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arXiv:1804.10342

Effective field theoretical Study of the Susceptibilities of the Amplitude Mode in 2D dilute Boson gas

Ji-Chong Yang, Yu Shi

Published Apr 27, 2018• 0 citations
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Abstract

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 $O(2)$ model. We also study the scalar susceptibility proposed in the $O(2)$ model study, and find that in effective field theory, the scalar susceptibility is as same as the longitudinal susceptibility.

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arXiv:0907.2779•Physical Review A•Oct 28, 2009•49 citations
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.
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 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.
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.
The amplitude (Higgs) mode near the two-dimensional superfluid--Mott glass quantum phase transition is studied. We map the Bose-Hubbard Hamiltonian of disordered interacting bosons onto an equivalent classical XY\mathit{XY}XY model in (2+12+12+1) dimensions and compute the scalar susceptibility of the order parameter amplitude via Monte Carlo simulation. Analytic continuation of the scalar susceptibilities from imaginary to real frequency to obtain the spectral densities is performed by a modified maximum entropy technique. Our results show that the introduction of disorder into the system leads to unconventional dynamical behavior of the Higgs mode that violates naive scaling, despite the underlying thermodynamics of the transition being of the conventional power-law type. The computed spectral densities exhibit a broad, noncritical response for all energies, and a momentum-independent dispersion for long wavelengths, indicating strong evidence for the localization of the Higgs mode for all dilutions.
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.
In a Bose superfluid, the coupling between transverse (phase) and longitudinal fluctuations leads to a divergence of the longitudinal correlation function, which is responsible for the occurrence of infrared divergences in the perturbation theory and the breakdown of the Bogoliubov approximation. We report a nonperturbative renormalization-group calculation of the one-particle Green's function of an interacting boson system at zero temperature. We find two regimes separated by a characteristic momentum scale kG{k}_{G}kG​ (``Ginzburg'' scale). While the Bogoliubov approximation is valid at large momenta and energies, $|\mathbf{p}|,\text{ }|\ensuremath{\omega}|/c⪢{k}_{G}$ (with ccc as the velocity of the Bogoliubov sound mode), in the infrared (hydrodynamic) regime, $|\mathbf{p}|,\text{ }|\ensuremath{\omega}|/c⪡{k}_{G}$, the normal and anomalous self-energies exhibit singularities reflecting the divergence of the longitudinal correlation function. In particular, we find that the anomalous self-energy agrees with the Bogoliubov result ${\ensuremath{\Sigma}}_{\text{an}}(\mathbf{p},\ensuremath{\omega})\ensuremath{\simeq}\text{const}$ at high energies and behaves as ${\ensuremath{\Sigma}}_{\text{an}}(\mathbf{p},\ensuremath{\omega})\ensuremath{\sim}{({c}^{2}{\mathbf{p}}^{2}\ensuremath{-}{\ensuremath{\omega}}^{2})}^{(d\ensuremath{-}3)/2}$ in the infrared regime (with ddd as the space dimension), in agreement with the Nepomnyashchii identity ${\ensuremath{\Sigma}}_{\text{an}}(0,0)=0$ and the predictions of Popov's hydrodynamic theory. We argue that the hydrodynamic limit of the one-particle Green's function is fully determined by the knowledge of the exponent $3\ensuremath{-}d$ characterizing the divergence of the longitudinal susceptibility and the Ward identities associated to gauge and Galilean invariances. The infrared singularity of ${\ensuremath{\Sigma}}_{\text{an}}(\mathbf{p},\ensuremath{\omega})$ leads to a continuum of excitations (coexisting with the sound mode) which shows up in the one-particle spectral function.