Ground-state information geometry and quantum criticality in an inhomogeneous spin model

doi:10.1088/1674-1056/24/9/090301

中国物理B ›› 2015, Vol. 24 ›› Issue (9): 90301-090301.doi: 10.1088/1674-1056/24/9/090301

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

马余全

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

收稿日期:2015-03-24 修回日期:2015-05-27 出版日期:2015-09-05 发布日期:2015-09-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11404023 and 11347131).

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

Ma Yu-Quan (马余全)

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received:2015-03-24 Revised:2015-05-27 Online:2015-09-05 Published:2015-09-05
Contact: Ma Yu-Quan E-mail:yqma@bistu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11404023 and 11347131).

摘要/Abstract

摘要： We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S¹, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter J_a=J_b, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase.

关键词: quantum geometry tensor, topological order, quantum phase transition

Abstract: We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S¹, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter J_a=J_b, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase.

Key words: quantum geometry tensor, topological order, quantum phase transition

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

75.10.Pq (Spin chain models) 73.43.Nq (Quantum phase transitions) 05.70.Jk (Critical point phenomena)

马余全. Ground-state information geometry and quantum criticality in an inhomogeneous spin model[J]. 中国物理B, 2015, 24(9): 90301-090301.

Ma Yu-Quan (马余全). Ground-state information geometry and quantum criticality in an inhomogeneous spin model[J]. Chin. Phys. B, 2015, 24(9): 90301-090301.

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Ground-state information geometry and quantum criticality in an inhomogeneous spin model

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

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