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Journal of Physics C Solid State Physics

Energy levels of a shallow bound polaron

Tapas Mitra

Published Nov 28, 1978• 5 citations
Publisher

Abstract

The canonical transformation of Lee, Low and Pines (1953) is suitably applied to the bound polaron Hamiltonian to obtain its energy levels in a series form with interesting bounds and to discuss the hitherto ill-understood role of the intermediate continuum states in an earlier calculation of the energy levels.
DOI
10.1088/0022-3719/11/22/009

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We consider the Fermi polaron problem at zero temperature, where a single impurity interacts with noninteracting host fermions. We approach the problem starting with a Fr\"ohlich-like Hamiltonian where the impurity is described with canonical position and momentum operators. We apply the Lee-Low-Pine (LLP) transformation to change the fermionic Fr\"ohlich Hamiltonian into the fermionic LLP Hamiltonian, which describes a many-body system containing host fermions only. We adapt the self-consistent Hartree-Fock (HF) approach, first proposed by Edwards, to the fermionic LLP Hamiltonian in which a pair of host fermions with momenta k\mathbf{k}k and ${\mathbf{k}}^{\ensuremath{'}}$ interact with a potential proportional to $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{k}}^{\ensuremath{'}}$. We apply the HF theory, which has the advantage of not restricting the number of particle-hole pairs, to repulsive Fermi polarons in one dimension. When the impurity and host fermion masses are equal our variational ansatz, where HF orbitals are expanded in terms of free-particle states, produces results in excellent agreement with McGuire's exact analytical results based on the Bethe ansatz. This work raises the prospect of using the HF ansatz and its time-dependent generalization as building blocks for developing all-coupling theories for both equilibrium and nonequilibrium Fermi polarons in higher dimensions.