Structure Function Sum rules for Systems with Large Scattering Lengths

Abstract

We use a dispersion relation in conjunction with the operator product expansion (OPE) to derive model independent sum rules for the dynamic structure functions of systems with large scattering lengths. We present an explicit sum rule for the structure functions that control the density and spin response of the many-body ground state. Our methods are general, and apply to either fermions or bosons which interact through two-body contact interactions with large scattering lengths. By employing a Borel transform of the OPE, the relevant integrals are weighted towards infrared frequencies, thus allowing for greater overlap low energy data. Similar sum rules can be derived for other response functions. The sum rules can be used to extract the contact parameter introduced by Tan, including universality violating corrections at finite scattering lengths.

Added sum rule for polarized correlator which is dominated by the contact operator. Some typos fixed

References in corpus (13)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Nonrelativistic conformal field theories
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Number of closed-channel molecules in the BEC-BCS crossover
• Universal Properties of the Ultra-Cold Fermi Gas
• Theory of RF-spectroscopy of strongly interacting Fermions
• Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas
• Coherence and clock shifts in ultracold Fermi gases with resonant interactions
• Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases
• Short-distance and short-time structure of a unitary Fermi gas
• Static structure factor of a strongly correlated Fermi gas at large momenta

Cited by in corpus (10)

• Quantum Monte Carlo approaches to nuclear and atomic physics
• Contact and Momentum Distribution of the Unitary Fermi Gas
• Probing strongly interacting atomic gases with energetic atoms
• OPE convergence in non-relativistic conformal field theories
• Universal Noise in Continuous Transport Measurements of Interacting Fermions
• Deep inelastic scattering on ultracold gases
• Universal relations for dipolar quantum gases
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• Optomechanical Response of a Strongly Interacting Fermi Gas