XX model on the circle

Abstract.We diagonalize the XX model with a finite number of spins and periodic boundary conditions. We solve for the ground state, focus on the rapidity of the convergence to the thermodynamic limit and study the features of multipartite entanglement.

[1]  Multipartite entanglement characterization of a quantum phase transition , 2006, quant-ph/0612098.

[2]  R. Rossignoli,et al.  Entanglement between distant qubits in cyclic X X chains , 2007, 0906.0801.

[3]  P. Pfeuty The one-dimensional Ising model with a transverse field , 1970 .

[4]  G. Vidal,et al.  Entanglement in quantum critical phenomena. , 2002, Physical review letters.

[5]  Realization of the optimal universal quantum entangler , 2004, quant-ph/0410224.

[6]  A. Osterloh,et al.  Scaling of entanglement close to a quantum phase transition , 2002, Nature.

[7]  D. Meyer,et al.  Global entanglement in multiparticle systems , 2001, quant-ph/0108104.

[8]  B. M. Fulk MATH , 1992 .

[9]  N. Christensen,et al.  Potential multiparticle entanglement measure , 2000, quant-ph/0010052.

[10]  M. Cao,et al.  Thermal entanglement between alternate qubits of a four-qubit heisenberg XX chain in a magnetic field , 2005 .

[11]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[12]  A. Starace,et al.  Anisotropy and magnetic field effects on the entanglement of a two qubit Heisenberg XY chain. , 2002, Physical review letters.

[13]  G. Florio,et al.  CHARACTERIZING AND MEASURING MULTIPARTITE ENTANGLEMENT , 2007 .

[14]  W. Wootters,et al.  Distributed Entanglement , 1999, quant-ph/9907047.

[15]  Studying quantum spin systems through entanglement estimators. , 2004, Physical review letters.

[16]  E. Lieb,et al.  Two Soluble Models of an Antiferromagnetic Chain , 1961 .

[17]  M. Lavagna Quantum Phase Transitions , 2001, cond-mat/0102119.

[18]  M Roncaglia,et al.  Long-distance entanglement in spin systems. , 2006, Physical review letters.

[19]  V. Karimipour,et al.  Thermal entanglement of spins in an inhomogeneous magnetic field (6 pages) , 2004, quant-ph/0407073.

[20]  J I Cirac,et al.  Entanglement versus correlations in spin systems. , 2004, Physical review letters.

[21]  V. Buzek,et al.  Quantum-information approach to the Ising model: Entanglement in chains of qubits , 2004 .