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Attractive polaron in a semi-Dirac system within ladder approximation

Chen-Huan Wu

Published Jan 20, 2019• 5 citations
OpenAlex

Abstract

We investigate the properties of the attractive polaron formed by a single impurity dressed with the particle-hole excitations in a two-dimensional semi-Dirac system both analytically and numerically, which to our knowledge not being studied before. The pair propagator, self-energy, spectral function are detailly calculated and discussed. The method of medium T-matrix approximation (non-self-consistent), which equivalent to the partially dressed interaction vertex by summing over all ladder diagrams, is applied, and compared with some other methods (for the many-body problem), like the leading-order 1/N expansion (GW approximation), Hartree-Fock theory, and the Nozieres-Schmitt-Rink theory. And since we foucs on the weak-coupling region, the mean-field approximation is indeed applicable and accurate.

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We investigate the properties of the attractive polaron formed by a single impurity dressed with the particle-hole excitations in a two-dimensional semi-Dirac system both analytically and numerically, which to our knowledge not being studied before. The pair propagator, self-energy, spectral function are detailly calculated and discussed. The method of medium T-matrix approximation (non-self-consistent), which equivalent to the partially dressed interaction vertex by summing over all ladder diagrams, is applied, and compared with some other methods (for the many-body problem), like the leading-order 1/N expansion (GW approximation), Hartree-Fock theory, and the Nozieres-Schmitt-Rink theory. And since we foucs on the weak-coupling region, the mean-field approximation is indeed applicable and accurate.
We investigate the properties of the attractive polaron formed by a single impurity dressed with the particle-hole excitations in a Dirac system at zero-temperature limit. Base on the single particle-hole variational ansatz, we deduce the expressions of the pair propagator, self-energy (negative), and the non-self-consistent medium TTT-matrix. Different to the self-consistent TTT-matrix which contains two channels due to the many-body effect, the non-self-consistent TTT-matrix discussed in this paper contains only the closed channel (i.e., the bare one) since we consider only a finite number of the majority particles. The chiral factor is also discussed within the pair propagator due to the scattering feature of the Dirac system (with a certain scattering angle aaa), and we found that the fluctuation of the pair propagator is proportional to the term cos a{\rm cos}\ acos a. Finally, we also discuss the particle spectral function of the polaron in the presence of quantum many-body effect as well as the pair-propagator at finite temperature.
We study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. We find that most of the spectral weight is contained in a coherent attractive and a metastable repulsive polaron branch. We show that the qualitative behavior of the Bose polaron is well described by a non-self-consistent TTT-matrix approximation by comparing analytical results to numerical data obtained from a fully self-consistent TTT-matrix approach. The latter takes into account an infinite number of bosons excited from the condensate.
An impurity particle interacting with a Bose-Einstein condensate (BEC) leads to the formation of a quasiparticle known as the Bose polaron. We investigate the properties of the two-dimensional Bose polaron, applying a variational ansatz that contains up to three Bogoliubov excitations of the BEC. Similar to its three-dimensional counterpart, we observe the existence of two quasiparticle branches, namely, the attractive and the repulsive polarons, at different coupling strengths. We find that their energies agree well with recent quantum Monte Carlo calculations. In particular, we observe that the inclusion of three excitations is crucial to capture the attractive polaron energy towards the regime of strong attraction, where the quasiparticle properties are dominated by few-body correlations. We also calculate the attractive polaron effective mass and residue, where we find significant differences between considering a weakly interacting Bose medium and taking the noninteracting limit, signaling enhanced impurity dressing by excitations in the latter case. By contrast, the spectral weight of the metastable repulsive polaron is largely insensitive to the interactions in the BEC and the number of Bogoliubov excitations. Our model may be experimentally realized in dilute atomic vapors and atomically thin semiconductors.
A mobile impurity immersed in a noninteracting Fermi sea is dressed by the gapless particle-hole excitations of the fermionic medium. This conventional Fermi-polaron setting is well described by the so-called ladder approximation, which consists of neglecting impurity-hole scattering processes. In this work, we analyze polaron formation in the context of insulating states of matter, considering increasing levels of correlation in the medium: band insulators originating from external periodic potentials, spontaneously formed charge density waves, and a Fermi-Hubbard system undergoing a metal-Mott insulator transition. The polaron spectral function is shown to exhibit striking signatures of the underlying fermionic background, such as the single-particle band gap, particle-hole symmetry and the transition to the Mott state. These signatures are identified within the framework of the Chevy ansatz, i.e., upon restricting the Hilbert space to single particle-hole excitations. Interestingly, we find that the ladder approximation is inaccurate in these band systems, due to the fact that the particle and hole scattering phase spaces are comparable. Our results provide a step forward in the understanding of polaron formation in correlated many-body media, which are relevant to both cold-atom and semiconductor experiments. Published by the American Physical Society 2024
We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron Ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of particle-hole pairs in lower dimensions and makes simple variational calculations unreliable. We show that the energy of an impurity gives important information about its dressing cloud, for which both Ans\"atze give inaccurate results.
The interactions between holes in the Hubbard model, in the low density, intermediate- to strong-coupling limit, are investigated by systematically improving mean field calculations. The configuration-interaction basis set is constructed by applying to local unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far apart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for $4\ifmmode\times\else\texttimes\fi{}4$ clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of 2\sqrt{2}2​ times the lattice spacing, in agreement with exact results and the $t\ensuremath{-}J$ model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons.