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Register a new userEffective field theory for dilute Fermi systems at fourth order
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Added by
Corbinian Wellenhofer
Publication date
2021
fields
Physics
and research's language is
English
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We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or $k_{rm F} a_s$ expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well-converged at this order for ${| k_{rm F} a_s | lesssim 0.5}$. Further, we show that Pad{e}-Borel resummations can improve the convergence for ${| k_{rm F} a_s | lesssim 1}$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.
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Using effective field theory methods, we calculate for the first time the complete fourth-order term in the Fermi-momentum or $k_{rm F} a_s$ expansion for the ground-state energy of a dilute Fermi gas. The convergence behavior of the expansion is examined for the case of spin one-half fermions and compared against quantum Monte-Carlo results, showing that the Fermi-momentum expansion is well-converged at this order for $| k_{rm F} a_s | lesssim 0.5$.
We develop a method that uses truncation-order-dependent re-expansions constrained by generic strong-coupling information to extrapolate perturbation series to the nonperturbative regime. The method is first benchmarked against a zero-dimensional model field theory and then applied to the dilute Fermi gas in one and three dimensions. Overall, our method significantly outperforms Pade and Borel extrapolations in these examples. The results for the ground-state energy of the three-dimensional Fermi gas are robust with respect to changes of the form of the re-expansion and compare well with quantum Monte Carlo simulations throughout the BCS regime and beyond.
We use a finite temperature effective field theory recently developed for superfluid Fermi gases to investigate the properties of dark solitons in these superfluids. Our approach provides an analytic solution for the dip in the order parameter and the phase profile accross the soliton, which can be compared with results obtained in the framework of the Bogoliubov - de Gennes equations. We present results in the whole range of the BCS-BEC crossover, for arbitrary temperatures, and taking into account Gaussian fluctuations about the saddle point. The obtained analytic solutions yield an exact energy-momentum relation for a dark soliton showing that the soliton in a Fermi gas behaves like a classical particle even at nonzero temperatures. The spatial profile of the pair field and for the parameters of state for the soliton are analytically studied. In the strong-coupling regime and/or for sufficiently high temperatures, the obtained analytic solutions match well the numeric results obtained using the Bogoliubov - de Gennes equations.
Working within the post-Newtonian (PN) approximation to General Relativity, we use the effective field theory (EFT) framework to study the conservative dynamics of the two-body motion at fourth PN order, at fifth order in the Newton constant. This is one of the missing pieces preventing the computation of the full Lagrangian at fourth PN order using EFT methods. We exploit the analogy between diagrams in the EFT gravitational theory and 2-point functions in massless gauge theory, to address the calculation of 4-loop amplitudes by means of standard multi-loop diagrammatic techniques. For those terms which can be directly compared, our result confirms the findings of previous studies, performed using different methods.
Isotropic scattering in various spatial dimensions is considered for arbitrary finite-range potentials using non-relativistic effective field theory. With periodic boundary conditions, compactifications from a box to a plane and to a wire, and from a plane to a wire, are considered by matching S-matrix elements. The problem is greatly simplified by regulating the ultraviolet divergences using dimensional regularization with minimal subtraction. General relations among (all) effective-range parameters in the various dimensions are derived, and the dependence of bound states on changing dimensionality are considered. Generally, it is found that compactification binds the two-body system, even if the uncompactified system is unbound. For instance, compactification from a box to a plane gives rise to a bound state with binding momentum given by $ln left({scriptstyle frac{1}{2}}left(3+sqrt{5} right) right)$ in units of the inverse compactification length. This binding momentum is universal in the sense that it does not depend on the two-body interaction in the box. When the two-body system in the box is at unitarity, the S-matrices of the compactified two-body system on the plane and on the wire are given exactly as universal functions of the compactification length
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