Spectral function of the Higgs mode in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>4</mml:mn><mml:mo>−</mml:mo><mml:mi>ε</mml:mi></mml:math>dimensions

Katan, Yaniv Tenenbaum; Podolsky, Daniel K.

doi:10.1103/physrevb.91.075132

Cited by 26 publications

(66 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2(b) we compare the extrapolated Higgs energies in the AFM phase with the triplet gaps in the QD phase at the same distance, |g − g c |/g c , from the QCP. The predicted √ 2 ratio [44,46,48] between ∆ H and ∆ T is clearly obeyed over this rather broad coupling range. We stress that this relation implies the presence of equivalent multiplicative log corrections [Eq.…”

Section: Fig 1 Schematic Representation Of Ground States Excitationmentioning

confidence: 81%

“…In the AFM phase, this gap corresponds to the lowest Goldstone mode, which has only a finite-size energy proportional to 1/N . Thus S(Q, τ ) decays very slowly with τ in this case and the dominant Goldstone contribution threatens to obscure the Higgs contribution [14][15][16][17]44]. Examples of imaginary-time data for S(Q, τ ) and of gap extractions are presented in Secs.…”

Section: Fig 1 Schematic Representation Of Ground States Excitationmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

et al. 2017

View full text Add to dashboard Cite

The amplitude ("Higgs") mode is a ubiquitous collective excitation related to spontaneous breaking of a continuous symmetry. We combine quantum Monte Carlo (QMC) simulations with stochastic analytic continuation to investigate the dynamics of the amplitude mode in a three-dimensional dimerized quantum spin system. We characterize this mode by calculating the spin and dimer spectral functions on both sides of the quantum critical point, finding that both the energies and the intrinsic widths of the excitations satisfy field-theoretical scaling predictions. While the line width of the spin response is close to that observed in neutron scattering experiments on TlCuCl3, the dimer response is significantly broader. Our results demonstrate that highly non-trivial dynamical properties are accessible by modern QMC and analytic continuation methods.The spontaneous breaking of a continuous symmetry allows collective excitations of the direction and amplitude of the order parameter; for O(N ) symmetry, there are N−1 massless directional (Goldstone) modes and one massive amplitude mode [1][2][3][4]. In loose analogy with the Standard Model, the latter is often called a Higgs mode. A strongly damped amplitude mode has been reported in two dimensions (2D) at the Mott transition of ultracold bosons [5] and at the disorder-driven superconductorinsulator transition [6,7]. In 3D, the amplitude mode is expected on theoretical grounds to be more robust, and indeed the cleanest observation to date of a "Higgs boson" in condensed matter is at the pressure-induced magnetic quantum phase transition (QPT) in the dimerized quantum antiferromagnet TlCuCl 3 [8][9][10].Below the upper critical number of space-time dimensions, which for an O(N ) model is D c = 4, the amplitude mode is unstable, decaying primarily into pairs of Goldstone bosons [11][12][13]. In both 2D and 3D, the longitudinal dynamic susceptibility exhibits an infrared singularity due to the Goldstone modes [14], whose consequences for the visibility of the amplitude mode have been investigated extensively in 2D [15][16][17]. It was noted [14] that the scalar O(N )-symmetric susceptibility remains uncontaminated by infrared contributions, which should permit the amplitude mode to be observed as a welldefined peak. The (3+1)D O(3) case of TlCuCl 3 is at D c and the amplitude mode is critically damped, meaning that its width is proportional to its energy at the meanfield level [9,[18][19][20]. This mode can be probed through the spin response (longitudinal susceptibility) by neutron spectroscopy, and measurements over a wide range of pressures reveal a rather narrow peak width of just 15% of the excitation energy [10]. The value of this nearconstant width-to-energy ratio is the key to the mode visibility, thus calling for unbiased numerical calculations in suitable model Hamiltonians.FIG. 1. Schematic representation of ground states, excitation processes, and corresponding gaps in a dimerized antiferromagnet. The ratio g = J /J of the intra-and inter-dimer coupling constants ...

show abstract

Section: Fig 1 Schematic Representation Of Ground States Excitationmentioning

confidence: 81%

Section: Fig 1 Schematic Representation Of Ground States Excitationmentioning

confidence: 99%

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

et al. 2017

View full text Add to dashboard Cite

show abstract

“…IVA), we consider only the Higgs contributions to χ ϕ 2 ϕ 2 at order α; an alternative derivation may be found in Refs. [20,30]. We note first that…”

Section: B Scalar Response Functionmentioning

confidence: 86%

“…The weakness of QFTs is that, as effective low-energy, long-wavelength theories, their connection to real systems is only through phenomenological parameters, and thus it is essential to benchmark them against numerical and experimental realizations. Indeed the effective O(3), d = 3 + 1 QFT has already been used to provide an accurate analytical description of the critical properties observed in TlCuCl 3 [13,[28][29][30][31][32]. Numerically, the method of choice for computing the properties of the unfrustrated QAF is Quantum Monte Carlo (QMC), with which recent large-scale simulations of the 3D dimerized QAF across the quantum critical regime have been performed for S = 1/2 spins with Heisenberg interactions on the double-cubic geometry depicted in Fig.…”

Section: Introductionmentioning

confidence: 99%

Unifying static and dynamic properties in three-dimensional quantum antiferromagnets

et al. 2017

View full text Add to dashboard Cite

Quantum Monte Carlo simulations offer an unbiased means to study the static and dynamic properties of quantum critical systems, while quantum field theory provides direct analytical results. We study three dimensional, critical quantum antiferromagnets by performing a combined analysis using both quantum field theory calculations and quantum Monte Carlo data. Explicitly, we analyze the order parameter (staggered magnetization), Néel temperature, quasiparticle gaps, and the susceptibilities in the scalar and vector channels. We connect the two approaches by deriving descriptions of the quantum Monte Carlo observables in terms of the quasiparticle excitations of the field theory. The remarkable agreement not only unifies the description of the static and dynamic properties of the system, but also constitutes a thorough test of perturbative O(3) quantum field theory and opens new avenues for the analytical guidance of detailed numerical studies.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Spectral function of the Higgs mode in4−εdimensions

Cited by 26 publications

References 36 publications

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

Unifying static and dynamic properties in three-dimensional quantum antiferromagnets

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

Contact Info

Product

Resources

About