Entanglement in valence-bond-solid states on symmetric graphs
作者： Hosho Katsura , Naoki Kawashima , Anatol N Kirillov , Vladimir E Korepin , Shu Tanaka
DOI: 10.1088/1751-8113/43/25/255303
关键词:
摘要: We study quantum entanglement in the ground state of Affleck–Kennedy–Lieb–Tasaki model defined on two-dimensional graphs with reflection and/or inversion symmetry. The this spin is known as valence-bond-solid state. investigate properties a reduced density matrix subsystem which mirror image other one. Thanks to symmetry, eigenvalues can be obtained by numerically diagonalizing real symmetric whose elements are calculated Monte Carlo integration. calculate von Neumann entropy matrix. results indicate that there some deviation from naive expectation per valence bond boundary between subsystems ln 2. This interpreted terms hidden chain along subsystems. In cases where ladders, numerical analytically or algebraically confirmed.
harvard.edu
elsevier.com
sci-hub.se 参考文章(113)
H. Niggemann, J. Zittartz, Quantum spin-\({3 \over 2}\) models on the Cayley tree - optimum ground state approach European Physical Journal B. ,vol. 10, pp. 731- 738 ,(1999) , 10.1007/S100510050904
Michael A. Nielsen, Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state arXiv: Quantum Physics. ,(2001) , 10.1016/S0375-9601(02)01803-0
Heng Fan, Vladimir Korepin, Vwani Roychowdhury, Christopher Hadley, Sougato Bose, None, Boundary effects on entropy and two-site entanglement of the spin-1 valence-bond solid Physical Review B. ,vol. 76, pp. 014428- ,(2007) , 10.1103/PHYSREVB.76.014428
Daniel Gottesman, Daniel Gottesman, Isaac L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations Nature. ,vol. 402, pp. 390- 393 ,(1999) , 10.1038/46503
Ying Xu, Vladimir E Korepin, Entanglement of Valence-Bond-Solid on an Arbitrary Graph arXiv: Quantum Physics. ,(2008) , 10.1088/1751-8113/41/50/505302
Jeffrey Bub, Quantum information and computation Nature. ,vol. 404, pp. 247- 255 ,(2000) , 10.1038/35005001
D. Scalapino, Shou-Cheng Zhang, W. Hanke, SO(5) symmetric ladder Physical Review B. ,vol. 58, pp. 443- 452 ,(1998) , 10.1103/PHYSREVB.58.443
V. E. Korepin, Universality of entropy scaling in one dimensional gapless models. Physical Review Letters. ,vol. 92, pp. 096402- ,(2004) , 10.1103/PHYSREVLETT.92.096402
J. Eisert, M. Cramer, M. B. Plenio, Colloquium: Area laws for the entanglement entropy Reviews of Modern Physics. ,vol. 82, pp. 277- 306 ,(2010) , 10.1103/REVMODPHYS.82.277
H. Niggemann, J. Zittartz, Ground state properties of a spin-3/2 model on a decorated square lattice European Physical Journal B. ,vol. 13, pp. 377- 379 ,(2000) , 10.1007/S100510050044