Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction

被引:128
作者
Chen, Shu [1 ]
Wang, Li [1 ]
Gu, Shi-Jian [2 ,3 ]
Wang, Yupeng [1 ]
机构
[1] Chinese Acad Sci, Inst Phys, Beijing Natl Lab Condensed Matter Phys, Beijing 100080, Peoples R China
[2] Chinese Univ Hong Kong, Dept Phys, Hong Kong, Hong Kong, Peoples R China
[3] Chinese Univ Hong Kong, Inst Theoret Phys, Hong Kong, Hong Kong, Peoples R China
来源
PHYSICAL REVIEW E | 2007年 / 76卷 / 06期
关键词
D O I
10.1103/PhysRevE.76.061108
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J(1)-J(2) model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the J(1)-J(2) model cannot be well characterized by the ground-state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.
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页数:4
相关论文
共 36 条
[1]   CRITICAL-BEHAVIOR OF SPIN-S HEISENBERG ANTIFERROMAGNETIC CHAINS - ANALYTIC AND NUMERICAL RESULTS [J].
AFFLECK, I ;
GEPNER, D ;
SCHULZ, HJ ;
ZIMAN, T .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (05) :511-529
[2]  
AMICO L, ARXIVQUANTPH0703044
[3]  
[Anonymous], 2000, QUANTUM PHASE TRANSI, DOI [DOI 10.1017/CBO9780511622540, DOI 10.1017/CBO9780511973765]
[4]  
[Anonymous], ARXIVCONDMAT0701608
[5]  
BEREZINSKII VL, 1971, SOV PHYS JETP-USSR, V32, P493
[6]   Metal theory [J].
Bethe, H. .
ZEITSCHRIFT FUR PHYSIK, 1931, 71 (3-4) :205-226
[7]   Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model [J].
Buonsante, P. ;
Vezzani, A. .
PHYSICAL REVIEW LETTERS, 2007, 98 (11)
[8]   NUMERICAL AND APPROXIMATE ANALYTICAL RESULTS FOR THE FRUSTRATED SPIN-1/2 QUANTUM SPIN CHAIN [J].
BURSILL, R ;
GEHRING, GA ;
FARNELL, DJJ ;
PARKINSON, JB ;
XIANG, T ;
ZENG, C .
JOURNAL OF PHYSICS-CONDENSED MATTER, 1995, 7 (45) :8605-8618
[9]   QUANTUM MAGNETISM OF CUGEO3 [J].
CASTILLA, G ;
CHAKRAVARTY, S ;
EMERY, VJ .
PHYSICAL REVIEW LETTERS, 1995, 75 (09) :1823-1826
[10]   Entanglement in the Majumdar-Ghosh model [J].
Chhajlany, Ravindra W. ;
Tomczak, Piotr ;
Wojcik, Antoni ;
Richer, Johannes .
PHYSICAL REVIEW A, 2007, 75 (03)