Bound states of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>model via the nonperturbative renormalization group

Rose, Félix; Benitez, Federico; Léonard, Frédéric; Delamotte, Bertrand

doi:10.1103/physrevd.93.125018

Cited by 26 publications

(31 citation statements)

References 64 publications

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“…21 There have been some attempts at constructing two-particle bound states in φ 4 -theory using different techniques, see [64][65][66][67][68] for an incomplete list. Conversely, it has also been claimed that such bound states do not exist [69]. Our simple scaling argument supports the latter option.…”

Section: Comments On the Non-gravitational Theorysupporting

confidence: 81%

A conjecture on the minimal size of bound states

et al. 2020

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We conjecture that, in a renormalizable effective quantum field theory where the heaviest stable particle has mass m , there are no bound states with radius below 1/m (Bound State Conjecture). We are motivated by the (scalar) Weak Gravity Conjecture, which can be read as a statement forbidding certain bound states. As we discuss, versions for uncharged particles and their generalizations have shortcomings.This leads us to the suggestion that one should only constrain rather than exclude bound objects. In the gravitational case, the resulting conjecture takes the sharp form of forbidding the adiabatic construction of black holes smaller than 1/m . But this minimal bound-state radius remains non-trivial as M P → ∞ , leading us to suspect a feature of QFT rather than a quantum gravity constraint. We find support in a number of examples which we analyze at a parametric level.

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Section: Comments On the Non-gravitational Theorysupporting

confidence: 81%

A conjecture on the minimal size of bound states

et al. 2020

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“…2 we show the real-frequency conductivity σ(ω) obtained from σ k=0 (iω n ) by analytical continuation using Padé approximants, 24 a method which has proven to be re-liable in the NPRG approach. 10,25,26 As expected, the system is insulating. The real part of the conductivity vanishes below the two-particle excitation gap 2∆ and the system behaves as a perfect capacitor for |ω| ∆, i.e.…”

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confidence: 78%

Superuniversal transport near a (2+1) -dimensional quantum critical point

Rose

Dupuis

2017

Phys. Rev. B

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We compute the zero-temperature conductivity in the two-dimensional quantum O(N ) model using a nonperturbative functional renormalization-group approach. At the quantum critical point we find a universal conductivity σ * /σ Q (with σ Q = q 2 /h the quantum of conductance and q the charge) in reasonable quantitative agreement with quantum Monte Carlo simulations and conformal bootstrap results. In the ordered phase the conductivity tensor is defined, when N ≥ 3, by two independent elements, σA(ω) and σB(ω), respectively associated with SO(N ) rotations which do and do not change the direction of the order parameter. Whereas σA(ω → 0) corresponds to the response of a superfluid (or perfect inductance), the numerical solution of the flow equations shows that limω→0 σB(ω)/σ Q = σ * B /σ Q is a superuniversal (i.e. N -independent) constant. These numerical results, as well as the known exact value σ * B /σ Q = π/8 in the large-N limit, allow us to conjecture that σ * B /σ Q = π/8 holds for all values of N , a result that can be understood as a consequence of gauge invariance and asymptotic freedom of the Goldstone bosons in the low-energy limit.

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“…The one-loop correction to the bare effective actionΓ Λ [φ, A] = S[φ, A]can be retrieved from the exact flow equation(58) by replacing Γ S(2,0) in the rhs, i.e.,…”

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confidence: 99%

Nonperturbative functional renormalization-group approach to transport in the vicinity of a(2+1)-dimensional O(N)-symmetric quantum critical point

Rose

Dupuis

2017

Phys. Rev. B

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Using a nonperturbative functional renormalization-group approach to the two-dimensional quantum O(N ) model, we compute the low-frequency limit ω → 0 of the zero-temperature conductivity in the vicinity of the quantum critical point. Our results are obtained from a derivative expansion to second order of a scale-dependent effective action in the presence of an external (i.e., non-dynamical) non-Abelian gauge field. While in the disordered phase the conductivity tensor σ(ω) is diagonal, in the ordered phase it is defined, when N ≥ 3, by two independent elements, σ A (ω) and σ B (ω), respectively associated to SO(N ) rotations which do and do not change the direction of the order parameter. For N = 2, the conductivity in the ordered phase reduces to a single component σ A (ω). We show that limω→0 σ(ω, δ)σ A (ω, −δ)/σ 2 q is a universal number which we compute as a function of N (δ measures the distance to the quantum critical point, q is the charge and σq = q 2 /h the quantum of conductance). On the other hand we argue that the ratio σ B (ω → 0)/σq is universal in the whole ordered phase, independent of N and, when N → ∞, equal to the universal conductivity σ * /σq at the quantum critical point.

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Bound states of theϕ4model via the nonperturbative renormalization group

Cited by 26 publications

References 64 publications

A conjecture on the minimal size of bound states

A conjecture on the minimal size of bound states

Superuniversal transport near a (2+1) -dimensional quantum critical point

Nonperturbative functional renormalization-group approach to transport in the vicinity of a(2+1)-dimensional O(N)-symmetric quantum critical point

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