Quantum phase transitions about parity breaking in matrix product systems

  • According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.
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  • [1] Sachdev S. Quantum Phase Transitions. Cambridge: Cambridge University Press, 19992 Fannes M, Nachtergaele B, Werner R F. Commun. Math. Phys., 1992, 144: 4433 Verstraete F, Porras D, Cirac J I. Phys. Rev. Lett., 2004, 93: 2272054 Verstraete F, Cirac J I. 2005, arXiv:0505140 [cond-mat]5 Affleck I, Kennedy T, Lieb E H, Tasaki H. Commun. Math. Phys., 1988, 115: 4776 Klümper A, Schadschneider A, Zittartz J. J. Phys. A, 1991, 24: L9557 Klümper A, Schadschneider A, Zittartz J. Europhys. Lett., 1993, 24: 2938 Wolf M M, Ortiz G, Verstraete F, Ignacio Cirac J. Phys. Rev. Lett., 2006, 97: 1104039 ZHU J M. Chin. Phys. Lett., 2008, 25(10): 3574-357710 CEN L X, WANG Z D quant-ph/0707422311 ZHU J M. Commun. Theor. Phys., 2010, 54(2): 373-37912 Nachtergaele B. Commun. Math. Phys., 1996, 175: 56513 Nielsen N, Chuang I. Quantum Computation and Quantum Communication. Cambridge: Cambridge University Press, 200014 QIN M, TAO Y J. Chinese Physics C, 2008, 32(09): 710-71315 ZHU J M,WANG S J. Commun. Theor. Phys., 2010, 54(3): 524-52816 LIU W Z, ZHANG J F, LONG G L. Chinese Science Bulletin, 2009, 54: 4262-426517 Verstraete F, Cirac J I, Latorre J I, Rico E, Wolf M M. Phys. Rev. Lett., 2005, 94: 14060118 Vidal V, Latorre J I, Rico E, Kitaev A. Phys. Rev. Lett., 2003, 90: 227902
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ZHU Jing-Min. Quantum phase transitions about parity breaking in matrix product systems[J]. Chinese Physics C, 2011, 35(2): 144-148. doi: 10.1088/1674-1137/35/2/007
ZHU Jing-Min. Quantum phase transitions about parity breaking in matrix product systems[J]. Chinese Physics C, 2011, 35(2): 144-148.  doi: 10.1088/1674-1137/35/2/007 shu
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Received: 2010-05-10
Revised: 2010-06-16
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Quantum phase transitions about parity breaking in matrix product systems

  • College of Optoelectronic Technology, Chengdu University of Information Technology, Chengdu 610225, China

Abstract: According to our scheme to construct quantum phase transitions (QPTs) in spin chain systems with matrix product ground states, we first successfully combine matrix product state (MPS) QPTs with spontaneous symmetry breaking. For a concrete model, we take into account a kind of MPS QPTs accompanied by spontaneous parity breaking, though for either side of the critical point the GS is typically unique, and show that the kind of MPS QPTs occur only in the thermodynamic limit and are accompanied by the appearance of singularities, diverging correlation length, vanishing energy gap and the entanglement entropy of a half-infinite chain not only staying finite but also whose first derivative discontinuous.

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