Diagrammatic Monte Carlo study of the acoustic and the Bose–Einstein condensate polaron

Abstract

We consider two large polaron systems that are described by a Fröhlich type of Hamiltonian, namely the Bose-Einstein condensate (BEC) polaron in the continuum and the acoustic polaron in a solid. We present ground-state energies of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC) method and with a Feynman all-coupling approach. The DiagMC method evaluates up to very high order a diagrammatic series for the polaron's self-energy. The Feynman all-coupling approach is a variational method that has been used for a wide range of polaronic problems. For the acoustic and BEC polaron both methods provide remarkably similar non-renormalized ground-state energies that are obtained after introducing a finite momentum cutoff. For the renormalized groundstate energies of the BEC polaron, there are relatively large discrepancies between the DiagMC and the Feynman predictions. These differences can be attributed to the renormalization procedure for the contact interaction. k k k k k k k q k q k q pol 2 2 † † , † †Here, the ĉ k † (ĉ k ) are the creation (annihilation) operators of the charge carriers with band mass m and momentum k. The second term in the above Hamiltonian gives the energy of the phonons which carry the polarization. Thereby, the operator bˆk † (bˆk ) creates (annihilates) a phonon with wave vector k and energy ω k ( ). The last term in equation (1) denotes the interaction between the charge carrier and the phonons. A

All-coupling polaron optical response: Analytic approaches beyond the adiabatic approximation

“…The figure corresponds to the intermediate-coupling regime with α = 5.25. These radial wave functions represent analytically exact solutions of the Schrödinger equation for a particle with the reduced mass μ in the trial potential U (ρ) given by (8).…”

“…Polaronic effects are manifest in many interesting systems, such as magnetic polarons [3], polarons in semiconducting polymers [4], and complex oxides [5,6], which are described in terms of the small-polaron theory [7]. Large-polaron theory has recently been stimulated by the possibility to study polaronic effects using highly tunable quantum gases: the physics of an impurity immersed in an atomic Bose-Einstein condensate [8] can be modeled on the basis of a Fröhlich Hamiltonian. Another recent development in large-polaron physics stems from the experimental advances in the determination of the band structure of highly polar oxides [9], relevant for superconductivity, where the optical response of complex oxides explicitly shows the large-polaron features [10,11].…”

Impurity in a Bose-Einstein condensate: Study of the attractive and repulsive branch using quantum Monte Carlo methods

“…On the theoretical side, the self-localization of Bose polarons was investigated using mean-field approaches [9][10][11]21,22] as well as Feynman's variational method applied to the effective Hamiltonian describing the impurity [12,23]. Starting from the Fröhlich Hamiltonian other studies have focused on the calculation of the radio-frequency response of the polaron [24] and of its binding energy and effective mass using renormalization-group [25] and diagrammatic Monte Carlo [26] methods. A more microscopic approach based on the T-matrix approximation was used in Ref.…”

Visualizing the Efimov Correlation in Bose Polarons

“…Lots of theoretical efforts have been paid to study the Fermi polaron [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and the Bose polaron [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Nearby a Feshbach resonance, a Fermi polaron displays an attractive branch [20][21][22][23][24][25]29] and a repulsive branch [26][27][28], which directly manifests two-body correlations in this system.…”