Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Susceptibilities of the Amplitude Mode in 2D dilute Boson gas using in O(2) model up to 2-loop order

Ji-Chong Yang, Yu Shi

Published Apr 26, 2018• 0 citations
OpenAlex

Abstract

We investigate the spectral function of the amplitude mode in 2D Boson gas using $O(2)$ 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 $O(2)$ 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 $2m_{\sigma}$.

Related papers

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

Ji-Chong Yang, Yu Shi

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.

arXiv:1804.10342•Apr 27, 2018•0 citations

Susceptibilities of the Higgs Mode in a 2D dilute Bose gas

Ji-Chong Yang, Yu Shi

We investigate the spectral functions of the Higgs mode in a 2D Bose gas by using $O(2)$ 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 $O(2)$ 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 $2m_{\sigma}$ is also noted.

•Apr 26, 2018•0 citations

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

Ji-Chong Yang, Yu Shi

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.

arXiv:1804.10158•International Journal of Modern Physics B•Dec 23, 2021•0 citations

Higgs amplitude mode in the vicinity of a (2+1) -dimensional quantum critical point: A nonperturbative renormalization-group approach

Félix Rose, F. Léonard, N. Dupuis

We study the ``Higgs'' amplitude mode in the relativistic quantum $\mathrm{O}(N)$ 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 $\mathrm{O}(N)$-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 $N=2$ 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 $N=2$, 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 $d=3$.

arXiv:1503.08688•Physical Review B•Jun 1, 2015•52 citations

Infrared behavior in systems with a broken continuous symmetry: Classical O( N ) model versus interacting bosons

N. Dupuis

In systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued by infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result, the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O (N) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov's theory), large-N limit, and nonperturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale p{G}, below which the perturbative approach breaks down. Even though the action of (nonrelativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O(N) model and interacting bosons at zero temperature.

arXiv:1011.3324•Physical Review E•Mar 18, 2011•49 citations

Spectral and dynamic properties of a 2D Luttinger liquid with current-current interactions

J. W. Rasul, Yujoung Bai

We calculate the Green function, particle-hole susceptibility and Cooper pair susceptibility of a 2D Luttinger liquid that results from an electron gas with long-range current-current interactions. The Haldane bosonization scheme allows this model to be written in terms of boson operators, from which the required fermion operators are constructed. We find weakly decaying power law tails in the spectral function and a Kohn anomaly in the 2k F particle-hole susceptibility, but no divergence in the Cooper amplitude.

Journal of Physics Condensed Matter•Apr 25, 1994•0 citations
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 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 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.
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 systems with a spontaneously broken continuous symmetry, the perturbative loop expansion is plagued by infrared divergences due to the coupling between transverse and longitudinal fluctuations. As a result, the longitudinal susceptibility diverges and the self-energy becomes singular at low energy. We study the crossover from the high-energy Gaussian regime, where perturbation theory remains valid, to the low-energy Goldstone regime characterized by a diverging longitudinal susceptibility. We consider both the classical linear O (N) model and interacting bosons at zero temperature, using a variety of techniques: perturbation theory, hydrodynamic approach (i.e., for bosons, Popov's theory), large-N limit, and nonperturbative renormalization group. We emphasize the essential role of the Ginzburg momentum scale p{G}, below which the perturbative approach breaks down. Even though the action of (nonrelativistic) bosons includes a first-order time derivative term, we find remarkable similarities in the weak-coupling limit between the classical O(N) model and interacting bosons at zero temperature.
We calculate the Green function, particle-hole susceptibility and Cooper pair susceptibility of a 2D Luttinger liquid that results from an electron gas with long-range current-current interactions. The Haldane bosonization scheme allows this model to be written in terms of boson operators, from which the required fermion operators are constructed. We find weakly decaying power law tails in the spectral function and a Kohn anomaly in the 2k F particle-hole susceptibility, but no divergence in the Cooper amplitude.