arXiv subjects

Nicolas Dupuis

Publications and source records attributed to Nicolas Dupuis.

35 records · Page 2Linked to original sources

arXiv2023

Tan's two-body contact in a planar Bose gas: experiment vs theory

We determine the two-body contact in a planar Bose gas confined by a transverse harmonic potential, using the nonperturbative functional renormalization group. We use the three-dimensional thermodynamic definition of the contact where the latter is related to the derivation of the pressure of the quasi-two-dimensional system with respect to the three-dimensional scattering length of the bosons. Without any free parameter, we find a remarkable agreement with the experimental data of Zou {\it et al.} [Nat. Comm. {\bf 12}, 760 (2021)] from low to high temperatures, including the vicinity of the Berezinskii-Kosterlitz-Thouless transition. We also show that the short-distance behavior of the pair distribution function and the high-momentum behavior of the momentum distribution are determined by two contacts: the three-dimensional contact for length scales smaller than the characteristic length $\ell_z=\sqrt{\hbar/mω_z}$ of the harmonic potential and, for length scales larger than $\ell_z$, an effective two-dimensional contact, related to the three-dimensional one by a geometric factor depending on $\ell_z$.

cond-mat.quant-gas↗

arXiv2023

Automated Code generation for Information Technology Tasks in YAML through Large Language Models

The recent improvement in code generation capabilities due to the use of large language models has mainly benefited general purpose programming languages. Domain specific languages, such as the ones used for IT Automation, have received far less attention, despite involving many active developers and being an essential component of modern cloud platforms. This work focuses on the generation of Ansible-YAML, a widely used markup language for IT Automation. We present Ansible Wisdom, a natural-language to Ansible-YAML code generation tool, aimed at improving IT automation productivity. Ansible Wisdom is a transformer-based model, extended by training with a new dataset containing Ansible-YAML. We also develop two novel performance metrics for YAML and Ansible to capture the specific characteristics of this domain. Results show that Ansible Wisdom can accurately generate Ansible script from natural language prompts with performance comparable or better than existing state of the art code generation models. In few-shot settings we asses the impact of training with Ansible, YAML data and compare with different baselines including Codex-Davinci-002. We also show that after finetuning, our Ansible specific model (BLEU: 66.67) can outperform a much larger Codex-Davinci-002 (BLEU: 50.4) model, which was evaluated in few shot settings.

cs.SE↗

arXiv2022

Operator product expansion coefficients from the nonperturbative functional renormalization group

Using the nonperturbative functional renormalization group (FRG) within the Blaizot-Méndez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient $c_{112}$ associated with the operators $\mathcal{O}_1\simφ$ and $\mathcal{O}_2\simφ^2$ in the three-dimensional $\mathrm{O}(N)$ universality class and in the Ising universality class ($N=1$) in dimensions $2 \leq d \leq 4$. When available, exact results and estimates from the conformal bootstrap and Monte-Carlo simulations compare extremely well to our results, while FRG is able to provide values across the whole range of $d$ and $N$ considered.

hep-th↗

arXiv2022

Flowing bosonization in the nonperturbative functional renormalization-group approach

Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the "density" field $φ$ and its conjugate partner, the phase $\vartheta$ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for $\vartheta$ and $φ$ to remain conjugate variables at all energy scales, one must dynamically redefine the field $\vartheta$ along the renormalization-group flow. We derive explicit flow equations using a derivative expansion of the scale-dependent effective action to second order and show that they reproduce the flow equations of the sine-Gordon model (obtained by integrating out the field $\vartheta$ from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field $\vartheta$ do we obtain the standard phenomenology of the Luttinger liquid (when the periodic potential is sufficiently weak so as to avoid the Mott-insulating phase) characterized by two low-energy parameters, the velocity of the sound mode and the renormalized Luttinger parameter.

cond-mat.quant-gas↗

arXiv2022

Physical properties of the massive Schwinger model from the nonperturbative functional renormalization group

We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio $m/e$ between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fractional charges and deconfinement occur only at infinite temperature. Our results exemplify the possibility to obtain virtually all physical properties of an interacting system from the functional renormalization group.

hep-th↗

arXiv2021

Chaos in the Bose-glass phase of a one-dimensional disordered Bose fluid

We show that the Bose-glass phase of a one-dimensional disordered Bose fluid exhibits a chaotic behavior, i.e., an extreme sensitivity to external parameters. Using bosonization, the replica formalism and the nonperturbative functional renormalization group, we find that the ground state is unstable to any modification of the disorder configuration ("disorder" chaos) or variation of the Luttinger parameter ("quantum" chaos, analog to the "temperature" chaos in classical disordered systems). This result is obtained by considering two copies of the system, with slightly different disorder configurations or Luttinger parameters, and showing that inter-copy statistical correlations are suppressed at length scales larger than an overlap length $ξ_{\mathrm{ov}}\sim |ε|^{-1/α}$ ($|ε|\ll 1$ is a measure of the difference between the disorder distributions or Luttinger parameters of the two copies). The chaos exponent $α$ can be obtained by computing $ξ_{\mathrm{ov}}$ or by studying the instability of the Bose-glass fixed point for the two-copy system when $ε\neq 0$. The renormalized, functional, inter-copy disorder correlator departs from its fixed-point value -- characterized by cuspy singularities -- via a chaos boundary layer, in the same way as it approaches the Bose-glass fixed point when $ε=0$ through a quantum boundary layer. Performing a linear analysis of perturbations about the Bose-glass fixed point, we find $α=1$.

cond-mat.quant-gas↗

arXiv2020

Is there a Mott-glass phase in a one-dimensional disordered quantum fluid with linearly confining interactions?

We study a one-dimensional disordered quantum fluid with linearly confining interactions (disordered Schwinger model) using bosonization and the nonperturbative functional renormalization group. We find that the long-range interactions make the Anderson insulator (or, for bosons, the Bose-glass) fixed point (corresponding to a compressible state with a gapless optical conductivity) unstable, even if the latter may control the flow at intermediate energy scales. The stable fixed point describes an incompressible ground state with a gapped optical conductivity similar to a Mott insulator. These results disagree with the Gaussian variational method that predicts a Mott glass, namely a state with vanishing compressibility but a gapless optical conductivity.

cond-mat.quant-gas↗

arXiv2020

Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach

We present a path integral formalism for expressing matrix elements of the density matrix of a quantum many-body system between any two coherent states in terms of standard Matsubara action with periodic(anti-periodic) boundary conditions on bosonic(fermionic) fields. We show that this enables us to express several entanglement measures for bosonic/fermionic many-body systems described by a Gaussian action in terms of the Matsubara Green function. We apply this formalism to compute various entanglement measures for the two-dimensional Bose-Hubbard model in the strong-coupling regime, both in the presence and absence of Abelian and non-Abelian synthetic gauge fields, within a strong coupling mean-field theory. In addition, our method provides an alternative formalism for addressing time evolution of quantum-many body systems, with Gaussian actions, driven out of equilibrium without the use of Keldysh technique. We demonstrate this by deriving analytical expressions of the return probability and the counting statistics of several operators for a class of integrable models represented by free Dirac fermions subjected to a periodic drive in terms of the elements of their Floquet Hamiltonians. We provide a detailed comparison of our method with the earlier, related, techniques used for similar computations, discuss the significance of our results, and chart out other systems where our formalism can be used.

cond-mat.str-el↗

arXiv2020

Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets

We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale $k$, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter $K_k\sim k^θ$ that vanishes with an exponent $θ=z-1$ related to the dynamical critical exponent $z$. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics and yields a (dissipative) conductivity vanishing as $ω^2$ in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks" or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

cond-mat.quant-gas↗

arXiv2019

Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid

We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsible for the $ω^2$ behavior of the (dissipative) conductivity in the low-frequency limit. These results can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.

cond-mat.quant-gas↗

arXiv2018

Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions

We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot--Mendéz-Galain--Wschebor approximation scheme). As an application we consider the two-dimensional quantum O($N$) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular we show how, using Padé approximants to perform the analytic continuation $iω_n\toω+i0^+$ of imaginary frequency correlation functions $χ(iω_n)$ computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.

cond-mat.stat-mech↗

arXiv2018

Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems

We study the quasi-two-dimensional quantum O(2) model, a quantum generalization of the Lawrence-Doniach model, within the nonperturbative renormalization-group approach and propose a generic phase diagram for layered three-dimensional systems with an O(2)-symmetric order parameter. Below the transition temperature we identify a wide region of the phase diagram where the renormalization-group flow is quasi-two-dimensional for length scales smaller than a Josephson length $l_J$, leading to signatures of Kosterlitz-Thouless physics in the temperature dependence of physical observables. In particular the order parameter varies as a power law of the interplane coupling with an exponent which depends on the anomalous dimension (itself related to the stiffness) of the strictly two-dimensional low-temperature Kosterlitz-Thouless phase.

cond-mat.stat-mech↗

arXiv2017

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

We compute the zero-temperature conductivity in the two-dimensional quantum $\mathrm{O}(N)$ 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 $N\geq 3$, by two independent elements, $σ_{\mathrm{A}}(ω)$ and $σ_{\mathrm{B}}(ω)$, respectively associated to $\mathrm{O}(N)$ rotations which do and do not change the direction of the order parameter. Whereas $σ_{\mathrm{A}}(ω\to 0)$ corresponds to the response of a superfluid (or perfect inductance), the numerical solution of the flow equations shows that $\lim_{ω\to 0}σ_{\mathrm{B}}(ω)/σ_Q=σ_{\mathrm{B}}^*/σ_Q$ is a superuniversal (i.e. $N$-independent) constant. These numerical results, as well as the known exact value $σ_{\mathrm{B}}^*/σ_Q=π/8$ in the large-$N$ limit, allow us to conjecture that $σ_{\mathrm{B}}^*/σ_Q=π/8$ 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.

cond-mat.str-el↗

arXiv2017

Quantum criticality at the superconductor to insulator transition revealed by specific heat measurements

The superconductor-insulator transition (SIT) is considered an excellent example of a quantum phase transition which is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low energy fluctuations near quantum criticality may be experimentally detected by specific heat, $c_{\rm p}$, measurements. Here, we use a unique highly sensitive experiment to measure $c_{\rm p}$ of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature $T_{\rm c}^{\rm {mf}}$ marking the onset of Cooper pairs formation. As the film thickness is tuned toward the SIT, $T_{\rm c}^{\rm {mf}}$ is relatively unchanged, while the magnitude of the jump and low temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition.

cond-mat.supr-con↗

arXiv2016

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

Using a nonperturbative functional renormalization-group approach to the two-dimensional quantum O($N$) model, we compute the low-frequency limit $ω\to 0$ 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 $N\geq 3$, by two independent elements, $σ_{\rm A}(ω)$ and $σ_{\rm B}(ω)$, 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 $σ_{\rm A}(ω)$. We show that $\lim_{ω\to 0}σ(ω,δ)σ_{\rm A}(ω,-δ)/σ_q^2$ 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 $σ_q=q^2/h$ the quantum of conductance). On the other hand we argue that the ratio $σ_{\rm B}(ω\to 0)/σ_q$ is universal in the whole ordered phase, independent of $N$ and, when $N\to\infty$, equal to the universal conductivity $σ^*/σ_q$ at the quantum critical point.

cond-mat.str-el↗

arXiv2016

Critical Casimir forces from the equation of state of quantum critical systems

The mapping between a classical length and inverse temperature as imaginary time provides a direct equivalence between the Casimir force of a classical system in $D$ dimensions and internal energy of a quantum system in $d$$=$$D$$-$$1$ dimensions. The scaling functions of the critical Casimir force of the classical system with periodic boundaries thus emerge from the analysis of the symmetry related quantum critical point. We show that both non-perturbative renormalization group and quantum Monte Carlo analysis of quantum critical points provide quantitative estimates for the critical Casimir force in the corresponding classical model, giving access to widely different aspect ratios for the geometry of confined systems. In the light of these results we propose protocols for the experimental realization of critical Casimir forces for periodic boundaries through state-of-the-art cold-atom and solid-state experiments.

cond-mat.stat-mech↗

arXiv2015

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

We study the "Higgs" amplitude mode in the relativistic quantum O($N$) model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot--Méndez-Galain--Wschebor approximation (which we generalize to compute 4-point correlation functions), we compute the 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 $N=3$ and determine its universal properties. No resonance is found for $N\geq 4$. 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 $ε=4-(d+1)$ expansion near $d=3$.

cond-mat.quant-gas↗