“Symmetry-protected topological phases in SU(N) cold fermion systems” Keisuke Totsuka (YITP, Kyoto University)

Seminar Information:

• Speaker: Keisuke Totsuka, Yukawa Institute for Theoretical Physics, Kyoto University
• Date: Tuesday, 8^th November
• Time: 14:00-15:00
• Venue: D015, Lab1

“Symmetry-protected topological phases in SU(N) cold fermion systems

-- entanglement, order parameters, and group cohomology”

There are a variety of states of matter called “topological”, that defy the traditional Landau-type description based on broken symmetries and local order parameters.  Prototypical examples are fractional quantum Hall states and quantum spin liquids which are characterized by long-range entanglement and are known to host fractionalized exotic quasi-particles. The discovery of topological insulators/superconductors [1] sparked the study of another species of (interacting) topological phases, now dubbed “symmetry-protected topological (SPT)”, which is stable only in the presence of certain symmetries (e.g., time-reversal, reflection, space groups, etc.) [1,2].

In this talk, I show how various SPT phases appear in SU(N)-symmetric ultra-cold fermions [3] loaded in one-dimensional optical lattice and characterize these phases by using entanglement spectrum and other means [4].  An interesting connection between entanglement spectrum and non-local order parameters [5] will be discussed, too.  

[1] X-L. Qi and S-C. Zhang, Rev.Mod.Phys. 83, 1057 (2011).

[2] Z. Gu and X-G. Wen, Phys.Rev.B 80, 155131 (2009); F. Pollmann et al.,Phys.Rev.B 81, 064439 (2010)

[2] Z. Gu et al., Phys.Rev.B 83, 035107 (2011); ibid 87, 155114 (2013); A. Vishwanath and T.Senthil, Phys.Rev.X 3, 011016 (2013). 
[3] A.V. Gorshkov et al., Nat.Phys. 6, 289 (2010);  S. Taie et al., ibid., 8, 825 (2012); C.  Hofrichter et al., Phys. Rev. X, 6, 021030 (2016).
[4] H. Nonne et al., Europhys.Lett. 102, 37008 (2013); V. Bois et al., Phys.Rev.B 91, 075121 (2015); S. Capponi, P. Lecheminant, and K. Totsuka, Ann.Phys.367, 50 (2016).

[5] K. Tanimoto and K. Totsuka, arXiv:1508.07601

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