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Tuesday, November 3rd 2015

4:30 pm:

It is well known that spontaneous broken continuous symmetry leads to the existence of a massless bosonic excitation, which is called Nambu-Goldstone bosons(NGB). Examples of NGB are pions in high energy physics, phonons and magnons(spin wave) in condensed matter physics. NGB usually interact 'weakly' with other degrees of freedom, in the sense that only its gradient couples to other particles, and so they can survive. This is the so-called Adler's principle(or Adler zero). As first discovered by Adler, forward scattering amplitude of particles off a pion vanishes quadratically as the momentum of pions goes to zero. Similarly in condensed matter physics, phonons(or magnons) have vanishing coupling with electrons as the wavevector of phonons(or magnons) goes to zero. However, Adler's principle is not always true. There is a criterion [1], saying that if the broken symmetry generator doesn't commute with translations, the coupling is non-vanishing and sometimes it results in breakdown of Fermi liquid and overdamping of NGB. The case of non-vanishing coupling is relevant to nematic fermi fluid [2].

I will talk about:

(1)Introduction: Goldstone mode in phi-4 theory and why phonons and magnons are Goldstone modes. Goldstone theorem.

(2)Warm up: phonon-electron coupling.

(3)Major part: criterion of vanishing coupling (gradient coupling) between Goldstone bosons and electrons [1].

(4)More example: magnon-electron coupling in antiferromagnets [3][4].

(5)Comments: about long range interaction and Anderson-Higgs mechanism in superconductors.(if time permits)

[1] Haruki Watanabe and Ashvin Vishwanath, Proc. Natl. Acad. Sci. 111, 16314 (2014), http://arxiv.org/abs/1404.3728

[2] Vadim Oganesyan, Steven Kivelson, and Eduardo Fradkin, Phys. Rev. B 64, 195109 (2001)

[3] John R Schrieffer, Journal of Low Temperature Physics, 1995, 99(3-4): 397-402.

[4] Andrey V. Chubukov and Dirk K. Morr, Phys. Rep. 288, 355(1997)

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