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

arXiv:1503.08688 · Physical Review B

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

Published Jun 1, 2015• 52 citations
arXivHTMLPDF

Abstract

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 $d=3$.

DOI
10.1103/physrevb.91.224501

Related papers

Higgs amplitude mode in the vicinity of a (2+1) -dimensional quantum critical point

Adam Rançon, N. Dupuis

We study the ``Higgs'' amplitude mode in the relativistic quantum $O(N)$ model in two space dimensions. Using the nonperturbative renormalization group we compute the $O(N)$-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 $N=2$ 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 $N\ensuremath{\ge}3$.

arXiv:1402.3098•Physical Review B•May 6, 2014•57 citations

Spectral function of the Higgs mode in 4−ε dimensions

Yaniv Tenenbaum Katan, Daniel K. Podolsky

We investigate the amplitude (Higgs) mode of the relativistic $O\left(N\right)$ model in the vicinity of the Wilson-Fisher quantum critical point in $D=4\ensuremath{-}\ensuremath{\varepsilon}$ 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 $D\ensuremath{\rightarrow}3+1$ limit, evolving smoothly with dimensionality to become purely imaginary at $D=2+1$ in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ 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.

arXiv:1412.4546•Physical Review B•Feb 26, 2015•22 citations

Spectral functions of the Higgs mode near two-dimensional quantum critical points

Daniel K. Podolsky, Subir Sachdev A

We study the Higgs excitation in the Goldstone phase of the relativistic O($N$) 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 $1/N$. 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 $1/N$, 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($N$)-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.

arXiv:1205.2700•Physical Review B•Aug 10, 2012•111 citations

Fate of the Higgs Mode Near Quantum Criticality

Snir Gazit, Daniel K. Podolsky, Assa Auerbach

We study a relativistic O(N) model near the quantum critical point in 2 + 1 dimensions for N = 2 and N = 3. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a well-defined peak associated with the Higgs mode arbitrarily close to the critical point. The peak fidelity and the amplitude ratio between the critical energy scales on both sides of the transition are determined.

arXiv:1212.3759•Physical Review Letters•Apr 2, 2013•87 citations

Higgs Mode in a Two-Dimensional Superfluid

Lode Pollet, Nikolay V. Prokof'ev

We present solid evidence for the existence of a well-defined Higgs amplitude mode in two-dimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultracold (87)Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of a strong response is preserved.

arXiv:1204.5190•Physical Review Letters•Jul 6, 2012•108 citations

The Higgs Mode in Two Dimensional Superfluid

Nikolay V. Prokof'ev

We present solid evidence for the existence of a well-defined Higgs amplitude mode in twodimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz-invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultra-cold Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of strong response is preserved.

Bulletin of the American Physical Society•Mar 19, 2013•1 citation
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≥4N\ensuremath{\ge}4N\ensuremath≥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 \ensuremathϵ=4\ensuremath−(d+1)\ensuremath{\epsilon}=4\ensuremath{-}(d+1)\ensuremathϵ=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 investigate the amplitude (Higgs) mode of the relativistic O(N)O\left(N\right)O(N) model in the vicinity of the Wilson-Fisher quantum critical point in $D=4\ensuremath{-}\ensuremath{\varepsilon}$ 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 $D\ensuremath{\rightarrow}3+1$ limit, evolving smoothly with dimensionality to become purely imaginary at D=2+1D=2+1D=2+1 in the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ 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.
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 present solid evidence for the existence of a well-defined Higgs amplitude mode in two-dimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultracold (87)Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of a strong response is preserved.
We present solid evidence for the existence of a well-defined Higgs amplitude mode in twodimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid-Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz-invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultra-cold Rb atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of strong response is preserved.