We present a unified theory that connects the quasiparticle picture of Fermi polarons for mobile impurities to the Anderson orthogonality catastrophe for static impurities. By operator reordering of the underlying many-body Hamiltonian, we obtain a modified fermionic dispersion relation that features a recoil-induced energy gap, which we call the "mass gap." We show that the resulting mean-field Hamiltonian exhibits an in-gap state for finite impurity mass, which takes a key role in Fermi polaron and molecule formation. We identify the mass gap as the microscopic origin of the quasiparticle weight of Fermi polarons and derive a power-law scaling of the weight with the impurity-to-fermion mass ratio. The associated in-gap state is shown to give rise to the emergence of the polaron-to-molecule transition away from the limiting case of the Anderson orthogonality catastrophe in which the transition is absent.We present a unified theory that connects the quasiparticle picture of Fermi polarons for mobile impurities to the Anderson orthogonality catastrophe for static impurities. By operator reordering of the underlying many-body Hamiltonian, we obtain a modified fermionic dispersion relation that features a recoil-induced energy gap, which we call the "mass gap." We show that the resulting mean-field Hamiltonian exhibits an in-gap state for finite impurity mass, which takes a key role in Fermi polaron and molecule formation. We identify the mass gap as the microscopic origin of the quasiparticle weight of Fermi polarons and derive a power-law scaling of the weight with the impurity-to-fermion mass ratio. The associated in-gap state is shown to give rise to the emergence of the polaron-to-molecule transition away from the limiting case of the Anderson orthogonality catastrophe in which the transition is absent.

arXiv:2507.15957Physical Review LettersNov 6, 20254 citations

Density Functional Theory of the Lattice Fermion Model

Román López-Sandoval, G. M. Pastor

Springer eBooksJan 1, 20010 citations

Renormalization approach to many-particle systems

K. W. Becker, A. Hübsch, T. Sommer

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian $\mathcal{H}={\mathcal{H}}_{0}+{\mathcal{H}}_{1}$ with an unperturbed part ${\mathcal{H}}_{0}$ and a perturbation ${\mathcal{H}}_{1},$ we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of ${\mathcal{H}}_{0}.$ This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff $\ensuremath{\lambda}$ that is smaller than the cutoff $\ensuremath{\Lambda}$ of the original Hamiltonian. This property resembles a recent flow equation approach on the basis of continuous unitary transformations. For demonstration of the method we discuss an exact solvable model, as well as the Anderson-lattice model where the well-known quasiparticle behavior of heavy fermions is derived.This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian $\mathcal{H}={\mathcal{H}}_{0}+{\mathcal{H}}_{1}$ with an unperturbed part ${\mathcal{H}}_{0}$ and a perturbation ${\mathcal{H}}_{1},$ we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of ${\mathcal{H}}_{0}.$ This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff $\ensuremath{\lambda}$ that is smaller than the cutoff $\ensuremath{\Lambda}$ of the original Hamiltonian. This property resembles a recent flow equation approach on the basis of continuous unitary transformations. For demonstration of the method we discuss an exact solvable model, as well as the Anderson-lattice model where the well-known quasiparticle behavior of heavy fermions is derived.

arXiv:cond-mat/0208351Physical review. B, Condensed matterDec 27, 200238 citations

Strongly interacting fermion systems: Emphasis on heavy fermions

Jayne Wilkins

Jan 1, 19880 citations

Scaling between periodic Anderson and Kondo lattice models

Ruanchen Dong, Junya Otsuki, Sergey Yu. Savrasov

Continuous-time quantum Monte Carlo method combined with dynamical mean field theory is used to calculate both periodic Anderson model (PAM) and Kondo lattice model (KLM). Different parameter sets of both models are connected by the Schrieffer-Wolff transformation. For degeneracy $N=2$ , a special particle-hole symmetric case of PAM at half filling which always fixes one electron per impurity site is compared with the results of the KLM. We find a good mapping between PAM and KLM in the limit of large on-site Hubbard interaction $U$ for different properties like self-energy, quasiparticle residue and susceptibility. This allows us to extract quasiparticle mass renormalizations for the $f$ electrons directly from KLM. The method is further applied to higher degenerate case and to realistic heavy fermion system CeRh ${\text{In}}_{5}$ in which the estimate of the Sommerfeld coefficient is proven to be close to the experimental value.Continuous-time quantum Monte Carlo method combined with dynamical mean field theory is used to calculate both periodic Anderson model (PAM) and Kondo lattice model (KLM). Different parameter sets of both models are connected by the Schrieffer-Wolff transformation. For degeneracy $N=2$, a special particle-hole symmetric case of PAM at half filling which always fixes one electron per impurity site is compared with the results of the KLM. We find a good mapping between PAM and KLM in the limit of large on-site Hubbard interaction $U$ for different properties like self-energy, quasiparticle residue and susceptibility. This allows us to extract quasiparticle mass renormalizations for the $f$ electrons directly from KLM. The method is further applied to higher degenerate case and to realistic heavy fermion system CeRh${\text{In}}_{5}$ in which the estimate of the Sommerfeld coefficient is proven to be close to the experimental value.

arXiv:1212.5867Physical Review BApr 2, 20136 citations

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian

\mathcal{H}={\mathcal{H}}_{0}+{\mathcal{H}}_{1}

with an unperturbed part

{\mathcal{H}}_{0}

and a perturbation

{\mathcal{H}}_{1},

we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of

{\mathcal{H}}_{0}.

This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff $\ensuremath{\lambda}$ that is smaller than the cutoff $\ensuremath{\Lambda}$ of the original Hamiltonian. This property resembles a recent flow equation approach on the basis of continuous unitary transformations. For demonstration of the method we discuss an exact solvable model, as well as the Anderson-lattice model where the well-known quasiparticle behavior of heavy fermions is derived.

N=2

, a special particle-hole symmetric case of PAM at half filling which always fixes one electron per impurity site is compared with the results of the KLM. We find a good mapping between PAM and KLM in the limit of large on-site Hubbard interaction

U

for different properties like self-energy, quasiparticle residue and susceptibility. This allows us to extract quasiparticle mass renormalizations for the

f

electrons directly from KLM. The method is further applied to higher degenerate case and to realistic heavy fermion system CeRh

{\text{In}}_{5}

in which the estimate of the Sommerfeld coefficient is proven to be close to the experimental value.