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find an XY model such that after the Jordan Wigner transformation one obtains a quadratic fermionic Hamiltonian directly diagonalizable. (C) 2013 Elsevier B.V. All rights reserved.
Quantum spins on star graphs and the Kondo model
Trombettoni A
2013
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-l/2 fermions with a spin-l/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find an XY model such that after the Jordan Wigner transformation one obtains a quadratic fermionic Hamiltonian directly diagonalizable. (C) 2013 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
