Superconductivity and charge density wave order in the two-dimensional Holstein model

The Holstein Hamiltonian describes fermions hopping on a lattice and interacting locally with dispersionless phonon degrees of freedom. In the low-density limit, dressed quasiparticles, polarons and bipolarons, propagate with an effective mass. At higher densities, pairs can condense into a low-temperature superconducting phase and, at or near commensurate filling on a bipartite lattice, to charge density wave (CDW) order. CDW formation breaks a discrete symmetry and hence occurs via a second-order (Ising) transition and therefore at a finite T-cdw in two dimensions. Quantum Monte Carlo calculations have determined T-cdw for a variety of geometries, including square, honeycomb, and Lieb lattices. The superconducting transition, on the other hand, in d = 2 is in the Kosterlitz-Thouless universality class and is much less well characterized. In this paper we determine T-sc for the square lattice for several values of the density rho and phonon frequency omega(0). We find that quasilong-range order sets in at T-sc less than or similar to t/20, where t is the near-neighbor hopping amplitude, consistent with previous rough estimates from simulations which extrapolated to only the temperatures we reach from considerably higher T. We also show evidence of a discontinuous evolution of the density as the CDW transition is approached at half filling.

Automated summary

The Holstein Hamiltonian describes fermions interacting with phonons on a lattice. It predicts the behavior of dressed quasiparticles and the formation of superconducting and charge density wave phases at different densities. Quantum Monte Carlo calculations have been used to determine critical temperatures for these phase transitions in various lattice geometries.