Supersolid Phase in the Diluted Holstein Model

TL;DR

This study demonstrates that diluting local phonon degrees of freedom in the Holstein model at half-filling induces a supersolid phase characterized by coexisting charge density wave and superconducting order, offering a new pathway to realize supersolidity.

Contribution

It reveals that impurity-induced dilution stabilizes a supersolid phase in the Holstein model, contrasting with traditional doping methods.

Findings

CDW persists up to 15% dilution

Long-range pairing is stabilized with increasing dilution

Supersolid phase appears around 10% dilution

Abstract

The Holstein model on a square lattice at half-filling has a well-established finite temperature phase transition to an insulating state with long range charge density wave (CDW) order. Because this CDW formation suppresses pairing, a superconducting (SC) phase emerges only with doping. In this work, we study the effects of dilution of the local phonon degrees of freedom in the Holstein model while keeping the system at half filling. We find not only that the CDW remains present up to a dilution fraction $f \sim 0.15$, but also that long range pairing is stabilized with increasing $f$, resulting in a {\it supersolid} regime centered at $f \approx 0.10$, where long range diagonal and off-diagonal correlations coexist. Further dilution results in a purely SC phase, and ultimately in a normal metal. Our results provide a new route to the supersolid phase via the introduction of impurities at fixed positions which both increase quantum fluctuations and also are immune to the competing tendency to phase separation often observed in the doped case.