Abelian-Higgs dualities in quantum defect-mediated melting phase transitions

量子物理学・ナノサイエンス第68回特別セミナー

概要

In the study of zero-temperature quantum phase transitions, instead of looking how symmetry is broken, it is often useful to see how symmetry can be restored by the condensation of topological defects. Through a duality mapping, Nambu-Goldstone modes are represented by gauge bosons, mediating long-range interactions between topological defects. When the latter condense, those bosons get a mass via the Anderson-Higgs mechanism, which signals the loss of rigidity and the restoration of symmetry.

I will first review the best-studied case: the 2+1D superfluid-insulator transitions where the defects are U(1) vortices. Consecutively several extensions are discussed: going to 3+1D where the defects are not point particles but strings, and quantum elasticity, which studies breaking of spatial translations and rotations.

• S. Sachev, Harvard University lecture notes http://qpt.physics.harvard.edu/phys268/Lec5_Boson_vortex_duality.pdf
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• A.J. Beekman et al., Physics Reports 683,1 (2017) arXiv:1603.04254
• A.J. Beekman, J. Nissinen, K. Wu and J. Zaanen, Physical Review B 96, 1651115 (2017) arXiv:1703.03157
• A.J. Beekman, G. Fejos -- arXiv:1903.05331

• 量子物理学・ナノサイエンス第68回特別セミナー

• 量子物理学・ナノサイエンス先端研究センター 主催
• 東京工業大学理学院・物理学系 共催