arXiv subjects

Silas R. Beane

Publications and source records attributed to Silas R. Beane.

At least 19 recordsLinked to original sources

arXiv2026

Andreev reflections and optimal truncation in the unitary Fermi droplet

We study the unitary Fermi gas in an external trap in the double-scaling limit of large flavor number N and large charge Q at fixed Q/N. At leading order, the problem reduces to the spectral zeta function of a BdG operator in an inhomogeneous pairing background. The grand potential admits a gradient expansion with distinct bulk and edge sectors. We show that when the trap is harmonic, the bulk sector expansion terminates: beyond the first three terms every bulk contribution integrates to zero. This cancellation is general and follows from zeros of the Euler beta function computed in the Son-Wingate effective field theory, independent of the low-energy constants. The truncation persists for anisotropic traps in any odd dimension. All higher-order dependence for harmonic potentials is therefore carried by the droplet edge. For anharmonic traps, the asymptotic bulk series is factorially divergent. Using a heat-kernel WKB analysis, we show that its large-order growth, sign oscillations, and optimal truncation are fixed by complex periodic orbits of the BdG problem, which are analytic continuations of Andreev reflections. We numerically confirm the predicted Borel singularities for quartic and sextic traps.

hep-th↗

arXiv2026

Reformulation of the pionless effective field theory for practical few- and many-body applications

The effective field theory (EFT) of contact forces which describes few-nucleon systems at distance scales larger than the pion Compton wavelength ${\rm EFT}({π\hskip-0.54em /})$ can be defined in terms of momentum-dependent potentials that contain a fixed number of simple poles and generate the effective-range expansion to a given fixed order. These potentials provide a practical generalization of the standard ${\rm EFT}({π\hskip-0.54em /})$ power-counting scheme which, for instance, naturally accounts for the large effective ranges in the s-wave channels. Nucleon-nucleon phase shifts computed in this formulation of ${\rm EFT}({π\hskip-0.54em /})$ are compared to modern phase-shift analyses, and effective-range parameters are tabulated. The ${\rm EFT}({π\hskip-0.54em /})$ potentials, which provide a rational approximation of the S-matrix, are easily extended into the regime of pion physics through the inclusion of additional S-matrix poles and zeros, and provide an accurate description of data up to pion-production threshold. The potentials in this scheme are in an important sense weak over all relevant distance scales, and are therefore of utility for systematic calculations of many-nucleon observables.

nucl-th↗

arXiv2026

Universal enhancement of the pairing gap in a dilute Fermi superfluid

At zero temperature, a dilute Fermi gas with an attractive contact interaction forms a superfluid with gapped fermionic excitations. We show that the gap at weak coupling can be organized as a trans-series expansion in the interaction strength and the asymptotic Gor'kov-Melik-Barkhudarov gap. Low-energy virtual quasiparticles generate corrections that are linear in the gap with a leading coefficient nearly 25$\times$ larger than the other known coefficients. This substantially increases the gap at intermediate densities, highlighting that systematic corrections are crucial for quantitative predictions.

cond-mat.quant-gas↗

arXiv2026

Local universality of non-local quantum resources in rotationally invariant scattering

Elastic scattering can generate entanglement and non-local magic between the spins of the two outgoing particles. The amount of entanglement and magic produced is encoded in the S-matrix; a unitary quantum gate that acts on the joint Hilbert space of the two spin-J particles. Previous work derived the entanglement power in terms of the scattering phase shifts for rotationally invariant S-matrices with J=1/2,1,3/2. In this paper, a closed form solution is derived for all J. We further prove that a broad class of non-local quantum resources depend to leading order only on the squared projective Hilbert-Schmidt distance from the nearest non-entangling gate. This holds for the entanglement power and non-local magic power, and the choice of resource simply changes the overall normalization. This universality establishes a common geometric origin for the leading resource-generating capacity of scattering, independent of the details of the interaction.

quant-ph↗

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, $χ\,ξ^{1/6}(24Q)^{1/9}\,\hbarω+ \cdots$ where $ξ$ is the Bertsch parameter, and $χ$ 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

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

Universal corrections to the superfluid gap in a cold Fermi gas

A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. Together, these effects are found to reduce the gap at low densities. Applications to neutron superfluidity in neutron stars are also discussed.

nucl-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 Schrödinger-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 Schrödinger-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 Schrödinger-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 Schrödinger-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 Schrödinger 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

Toward precision Fermi liquid theory in two dimensions

The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an effective field theory framework. It has long been observed that universal corrections to the energy density to two orders in the interaction strength do not agree with Monte Carlo simulations in the weak-coupling regime. Here, universal corrections to three orders in the interaction strength are obtained for the first time, and are shown to provide agreement between theory and simulation. Special consideration is given to the scale ambiguity associated with the non-trivial renormalization of the singular contact interactions. The isotropic superfluid gap is obtained to next-to-leading order, and nonuniversal contributions to the energy density due to effective range effects, p-wave interactions and three-body forces are computed. Results are compared with precise Monte Carlo simulations of the energy density and the contact in the weakly-coupled attractive and repulsive Fermi liquid regimes. In addition, the known all-orders sum of ladder and ring diagrams is compared with Monte Carlo simulations at weak coupling and beyond.

cond-mat.quant-gas↗

arXiv2022

UV/IR symmetries of the $S$-matrix and RG flow

The low energy $S$-matrix which describes non-relativistic scattering arising from finite-range forces has UV/IR symmetries that are hidden in the corresponding effective field theory (EFT) action. It is shown that the $S$-matrix symmetries are manifest as geometric symmetries of the RG flow of coupling constants in the EFT action in both three and two spatial dimensions. An example is given demonstrating that UV/IR symmetry breaking in the $S$-matrix implies strong constraints on the RG flow of the coefficients of the corresponding symmetry-breaking operators in the EFT.

hep-ph↗

arXiv2022

Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions

The s-wave nucleon-nucleon (NN) scattering matrix ($S$-matrix) exhibits UV/IR symmetries which are hidden in the effective field theory (EFT) action and scattering amplitudes, and which explain some generic features of the phase shifts. These symmetries offer clarifying interpretations of existing pionless EFT expansions, and suggest starting points for novel expansions. The leading-order (LO) $S$-matrix obtained in the pionless EFT with scattering lengths treated exactly is shown to have a UV/IR symmetry which leaves the sum of s-wave phase shifts invariant. A new scheme, which treats effective range corrections exactly, and which possesses a distinct UV/IR symmetry at LO, is developed up to NLO (next-to-LO) and compared with data.

nucl-th↗

arXiv2022

Causality and dimensionality in geometric scattering

The scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly arXiv:2011.01278. In the case of zero-range forces, causality leads to constraints on scattering trajectories in the geometric picture. The effect of spatial dimensionality is also investigated by considering scattering in two and three dimensions. In the geometric formulation it is found that dimensionality is encoded in the phase of the harmonic potential that appears in the geometric action.

quant-ph↗

arXiv2022

Entanglement minimization in hadronic scattering with pions

Recent work arXiv:1812.03138 [nucl-th] conjectured that entanglement is minimized in low-energy hadronic scattering processes. It was shown that the minimization of the entanglement power (EP) of the low-energy baryon-baryon $S$-matrix implies novel spin-flavor symmetries that are distinct from large-$N_c$ QCD predictions and are confirmed by high-precision lattice QCD simulations. Here the conjecture of minimal entanglement is investigated for scattering processes involving pions and nucleons. The EP of the $S$-matrix is constructed for the $ππ$ and $πN$ systems, and the consequences of minimization of entanglement are discussed and compared with large-$N_c$ QCD expectations.

hep-ph↗

arXiv2021

Geometry and entanglement in the scattering matrix

A formulation of nucleon-nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix -- that appears at leading-order in the EFT description -- possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code.

hep-th↗

arXiv2021

Low-energy Scattering and Effective Interactions of Two Baryons at $m_π\sim 450$ MeV from Lattice Quantum Chromodynamics

The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_π\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $ΣN$ ($I=3/2$), and $ΞΞ$ states, the spin-singlet $ΣΣ$ ($I=2$) and $ΞΣ$ ($I=3/2$) states, and the spin-triplet $ΞN$ ($I=0$) state. The $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using Lüscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $ΣN$ and $ΞΞ$ channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.

hep-lat↗

arXiv2020

Two Nucleon Systems at $m_π\sim 450~{\rm MeV}$ from Lattice QCD

Nucleon-nucleon systems are studied with lattice quantum chromodynamics at a pion mass of $m_π\sim 450~{\rm MeV}$ in three spatial volumes using $n_f=2+1$ flavors of light quarks. At the quark masses employed in this work, the deuteron binding energy is calculated to be $B_d = 14.4^{+3.2}_{-2.6} ~{\rm MeV}$, while the dineutron is bound by $B_{nn} = 12.5^{+3.0}_{-5.0}~{\rm MeV}$. Over the range of energies that are studied, the S-wave scattering phase shifts calculated in the 1S0 and 3S1-3D1 channels are found to be similar to those in nature, and indicate repulsive short-range components of the interactions, consistent with phenomenological nucleon-nucleon interactions. In both channels, the phase shifts are determined at three energies that lie within the radius of convergence of the effective range expansion, allowing for constraints to be placed on the inverse scattering lengths and effective ranges. The extracted phase shifts allow for matching to nuclear effective field theories, from which low energy counterterms are extracted and issues of convergence are investigated. As part of the analysis, a detailed investigation of the single hadron sector is performed, enabling a precise determination of the violation of the Gell-Mann--Okubo mass relation. [An Erratum to the published version is included as an appendix. It details the impact of an error discovered in 2020 and corrects typographical errors.]

hep-lat↗

arXiv2019

Chiral symmetry breaking, entanglement, and the nucleon spin decomposition

The nucleon is naturally viewed as a bipartite system of valence spin -- defined by its non-vanishing chiral charge -- and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the resulting entanglement entropy acts as an order parameter of chiral symmetry breaking in the nucleon. In the large-$N_c$ limit, the entanglement entropy vanishes and the valence spin accounts for all of the nucleon spin, while in the limit of maximal entanglement entropy, the nucleon loses memory of the valence spin and consequently has spin dominated by the sea. The nucleon state vector in the chiral basis, fit to low-energy data, gives a valence spin content consistent with experiment and lattice QCD determinations, and has large entanglement entropy.

hep-ph↗