Universal Properties of the Higgs Resonance in (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-Dimensional U(1) Critical Systems

Chen, Kun; Liu, Longxiang; Deng, Youjin; Pollet, Lode; Prokof’ev, Nikolay

doi:10.1103/physrevlett.110.170403

Cited by 47 publications

(78 citation statements)

References 26 publications

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“…In the disordered phase, we have found that the scalar spectral function has a threshold at ω = 2∆ and no Higgs-like peak. This outcome is in disagreement with a previous QMC analysis which found a peak close to the threshold, which was interpreted as a precursor to the Higgs mode in the disordered phase 23 . A weak peak in the spectral function was also found in a separate QMC analysis 25 , as well as in a NPRG calculation 26 .…”

Section: Summary and Discussioncontrasting

confidence: 99%

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Spectral function of the Higgs mode in4−εdimensions

Katan

Podolsky

2015

Phys. Rev. B

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We investigate the amplitude (Higgs) mode of the relativistic O (N ) model in the vicinity of the Wilson-Fisher quantum critical point in D = 4 − ε spacetime dimensions. We compute the universal part of the scalar spectral function near the transition, to leading non-trivial 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 → 3 + 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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Section: Summary and Discussioncontrasting

confidence: 99%

“…For ε 1, we find indirect evidence for a peak in the spectral function at ω of order T , which may agree with Ref. 23 , although for ε = 1 no such peak is seen. Instead, only a threshold-like behavior is observed at low frequencies.…”

Section: Summary and Discussionsupporting

confidence: 92%

Spectral function of the Higgs mode in4−εdimensions

Katan

Podolsky

2015

Phys. Rev. B

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“…Precisely this type of response is measured in the lattice shaking experiment near the superfluid to Mott insulator transition performed by Endres etal 6 . As a result, a sharp peak due to a Higgs excitation appears even in 2D, as supported by a detailed theoretical analysis of this problem, both numerically 5,19,20 and analytically 21 . In particular, the Higgs mode remains well defined even near the quantum critical point because both its energy and width vanish with the same power in the distance from the critical point 5,[19][20][21][22] .…”

Section: Introductionmentioning

confidence: 74%

Higgs mode and magnon interactions in 2D quantum antiferromagnets from Raman scattering

Weidinger

Zwerger

2015

Eur. Phys. J. B

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We present a theory for Raman scattering on 2D quantum antiferromagnets. The microscopic Fleury-Loudon Hamiltonian is expressed in terms of an effective O(3) -model. Well within the Néel ordered phase, the Raman spectrum contains a two-magnon and a two-Higgs contribution, which are calculated diagramatically. The vertex functions for both the Higgs and magnon contributions are determined from a numerical solution of the corresponding Bethe-Salpeter equation. Due to the momentum dependence of the Raman vertex in the relevant B1g + E2g symmetry, the contribution from the Higgs mode is strongly suppressed. Except for intermediate values of the Higgs mass, it does not show up as separate peak in the spectrum but gives rise to a broad continuum above the dominant contribution from two-magnon excitations. The latter give rise to a broad, asymmetric peak at ω 2.44 J, which is a result of magnon-magnon interactions mediated by the Higgs mode. The full Raman spectrum is determined completely by the antiferromagnetic exchange coupling J and a dimensionless Higgs mass. Experimental Raman spectra of undoped cuprates turn out to be in very good agreement with the theory only with inclusion of the Higgs contribution. They thus provide a clear signature of the presence of a Higgs mode in spin one-half 2D quantum antiferromagnets.

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“…Specifically, at the low dimensions, such fluctuations enhance the decay channel of a Higgs mode into two NG modes so strongly that the Higgs mode is not necessarily well defined [29,[32][33][34][35][36][37][38][39][40]. Hence, in the following, we only consider the case of d = 3, where the Higgs mode is known to be long-lived [29,41,42] so that the use of the two methods is well justified.…”

Section: Methodsmentioning

confidence: 99%

Localized Higgs modes of superfluid Bose gases in optical lattices: A Gutzwiller mean-field study

Danshita

Tsuchiya

2017

Phys. Rev. A

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We study effects of a potential barrier on collective modes of superfluid Bose gases in optical lattices. We assume that the barrier is created by local suppression of the hopping amplitude. When the system is in a close vicinity of the Mott transition at commensurate fillings, where an approximate particle-hole symmetry emerges, there exist bound states of Higgs amplitude mode that are localized around the barrier. By applying the Gutzwiller mean-field approximation to the Bose-Hubbard model, we analyze properties of normal modes of the system with a special focus on the Higgs bound states. We show that when the system becomes away from the Mott transition point, the Higgs bound states turn into quasi-bound states due to inevitable breaking of the particlehole symmetry. We use a stabilization method to compute the resonance energy and line width of the quasi-bound states. We compare the results obtained by the Gutzwiller approach with those by the Ginzburg-Landau theory. We find that the Higgs bound states survive even in a parameter region far from the Mott transition, where the Ginzburg-Landau theory fails.

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Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems

Cited by 47 publications

References 26 publications

Spectral function of the Higgs mode in4−εdimensions

Spectral function of the Higgs mode in4−εdimensions

Higgs mode and magnon interactions in 2D quantum antiferromagnets from Raman scattering

Localized Higgs modes of superfluid Bose gases in optical lattices: A Gutzwiller mean-field study

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