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

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

References

[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)

[2] X. G. Wen, Vacuum degeneracy of chiral spin states in compactified space, Phys. Rev. B 40(10), 7387 (1989)

[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)

[4] A. Damascelli, Z. Hussain, and Z. X. Shen, Angleresolved photoemission studies of the cuprate supercon-ductors, Rev. Mod. Phys. 75(2), 473 (2003)

[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)

[6] W. Yang, Z. Y. Wang, and R. B. Liu, Preserving qubit coherence by dynamical decoupling, Front. Phys. 6(1), 2 (2011)

[7] S. Ryu and Y. Hatsugai, Topological origin of zeroenergy edge states in particle–hole symmetric systems, Phys. Rev. Lett. 89(7), 077002 (2002)

[8] M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)

[9] X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)

[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)

[11] B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors, New Jersey: Princeton University Press, 2013

[12] A. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Solitons in conducting polymers, Rev. Mod. Phys. 60(3), 781 (1988)

[13] S. Ryu and Y. Hatsugai, Entanglement entropy and the Berry phase in the solid state, Phys. Rev. B 73(24), 245115 (2006)

[14] C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95(22), 226801 (2005)

[15] C. L. Kane and E. J. Mele, Z₂ topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95(14), 146802 (2005)

[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)

[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)

[18] M. M. Vazifeh and M. Franz, Electromagnetic response of Weyl semimetals, Phys. Rev. Lett. 111(2), 027201 (2013)

[19] M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices, Oxford: Oxford University Press, 2012

[20] Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011)

[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)

[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)

[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)

[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)

[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)

[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)

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg