Spectral function of the Higgs mode in 4ε dimensions

Yaniv Tenenbaum Katan and Daniel Podolsky
Phys. Rev. B 91, 075132 – Published 26 February 2015

Abstract

We investigate the amplitude (Higgs) mode of the relativistic ON model in the vicinity of the Wilson-Fisher quantum critical point in D=4ɛ space-time dimensions. We compute the universal part of the scalar spectral function near the transition, to leading nontrivial order in the ordered phase, and to next to leading order in both the disordered phase and the quantum critical regime. We find that, in the disordered phase, the spectral function has a threshold behavior with no Higgs-like peak, whereas in the ordered phase, the Higgs mode appears as a well defined resonance. The pole associated with this resonance is purely real in the D3+1 limit, evolving smoothly with dimensionality to become purely imaginary at D=2+1 in the N limit. Our results complement previous studies of the scalar spectral function, and demonstrate that the resonance found in these studies can indeed be directly identified with the Higgs mode.

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  • Received 16 December 2014
  • Revised 25 January 2015

DOI:https://doi.org/10.1103/PhysRevB.91.075132

©2015 American Physical Society

Authors & Affiliations

Yaniv Tenenbaum Katan and Daniel Podolsky

  • Physics Department, Technion – Israel Institute of Technology, Haifa 32000, Israel

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Issue

Vol. 91, Iss. 7 — 15 February 2015

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