Minimal Model for Disorder-induced Missing Moment of Inertia in Solid ${}^4$He

Abstract

The absence of a missing moment inertia in clean solid ${}^4$He suggests that the minimal experimentally relevant model is one in which disorder induces superfluidity in a bosonic lattice. To this end, we explore the relevance of the disordered Bose-Hubbard model in this context. We posit that a clean array ${}^4$He atoms is a self-generated Mott insulator, that is, the ${}^4$He atoms constitute the lattice as well as the `charge carriers'. With this assumption, we are able to interpret the textbook defect-driven supersolids as excitations of either the lower or upper Hubbard bands. In the experiments at hand, disorder induces a closing of the Mott gap through the generation of mid-gap localized states at the chemical potential. Depending on the magnitude of the disorder, we find that the destruction of the Mott state takes place for $d+z>4$ either through a Bose glass phase (strong disorder) or through a direct transition to a superfluid (weak disorder). For $d+z<4$, disorder is always relevant. The critical value of the disorder that separates these two regimes is shown to be a function of the boson filling, interaction and the momentum cut off. We apply our work to the experimentally observed enhancement ${}^3$He impurities has on the onset temperature for the missing moment of inertia. We find quantitative agreement with experimental trends.

9 pages, 5 figures: Extended version of previous paper in which the pase diagram for the disordered Bose-Hubbard model is computed using mean-field theory and one-loop RG. The criterion for the Bose glass is derived explicitly. (a few typos are corrected)

References in corpus (9)

• Disorder and the Supersolid State of Solid ${}^4$He
• Ring exchanges and the supersolid phase of 4He
• The fate of vacancy-induced supersolidity in 4He
• Pressure-driven flow of solid helium
• Supersolid Helium at High Pressure
• On the origin of the decrease in the torsional oscillator period of solid He4
• Entropy of solid He4: the possible role of a dislocation glass
• Vortex Glass is a Metal: Unified Theory of the Magnetic Field and Disorder-Tuned Bose Metals
• Absence of low temperature anomaly on the melting curve of ${}^4$He

Cited by in corpus (17)

• Strongly interacting bosons in a disordered optical lattice
• Disordered insulator in an optical lattice
• Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems
• Evidence for a Superglass State in Solid 4He
• Phase diagram of the disordered Bose-Hubbard model
• Stochastic Mean-Field Theory: Method and Application to the Disordered Bose-Hubbard Model at Finite Temperature and Speckle Disorder
• The superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model
• Interplay of Rotational, Relaxational, and Shear Dynamics in Solid 4He
• A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder
• Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model
• Two distinct Mott-Insulator to Bose-glass transitions and breakdown of self averaging in the disordered Bose-Hubbard model
• Anomalous quantum glass of bosons in a random potential in two dimensions
• Breakdown of self-averaging in the Bose glass
• Replica symmetry breaking in the Bose glass
• Tuning the disorder of superglasses
• Finite temperature phase diagram of the extended Bose-Hubbard model in the presence of disorder
• Off-diagonal Long-Range Order and Supersolidity in a Quantum Solid with Vacancies