Detecting ground-state degeneracy in many-body systems through qubit decoherence

doi:10.1007/s11467-016-0641-y

Front. Phys.

2017, Vol. 12

Issue (1) : 120304 https://doi.org/10.1007/s11467-016-0641-y

RESEARCH ARTICLE

Detecting ground-state degeneracy in many-body systems through qubit decoherence

Hai-Tao Cui (崔海涛)^1,²(

),Xue-Xi Yi (衣学喜)²(

)

¹. School of Physics and Electric Engineering, Anyang Normal University, Anyang 455000, China
². Center for Quantum Sciences, Northeast Normal University, Changchun 130024, China

Download: PDF(7254 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

By coupling with a qubit, we demonstrate that qubit decoherence can unambiguously detect the occurrence of ground-state degeneracy in many-body systems. We first demonstrate universality using the two-band model. Consequently, several exemplifications, focused on topological condensed matter systems in one, two, and three dimensions, are presented to validate our proposal. The key point is that qubit decoherence varies significantly when energy bands touch each other at the Fermi surface. In addition, it can partially reflect the degeneracy inside the band. This feature implies that qubit decoherence can be used for reliable diagnosis of ground-state degeneracy.

Keywords decoherence quantum phase transition ground-state degeneracy

Corresponding Author(s): Hai-Tao Cui (崔海涛),Xue-Xi Yi (衣学喜)

Issue Date: 19 December 2016

Cite this article:

Hai-Tao Cui (崔海涛),Xue-Xi Yi (衣学喜). Detecting ground-state degeneracy in many-body systems through qubit decoherence[J]. Front. Phys. , 2017, 12(1): 120304.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-016-0641-y
https://academic.hep.com.cn/fop/EN/Y2017/V12/I1/120304

1	D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a twodimensional periodic potential, Phys. Rev. Lett. 49(6), 405 (1982) https://doi.org/10.1103/PhysRevLett.49.405
2	X. G. Wen, Vacuum degeneracy of chiral spin states in compactified space, Phys. Rev. B 40(10), 7387 (1989) https://doi.org/10.1103/PhysRevB.40.7387
3	X. G. Wen and Q. Niu, Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces, Phys. Rev. B 41(13), 9377 (1990) https://doi.org/10.1103/PhysRevB.41.9377
4	A. Damascelli, Z. Hussain, and Z. X. Shen, Angleresolved photoemission studies of the cuprate supercon-ductors, Rev. Mod. Phys. 75(2), 473 (2003) https://doi.org/10.1103/RevModPhys.75.473
5	H. T. Quan, Z. Song, X. F. Liu, P. Zanardi, and C. P. Sun, Decay of Loschmidt echo enhanced by quantum criticality, Phys. Rev. Lett. 96(14), 140604 (2006) https://doi.org/10.1103/PhysRevLett.96.140604
6	W. Yang, Z. Y. Wang, and R. B. Liu, Preserving qubit coherence by dynamical decoupling, Front. Phys. 6(1), 2 (2011) https://doi.org/10.1007/s11467-010-0113-8
7	S. Ryu and Y. Hatsugai, Topological origin of zeroenergy edge states in particle–hole symmetric systems, Phys. Rev. Lett. 89(7), 077002 (2002) https://doi.org/10.1103/PhysRevLett.89.077002
8	M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010) https://doi.org/10.1103/RevModPhys.82.3045
9	X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011) https://doi.org/10.1103/RevModPhys.83.1057
10	X. L. Qi, Y. S. Wu, and S. C. Zhang, Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors, Phys. Rev. B 74(8), 085308 (2006) https://doi.org/10.1103/PhysRevB.74.085308
11	B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors, New Jersey: Princeton University Press, 2013 https://doi.org/10.1515/9781400846733
12	A. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Solitons in conducting polymers, Rev. Mod. Phys. 60(3), 781 (1988) https://doi.org/10.1103/RevModPhys.60.781
13	S. Ryu and Y. Hatsugai, Entanglement entropy and the Berry phase in the solid state, Phys. Rev. B 73(24), 245115 (2006) https://doi.org/10.1103/PhysRevB.73.245115
14	C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95(22), 226801 (2005) https://doi.org/10.1103/PhysRevLett.95.226801
15	C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95(14), 146802 (2005) https://doi.org/10.1103/PhysRevLett.95.146802
16	S. Murakami, Phase transition between the quantum spin Hall and insulator phases in 3D: Emergence of a topological gapless phase, New J. Phys. 9(9), 356 (2007) https://doi.org/10.1088/1367-2630/9/9/356
17	X. G. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011) https://doi.org/10.1103/PhysRevB.83.205101
18	M. M. Vazifeh and M. Franz, Electromagnetic response of Weyl semimetals, Phys. Rev. Lett. 111(2), 027201 (2013) https://doi.org/10.1103/PhysRevLett.111.027201
19	M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices, Oxford: Oxford University Press, 2012 https://doi.org/10.1093/acprof:oso/9780199573127.001.0001
20	Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011) https://doi.org/10.1038/nature09887
21	G. C. Liu, S. L. Zhu, S. J. Jiang, F. D. Sun, and W. M. Liu, Simulating and detecting the quantum spin Hall effect in the Kagome optical lattice, Phys. Rev. A 82(5), 053605 (2010) https://doi.org/10.1103/PhysRevA.82.053605
22	L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice, Nature 483(7389), 302 (2012) https://doi.org/10.1038/nature10871
23	G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, Experimental realization of the topological Haldane model with ultracold fermins, Nature 515(7526), 237 (2014) https://doi.org/10.1038/nature13915
24	L. Duca, T. Li, M. Reitter, I. Bloch, M. Schleier- Smith, and U. Schneider, An Aharanov–Bohm interferometer for determining Bloch band topology, Science 347(6219), 288 (2015) https://doi.org/10.1126/science.1259052
25	X. X. Yi, H. T. Cui, and L. C. Wang, Entanglement induced in spin-1/2 particles by a spin chain near its critical points, Phys. Rev. A 74(5), 054102 (2006) https://doi.org/10.1103/PhysRevA.74.054102
26	A. Abliz, H. J. Gao, X. C. Xie, Y. S. Wu, and W. M. Liu, Entanglement control in an anisotropic two-qubit Heisenberg XYZmodel with external magnetic fields, Phys. Rev. A 74(5), 052105 (2006) https://doi.org/10.1103/PhysRevA.74.052105

[1]	Ai-Yuan Hu, Lin Wen, Guo-Pin Qin, Zhi-Min Wu, Peng Yu, Yu-Ting Cui. Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature[J]. Front. Phys. , 2019, 14(5): 53601-.
[2]	Ai-Yuan Hu, Huai-Yu Wang. Phase transition of the frustrated antiferromagntic J₁-J₂-J₃ spin-1/2 Heisenberg model on a simple cubic lattice[J]. Front. Phys. , 2019, 14(1): 13605-.
[3]	Zhi Lin, Wanli Liu. Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices[J]. Front. Phys. , 2018, 13(5): 136402-.
[4]	Kai-Tong Wang, Fuming Xu, Yanxia Xing, Hong-Kang Zhao. Evolution of individual quantum Hall edge states in the presence of disorder[J]. Front. Phys. , 2018, 13(4): 137306-.
[5]	Zhi Lin, Jun Zhang, Ying Jiang. Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method[J]. Front. Phys. , 2018, 13(4): 136401-.
[6]	V. R. Shaginyan,A. Z. Msezane,G. S. Japaridze,K. G. Popov,V. A. Khodel. Strongly correlated Fermi systems as a new state of matter[J]. Front. Phys. , 2016, 11(5): 117103-.
[7]	V. R. Shaginyan,A. Z. Msezane,G. S. Japaridze,K. G. Popov,J. W. Clark,V. A. Khodel. Scaling behavior of the thermopower of the archetypal heavy-fermion metal YbRh₂Si₂[J]. Front. Phys. , 2016, 11(2): 117102-.
[8]	Bao An（保安）,Chen Yao-Hua（陈耀华）,Lin Heng-Fu（林恒福）,Liu Hai-Di（刘海迪）,Zhang Xiao-Zhong（章晓中）. Quantum phase transitions in two-dimensional strongly correlated fermion systems[J]. Front. Phys. , 2015, 10(5): 106401-.
[9]	Qiao Bi. Quantum computation in triangular decoherence-free subdynamic space[J]. Front. Phys. , 2015, 10(2): 100304-.
[10]	Wenxi Lai, Chao Zhang, Zhongshui Ma. Single molecular shuttle-junction: Shot noise and decoherence[J]. Front. Phys. , 2015, 10(1): 108501-.
[11]	Hong-Yi Fan, Shuai Wang, Li-Yun Hu. Evolution of the single-mode squeezed vacuum state in amplitude dissipative channel[J]. Front. Phys. , 2014, 9(1): 74-81.
[12]	Yao-hua Chen, Wei Wu, Guo-cai Liu, Hong-shuai Tao, Wu-ming Liu. Quantum phase transition of cold atoms trapped in optical lattices[J]. Front. Phys. , 2012, 7(2): 223-234.
[13]	Shi-jian Gu. Entropy majorization, thermal adiabatic theorem, and quantum phase transitions[J]. Front. Phys. , 2012, 7(2): 244-251.
[14]	Alice Sinatra, Jean-Christophe Dornstetter, Yvan Castin. Spin squeezing in Bose–Einstein condensates: Limits imposed by decoherence and non-zero temperature[J]. Front. Phys. , 2012, 7(1): 86-97.
[15]	Wen YANG, Zhen-Yu WANG, Ren-Bao LIU. Preserving qubit coherence by dynamical decoupling[J]. Front. Phys. , 2011, 6(1): 2-14.

Viewed

Full text

Abstract

Cited

Shared

Discussed