Multipolaron Problem

Abstract

For the weak-coupling regime, which is realized in most polar semiconductors, the ground-state energy of a gas of interacting continuous polarons has been derived in [320] by introducing a variational wave function:

$$|\psi_{{\rm LDB}}\rangle = U |\phi \rangle |\varphi_{el}\rangle,$$

(5.1)

where $|\varphi_{el}\rangle$ represents the ground-state many-body wave function for the electron (or hole) system, $|\phi \rangle$ is the phonon vacuum, and U is a many-body unitary operator. U defines the LDB-canonical transformation for a fermion gas interacting with a boson field:

$$U = \exp \left\{\sum\limits_{j = 1}^{N} \sum\limits_{{\rm q}} (f_{{\rm q}}d_{{\rm q}}e^{{\rm iq\cdot r}_{j}} - f^{\ast}_{{\rm q}}d^{+}_{{\rm q}} e^{-{\rm iq\cdot r}_{j}})\right\},$$

(5.2)

where r _j represent the position of the N constituent electrons (or holes). The f _q were determined variationally [320]. It may be emphasized that (5.2), although it appears like a straightforward generalization of the one-particle transformation in [321], constitutes – especially in its implementation – a nontrivial extension of a one-particle approximation to a many-body system. An advantage of the LDB-many-polaron canonical transformations introduced in [320] for the calculation of the ground-state energy of a polaron gas is that the many-body effects are contained in the static structure factor of the electron (or hole) system, which appears in the analytical expression for the energy. Within the approach, the minimum of the total ground-state energy per particle for a polaron gas lies at lower density than that for the electron gas.