Determinant Quantum Monte Carlo simulations of charge density waves in the Holstein model with a double well potential

Abstract

This work is concerned with transitions to the ordered charge density wave (CDW) phase. CDWs are well studied, but there is still more to explore, especially as they relate to superconductivity. In some instances, CDWs are proposed to assist or give rise to unconventional superconductivity, but there are other materials in which they are known to compete with the superconducting phase. Learning more about where they exist and how they interact with other phases is therefore of great interest. [1] We add to the existing literature by considering a different potential and showing that this may change the critical temperature below which CDWs form. While other investigations have considered the addition of an anharmonic term [2], we specifically consider an anharmonic potential with a double well or sombrero shape. The choice of this potential was inspired by the twofold degeneracy of minima in the original Holstein model potential that allows for particle hole symmetry and hence for charge density waves. The symmetry of the potential has been proposed to have applications to heavy fermions. Heavy fermions are tied to how conduction electrons in certain compounds interact with an underlying two level system in that compound. In general, this two level system is magnetic, such that a large external magnetic field should obliterate it, but there are some materials where the heavy fermions survive. Fuse et. al. have argued that a double well potential in the Holstein model may explain the persistence of the heavy fermion behavior even in strong magnetic fields [3]. We are interested in a better understanding of the double well potential in the hopes of revealing more potential connections to observed phenomena.