The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b_{4} of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b_{4}, our b_{4} agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b_{4} of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b_{4}, our b_{4} agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.

arXiv:1602.02328Physical Review LettersJun 7, 201629 citations

Path Integral Formalism of Fermi Fields

World Scientific lecture notes in physicsSep 1, 19850 citations

Functional Integral approach to quasi-particles in Fermi Liquid theory

Tai Kai Ng

In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals $ψ$ 's are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through $ψ$ 's in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle renormalization factor z does not appear explicitly. Consequences of our new formulation are discussed.In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals $ψ$'s are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through $ψ$'s in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle renormalization factor z does not appear explicitly. Consequences of our new formulation are discussed.

arXiv:cond-mat/9706033Jun 4, 19971 citation

Renormalization of many body fermion models with singular fermi surfaces

Daniel Brox

The physical system modelled is a periodic lattice that provides a background for interacting fermions. An effective model of the interacting fermions at zero temperature may be studied using standard techniques of many-body quantum mechanics. All the physical information of such a system is encoded in its Schwinger's functions that tell us how states evolve in time and what the matrix elements of all operators are. It is natural to do calculations on the interacting system by treating it as a perturbation of the corresponding noninteracting system, as the eigenstates and energy levels of the latter are known. All Schwinger functions may be conveniently cast in the path integral formalism, and combined into a generating functional. The Schwinger functions are shown to be sums of Feynman diagrams, where the electron propagators blow-up at the Fermi surface. Power counting is described and used to reveal subdiagram divergences. Renormalization via the renormalized Gallavotti-Nicolo Tree Expansion is implemented in an attempt to circumvent these subdiagram divergences and obtain finite values for the Schwinger functions. It is shown that if the Fermi surface has at worst quadratic singularities, the perturbation coefficients of the renormalizing counterterms are finite and remain so as the infrared cutoff is removed.The physical system modelled is a periodic lattice that provides a background for interacting fermions. An effective model of the interacting fermions at zero temperature may be studied using standard techniques of many-body quantum mechanics. All the physical information of such a system is encoded in its Schwinger's functions that tell us how states evolve in time and what the matrix elements of all operators are. It is natural to do calculations on the interacting system by treating it as a perturbation of the corresponding noninteracting system, as the eigenstates and energy levels of the latter are known. All Schwinger functions may be conveniently cast in the path integral formalism, and combined into a generating functional. The Schwinger functions are shown to be sums of Feynman diagrams, where the electron propagators blow-up at the Fermi surface. Power counting is described and used to reveal subdiagram divergences. Renormalization via the renormalized Gallavotti-Nicolo Tree Expansion is implemented in an attempt to circumvent these subdiagram divergences and obtain finite values for the Schwinger functions. It is shown that if the Fermi surface has at worst quadratic singularities, the perturbation coefficients of the renormalizing counterterms are finite and remain so as the infrared cutoff is removed.

Jan 1, 20090 citations

Path integrals for the nuclear many-body problem

Jean-Paul Blaizot, Henri Orland

WORLD SCIENTIFIC eBooksDec 1, 19940 citations

In this paper we propose a new way of organizing many-body perturbation theory in the Path-integral formulation where a set of quasi-particle wave-functionals

ψ

's are introduced and are identified with quasi-particles in Landau Fermi liquid theory. We show how Fermi liquid theory can be obtained through

ψ

's in this new framework of perturbation theory, where the only assumption is adiabaticity between non-interacting and interacting states and the quasi-particle renormalization factor z does not appear explicitly. Consequences of our new formulation are discussed.