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arXiv:1804.10158 · International Journal of Modern Physics B

Higgs mode in (2 + 1)-dimensional O(2) model

Ji-Chong Yang, Yu Shi

Published Dec 23, 2021• 0 citations
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Abstract

In this paper, we investigate the spectral functions of the Higgs mode in [Formula: see text] model, which can be experimentally realized in a two-dimensional Bose gas. Zero temperature limit is considered. Our calculation fully includes the 2-loop contributions. Peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. Thus, this model cannot explain the disappearance of the response at the weak interaction limit. Neither it can explain the similarity between the longitudinal and the scalar susceptibilities in the visibility of the Higgs mode. A possible lower peak at about [Formula: see text] is also noted.

DOI
10.1142/s0217979221503331

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In this paper, we investigate the spectral functions of the Higgs mode in [Formula: see text] model, which can be experimentally realized in a two-dimensional Bose gas. Zero temperature limit is considered. Our calculation fully includes the 2-loop contributions. Peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. Thus, this model cannot explain the disappearance of the response at the weak interaction limit. Neither it can explain the similarity between the longitudinal and the scalar susceptibilities in the visibility of the Higgs mode. A possible lower peak at about [Formula: see text] is also noted.
We investigate the spectral functions of the Higgs mode in a 2D Bose gas by using O(2)O(2)O(2) model in the zero temperature limit. Our calculation is done up to the full 2-loop contributions as well as some higher order contributions. The peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. We point out that the zero temperature limit of O(2)O(2)O(2) model cannot explain the disappearance of the response at the weak interaction limit, and that to use the longitudinal or scalar susceptibility is irrelevant to the visibility of the Higgs mode. A possible lower peak at about 2mσ2m_{\sigma}2mσ​ is also noted.
We investigate the spectral function of the amplitude mode in 2D Boson gas using O(2)O(2)O(2) model without large-N expansion at zero temperature limit. We calculate the spectral function with full 2-loop contributions and with higher order contributions included. We find that both the peeks of the spectral function of the longitudinal susceptibility and the scalar susceptibility could show up. We argue that the visibility of the amplitude does not depend on the choice of the longitudinal or scalar susceptibility. We also find that the O(2)O(2)O(2) model at zero temperature limit cannot explain the disappearance of the response when the weakly interaction limit is approached, which was observed in the experiments. We also find there could be another smaller peek in the spectral function at about 2mσ2m_{\sigma}2mσ​.
We study the ``Higgs'' amplitude mode in the relativistic quantum O(N)\mathrm{O}(N)O(N) model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot--M\'endez-Galain--Wschebor approximation (which we generalize to compute four-point correlation functions), we compute the O(N)\mathrm{O}(N)O(N)-invariant scalar susceptibility at zero temperature in the vicinity of the quantum critical point. In the ordered phase, we find a well-defined Higgs resonance for N=2N=2N=2 and 3 and determine its universal properties. No resonance is found for $N\ensuremath{\ge}4$. In the disordered phase, the spectral function exhibits a threshold behavior with no Higgs-like peak. We also show that for N=2N=2N=2, the Higgs mode manifests itself as a very broad peak in the longitudinal susceptibility in spite of the infrared divergence of the latter. We compare our findings with results from quantum Monte Carlo simulations and $\ensuremath{\epsilon}=4\ensuremath{-}(d+1)$ expansion near d=3d=3d=3.
We study the ``Higgs'' amplitude mode in the relativistic quantum O(N)O(N)O(N) model in two space dimensions. Using the nonperturbative renormalization group we compute the O(N)O(N)O(N)-invariant scalar susceptibility in the vicinity of the zero-temperature quantum critical point. In the zero-temperature ordered phase, we find a well-defined Higgs resonance for N=2N=2N=2 with universal properties in agreement with quantum Monte Carlo simulations. The resonance persists at finite temperature below the Berezinskii-Kosterlitz-Thouless transition temperature. In the zero-temperature disordered phase, we find a maximum in the spectral function which is, however, not related to a putative Higgs resonance. Furthermore we show that the resonance is strongly suppressed for $N\ensuremath{\ge}3$.
We study the Higgs excitation in the Goldstone phase of the relativistic O(NNN) model in two spatial dimensions at zero temperature. The response functions of the order parameter, and its magnitude squared, become universal functions of frequency in the vicinity of the quantum critical point described by the Wilson-Fisher fixed point, and we compute them to next-to-leading order in 1/N1/N1/N. The Higgs particle has an infrared singular decay to gapless Goldstone excitations, and its response functions are characterized by a pole in the lower half of the complex frequency plane. The pole acquires a nonzero real part only at next-to-leading order in 1/N1/N1/N, demonstrating that the Higgs excitation has an oscillatory component even in the scaling limit. Both the real and imaginary parts of the pole position vanish with the correlation length exponent $\ensuremath{\nu}$ upon approaching the critical point. We present evidence that the spectral density of the O(NNN)-invariant amplitude-squared of the order parameter has a peak at a nonzero frequency in the scaling limit. We connect our results to recent experimental studies of the superfluid-insulator quantum phase transition of ultracold bosonic atoms in optical lattices.
We investigate the spectral function of the amplitude mode in 2D Boson gas using the effective field theory at zero temperature limit. We find that the effective field theory can explain the experimental features that the peek of the spectral function is a soft continuum, rather than a sharp peek, and becomes broadened and then vanishes when the system goes into the superfluid phase. These features cannot be explained by the O(2)O(2)O(2) model. We also study the scalar susceptibility proposed in the O(2)O(2)O(2) model study, and find that in effective field theory, the scalar susceptibility is as same as the longitudinal susceptibility.