Exact Diagonalization for the Holstein Polaron in the Strong-Coupling Limit

The study of polarons (quasiparticles consisting of an electron coupled to phonon excitations) is of great interest for many applications, including the theory of superconductivity. The Holstein model provides an effective model for studying polaron formation. Exact numerical techniques have been applied extensively to the Holstein polaron, though the strong-coupling regime poses difficulties due to the large number of phonon excitations required to achieve well converged results. We treat the problem on an infinite lattice by modifying existing exact diagonalization methods, carefully constructing a finite subset of the infinite-dimensional Hilbert space. Our results suggest that in the strong-coupling regime, a comparatively small number of states are required to very accurately describe the ground state of the system; as such, our work naturally suggests a variational wavefunction with a very simple form which nevertheless yields accurate ground state properties. Additionally, generalizations to two- and three-dimensional systems are readily accessible. Our work paves the way for studying the two-electron problem and the formation of bipolarons, relevant for Cooper pairing in conventional superconductors.