arXiv subjects

Susanne Reffert

Publications and source records attributed to Susanne Reffert.

At least 19 recordsLinked to original sources

arXiv2026

The odd fermion at the edge: odd-even staggering in the trapped, unitary Fermi gas

We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge $Q$. Using both a large-$N$ BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, $\chi\,\xi^{1/6}(24Q)^{1/9}\,\hbar\omega + \cdots$ where $\xi$ is the Bertsch parameter, and $\chi$ is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same $Q$ scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.

cond-mat.quant-gas↗

arXiv2026

Semiclassics at the cusp

We study cusped Wilson line operators in the Abelian Higgs model in $ d = 4 - \epsilon $ at large external charges. Using a double-scaling limit $ Q \to \infty $, $ \epsilon \to 0 $ with $ Q\epsilon $ fixed, we develop a semiclassical framework that provides analytic control beyond fixed-order perturbation theory. We compute the cusp anomalous dimension for arbitrary charges up to next-to-next-to-leading order in the gauge coupling, while resumming scalar self-interactions to all orders. Our results interpolate between perturbative and large-charge regimes, accessing domains that are invisible in fixed-order perturbation theory. As an application, we provide new predictions for various defect CFT observables, including the Mandelstam-Schwinger-dressed two-point function characterizing the superconducting phase transition.

hep-th↗

arXiv2025

Trapping-potential dependence of the unitary Fermi gas at the BCS-BEC crossover

Cold-atom experiments which measure Fermi-gas properties near unitarity confine fermionic atoms to a region of space using trapping potentials of various shapes. The presence of a trapping potential introduces a new characteristic physical scale in the superfluid EFT which, inter alia, describes the acoustic branch of excitations in the far infrared well below the scale of the superfluid gap. In this EFT there is a clear hierarchy of scales, and corrections to the homogeneous system due to the trapping potential may be organized into three regions with distinct power counting that relies on both the EFT derivative expansion, and the WKB approximation, which is an expansion in gradients of the trapping potential. The energy spectrum of the superfluid system is obtained in each of the regions by explicit computation of the phonon-field fluctuations, and by the modifications to the dynamic structure factor due to the corresponding density fluctuations. The most significant deviations from linear dispersion due to the trapping potential are found in the far infrared region of the superfluid EFT.

cond-mat.quant-gas↗

arXiv2025

Resurgence Analysis of the Nambu-Jona-Lasinio model at large charge

We study the fixed point of the three-dimensional NJL model in a double-scaling limit where both the charge $Q$ and the number of fermion flavors $N$ become large with a fixed ratio $q=Q/(2N)$. While a similar analysis has been performed for the bosonic O(N) model, fermionic models pose new challenges. In this work, we systematically explore the CFT spectrum in both the large and small $q$ limits beyond the first few orders, and perform a resurgence analysis. Through this approach, we identify the exponential corrections that relate the convergent small-$q$ expansion to the asymptotic large-$q$ behavior. Our results are suggestive of a geometric interpretation of these results in terms of the worldline of particles moving along the geodesics on the cylinder.

hep-th↗

arXiv2025

Asymptotics in the bi-Yang-Baxter Sigma Model

Working in a sector of large charge is a powerful tool to analytically access models that are either strongly coupled or otherwise difficult to solve explicitly. In the context of integrable systems, Volin's method is exactly such a large-charge approach. In this note, we apply this method to the bi-Yang-Baxter deformed $SU(2)$ principal chiral model. Our main result is an explicit expression for the free energy density as an asymptotic expansion. We moreover determine the leading non-perturbative effects both via analytic methods and a resurgence analysis.

hep-th↗

arXiv2025

Unnuclear matter at large-charge

The utility of the non-relativistic large-charge EFT for physical systems, and neutron matter in particular, relies on controlled Schr\"odinger-symmetry breaking deformations due to scattering length and effective-range effects in the two-body system. A recently-found exact solution of the large-charge system is used to compute these effects for two-point correlation functions of large-charge operators in perturbation theory around the large-charge ground state. Notably, the leading effective-range effects are found to enter at second order in the effective range, in agreement with analogous calculations in the three-body system. The Schr\"odinger-symmetry breaking deformations are used -- together with input from Quantum Monte Carlo simulations -- to address the range of validity of the EFT with deformations both in general and in the special case of neutron matter. In particular, it is found that nuclear reactions with up to six low-energy neutrons in the final state can be described by the large-charge EFT with Schr\"odinger-symmetry breaking.

nucl-th↗

arXiv2024

Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr\"odinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schr\"odinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge.

hep-th↗

arXiv2023

The unitary Fermi gas at large charge and large N

We study the unitary Fermi gas in a harmonic trapping potential starting from a microscopic theory in the limit of large charge and large number of fermion flavors N. In this regime, we present an algorithmic procedure for extracting data from perturbation theory, order-by-order, without the need for other assumptions. We perform a gradient expansion in the interior of the particle cloud, sufficiently far from the cloud edge where the particle density drops rapidly to zero. In this latter region we present the first microscopic computation characterizing the contribution of the edge terms. The microscopic theory reproduces the predictions of the superfluid EFT, including the action, the form of the gap equation, and the energy of the system in a harmonic trap (which maps, via the non-relativistic state-operator correspondence, to the scaling dimension of the lowest operator of charge Q). We additionally give the Wilsonian coefficients at leading order in N up to NNLO in the large-charge expansion.

hep-th↗

arXiv2023

Fermionic CFTs at large charge and large N

We study the large-charge sector of large-N fermionic CFTs in three dimensions. Depending on the model and the nature of the fixed charge, we find two types of descriptions: in terms of a superfluid or a Fermi sphere. We explicitly compute the conformal dimensions of the lowest operator of fixed charge and in the superfluid case verify the EFT predictions for the phonon spectrum.

hep-th↗

arXiv2022

Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements

The unitary Fermi gas, by virtue of its description as a nonrelativistic conformal field theory, has proven an interesting system by which the quantum properties of CFT can be held to experimental verification. Here, we examine the structure of conformal dimensions of charge-Q operators in nonrelativistic CFT, in the large-Q regime, from the non-linear sigma model perspective. We discuss in detail the renormalization of edge divergences using dimensional regularization, elucidating the presence of $\log(Q)$ terms in the large-charge expansion. Finally we use dimensional regularization to compute the universal one-loop $Q^0 \log(Q)$ contribution to the ground-state energy in $d = 3$ spatial dimensions, with the result $\left.Δ(Q)\right|_{Q^0} = \frac{1}{3\sqrt{3}} \log(Q) + \text{const.}$

hep-th↗

arXiv2022

2D CFTs - Large Charge is not enough

In this note we study two-dimensional CFTs at large global charge. Since the large-charge sector decouples from the dynamics, it does not control the dynamics and an EFT construction that works in higher-dimensional theories fails. It is however possible to use large charge in a double-scaling limit when another controlling parameter is present. We find some general features of the spectrum of models that admit an NLSM description in a WKB approximation and use the large-charge sector of the solvable $SU(2)_k$ WZW model to argue the regimes of applicability of both the large-Q expansion and the double-scaling limit.

hep-th↗

arXiv2022

Spinning correlators in large-charge CFTs

We systematically study correlators of a generic conformal field theory with a global O(2) symmetry in a sector of large global charge. We focus in particular on three- and four-point correlators with conserved current insertions sandwiched between spinful excited states corresponding to phonons over the large-charge vacuum. We also discuss loop corrections to the scaling dimensions and observe multiple logarithms in even dimensions.

hep-th↗

arXiv2022

Convexity, large charge and the large-N phase diagram of the $φ^4$ theory

In this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2<D<4 and 4<D<6. Based on a simple discussion of the convexity properties of the grand potential, we find very different behavior in the two regimes: while in 2<D<4, the theory is well-behaved, the model in 4<D<6 leads to a complex CFT in the UV, consistently with earlier results. We also find a new metastable massive phase in the high-energy regime for the theory on the cylinder.

hep-th↗

arXiv2021

Following the flow for large N and large charge

We discuss the O(2N) vector model in three dimensions. While this model flows to the Wilson-Fisher fixed point when fine tuned, working in a double-scaling limit of large N and large charge allows us to study the model away from the critical point and even to follow the RG flow from the UV to the IR. The crucial observation is that the effective potential -- at leading order in N but exact to all orders in perturbation theory -- is the Legendre transform of the grand potential at fixed charge. This allows us to write an effective action and the free energy for generic values of the coupling in a very simple fashion and without evaluating any Feynman diagrams.

hep-th↗

arXiv2021

Selected Topics in the Large Quantum Number Expansion

In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are described by a hybrid form of Goldstone's theorem, involving its relativistic and non-relativistic forms. The associated effective field theory in the infrared allows the computation of anomalous dimensions, and operator product expansion coefficients in a well defined expansion in inverse powers of the global charge. This applies even when the initial theory does not have a reliable semiclassical approximation. The large quantum number expansion complements, and may provide an alternative approach to the bootstrap and numerical treatments. We will present some general features of the symmetry breaking patterns and the low-energy effective actions, and a fairly large number of examples exhibiting the salient features of this method.

hep-th↗

arXiv2021

Near-Schrödinger dynamics at large charge

In this note we discuss a non-relativistic system at large charge in a regime where Schrödinger symmetry is slightly broken by an explicit mass term for the dilaton field which non-linearly realizes non-relativistic scale invariance. To get there, we first develop the large-charge formalism from the linear sigma model perspective, including the harmonic trapping potential necessary for the non-relativistic state-operator correspondence. As a signature of the explicit breaking, we identify a $\sqrt{Q}\log{Q}$ term, which depending on the space dimension is either of the same order as the effects coming from the breakdown of the EFT at the edge of the particle cloud, or can be distinguished from these effects over a large range of orders of magnitude.

hep-th↗

arXiv2021

Resurgence of the large-charge expansion

We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the effective field theory to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data.

hep-th↗

arXiv2021

Quantum crystals, Kagome lattice and plane partitions fermion-boson duality

In this work, we study quantum crystal melting in three space dimensions. Using an equivalent description in terms of dimers in a hexagonal lattice, we recast the crystal melting Hamiltonian as an occupancy problem in a Kagome lattice. The Hilbert space is spanned by states labeled by plane partitions and writing them as a product of interlaced integer partitions, we define a fermion-boson duality for plane partitions. Finally, based upon the latter result we conjecture that the growth operators for the quantum Hamiltonian can be represented in terms of the affine Yangian ${\cal Y}[\widehat{\mathfrak{gl}}(1)]$.

hep-th↗