-
The quantum phase transitions of one-dimensional period-two anisotropic XY models in a transverse field with the Hamiltonian where the anisotropy parameters i take and alternately, are studied. The Hamiltonian can be reduced to the diagonal form by Jordan-Wigner and Bogoliubov transformations. The long-range correlations Cx and Cy are calculated numerically. The phase with Cx Cy0 (or Cy Cx0) is referred to as the ferromagnetic (FM) phase along the x (or y) direction, while the phase with Cx=Cy=0 is the paramagnetic (PM) phase. It is found that the phase diagrams with the ratio -1 and =-1 are different obviously. For the case with -1, the line h=hc1=1-[(1-)/2]2 separates an FM phase from a PM phase, while the line =0 is the boundary between a ferromagnetic phase along the x direction (FMx) and a ferromagnetic phase along the y direction (FMy). These are similar to those of the uniform XY chains in a transverse field (i.e., =1). When =-1, the FMx and FMy phases disappear and there appears a new FM phase. The line h=hc2=1-2 separates this new FM phase from the PM phase. The new phase is gapless with two zeros in single particle energy spectrum. This is due to the new symmetry in the system with =-1, i.e., the Hamiltonian is invariant under the transformation 2ix 2i+1y,2iy 2i+1x. The correlation function between the 2i-1 and 2i lattice points along the x (y) direction is equal to that between the 2i and 2i+1 lattice points along the y (x) direction. As a result, the long-range correlation functions along two directions are equivalent. In order to facilitate the description, we call this gapless phase the isotropic ferromagnetic (FMxx) phase. Finally, the relationship between quantum entanglement and quantum phase transitions of the system is studied. The scaling behaviour of the von Neumann entropy at each point in the FMxx phase is SL~1/3log2L+ Const, which is similar to that at the anisotropic phase transition point of the uniform XY model in a transverse field, and different from those in the FMx and FMy phases.
-
Keywords:
- period-two anisotropic XY model /
- quantum phase transition /
- isotropic ferromagnetic phase /
- von Neumann entropy
[1] Suzuki S, Inoue J I, Chakrabarti B K 2013 Quantum Ising Phases and Transitions in Transverse Ising Models (Berlin:Springer-Verlag) p13
[2] de Gennes P G 1963 Solid State Commun. 1 132
[3] Bitko D, Rosenbaum T F, Aeppli G 1996 Phys. Rev. Lett. 77 940
[4] Vtyurina N N, Dulin D, Docter M W, Meyer A S, Dekker N H, Abbondanzieri E A 2016 Proc. Nat. Acad. Sci. USA 113 4982
[5] Fan B, Branch R W, Nicolau D V, Pilizota T, Steel B C, Maini P K, Berry R M 2010 Science 327 685
[6] Shi Y, Duke T 1998 Phys. Rev. E 58 6399
[7] Sornette D 2014 arXiv:1404.0243v1[q-fin.GN]
[8] Jin B Q, Korepin V E 2004 I. Stat. Phys. 116 79
[9] Islói F, Juhász R 2008 Europhys. Lett. 81 57003
[10] Babkevich P, Jeong M, Matsumoto Y, Kovacevic I, Finco A, Toft-Petersen R, Ritter C, Månsson M, Nakatsuji S, Rønnow H M 2016 Phys. Rev. Lett. 116 197202
[11] Kenzelmann M, Coldea R, Tennant D A, Visser D, Hofmann M, Smeibidl P, Tylczynski Z 2002 Phys. Rev. B 65 144432
[12] Lieb E, Schultz T, Mattis D 1961 Ann. Phys. NY 16 407
[13] Pfeuty P 1970 Ann. Phys. NY 57 79
[14] Osterloh A, Amieo L, Falci G, Fazio R 2002 Nature 416 608
[15] Vidal G, Latorre J I, Rico E, Kitaev A 2003 Phys. Rev. Lett. 90 227902
[16] Franchini F, Its A R, Korepin V E 2008 J. Phys. A:Math. Theor. 41 025302
[17] Raoul D 2008 Phys. Rev. B 78 224413
[18] Guo J L, Wei J L, Qin W, Mu Q X 2015 Quantum Int. Process 14 1429
[19] Cheng W W, Li J X, Shan C J, Gong L Y, Zhao S M 2015 Quantum Int. Process 14 2535
[20] Zanardi P, Paunkovic N 2006 Phys. Rev. E 74 031123
[21] Quan H T, Song Z, Liu X F, Zanardi P, Sun C P 2006 Phys. Rev. Lett. 96 140604
[22] Fisher D 1994 Phys.Rev.B 50 3799
[23] Bunder J, McKenzie R 1999 Phys. Rev. B 60 344
[24] Luck J M 1993 J.Stat.Phys. 72 417
[25] Zhang Z J, Li W J, Zhu X, Xiong Y, Tong P Q 2015 Acta Phys. Sin. 64 190501(in Chinese)[张振俊, 李文娟, 朱璇, 熊烨, 童培庆2015物理学报 64 190501]
[26] Tong P Q, Zhong M 2001 Physica B 304 91
[27] Zhong M, Tong P Q 2010 J. Phys. A:Math. Theor. 43 505302
[28] Tong P Q, Liu X X 2006 Phys. Rev. Lett. 97 017201
[29] Zhong M, Liu X X, Tong P Q 2007 Int. J. Mod. Phys. B 21 4225
[30] Latorre J I, Rico E, Vidal G 2004 Quantum Int. Comput. 4 48
[31] Sachdev S 2011 Quantum Phase Transitions (Cambridge:Cambridge University Press) p133
-
[1] Suzuki S, Inoue J I, Chakrabarti B K 2013 Quantum Ising Phases and Transitions in Transverse Ising Models (Berlin:Springer-Verlag) p13
[2] de Gennes P G 1963 Solid State Commun. 1 132
[3] Bitko D, Rosenbaum T F, Aeppli G 1996 Phys. Rev. Lett. 77 940
[4] Vtyurina N N, Dulin D, Docter M W, Meyer A S, Dekker N H, Abbondanzieri E A 2016 Proc. Nat. Acad. Sci. USA 113 4982
[5] Fan B, Branch R W, Nicolau D V, Pilizota T, Steel B C, Maini P K, Berry R M 2010 Science 327 685
[6] Shi Y, Duke T 1998 Phys. Rev. E 58 6399
[7] Sornette D 2014 arXiv:1404.0243v1[q-fin.GN]
[8] Jin B Q, Korepin V E 2004 I. Stat. Phys. 116 79
[9] Islói F, Juhász R 2008 Europhys. Lett. 81 57003
[10] Babkevich P, Jeong M, Matsumoto Y, Kovacevic I, Finco A, Toft-Petersen R, Ritter C, Månsson M, Nakatsuji S, Rønnow H M 2016 Phys. Rev. Lett. 116 197202
[11] Kenzelmann M, Coldea R, Tennant D A, Visser D, Hofmann M, Smeibidl P, Tylczynski Z 2002 Phys. Rev. B 65 144432
[12] Lieb E, Schultz T, Mattis D 1961 Ann. Phys. NY 16 407
[13] Pfeuty P 1970 Ann. Phys. NY 57 79
[14] Osterloh A, Amieo L, Falci G, Fazio R 2002 Nature 416 608
[15] Vidal G, Latorre J I, Rico E, Kitaev A 2003 Phys. Rev. Lett. 90 227902
[16] Franchini F, Its A R, Korepin V E 2008 J. Phys. A:Math. Theor. 41 025302
[17] Raoul D 2008 Phys. Rev. B 78 224413
[18] Guo J L, Wei J L, Qin W, Mu Q X 2015 Quantum Int. Process 14 1429
[19] Cheng W W, Li J X, Shan C J, Gong L Y, Zhao S M 2015 Quantum Int. Process 14 2535
[20] Zanardi P, Paunkovic N 2006 Phys. Rev. E 74 031123
[21] Quan H T, Song Z, Liu X F, Zanardi P, Sun C P 2006 Phys. Rev. Lett. 96 140604
[22] Fisher D 1994 Phys.Rev.B 50 3799
[23] Bunder J, McKenzie R 1999 Phys. Rev. B 60 344
[24] Luck J M 1993 J.Stat.Phys. 72 417
[25] Zhang Z J, Li W J, Zhu X, Xiong Y, Tong P Q 2015 Acta Phys. Sin. 64 190501(in Chinese)[张振俊, 李文娟, 朱璇, 熊烨, 童培庆2015物理学报 64 190501]
[26] Tong P Q, Zhong M 2001 Physica B 304 91
[27] Zhong M, Tong P Q 2010 J. Phys. A:Math. Theor. 43 505302
[28] Tong P Q, Liu X X 2006 Phys. Rev. Lett. 97 017201
[29] Zhong M, Liu X X, Tong P Q 2007 Int. J. Mod. Phys. B 21 4225
[30] Latorre J I, Rico E, Vidal G 2004 Quantum Int. Comput. 4 48
[31] Sachdev S 2011 Quantum Phase Transitions (Cambridge:Cambridge University Press) p133
Catalog
Metrics
- Abstract views: 6960
- PDF Downloads: 1158
- Cited By: 0
下载:
