Classical-Field Renormalization Flow of One-Dimensional Disordered Bosons

We show that in the regime when strong disorder is more relevant than field quantization the superfluid--to--Bose-glass criticality of one-dimensional bosons is preceded by the prolonged logarithmically slow classical-field renormalization flow of the superfluid stiffness at mesoscopic scales. With the system compressibility remaining constant, the quantum nature of the system manifests itself only in the renormalization of dilute weak links. On the insulating side, the flow ultimately reaches a value of the Luttinger parameter at which the instanton--anti-instanton pairs start to proliferate, in accordance with the universal quantum scenario. This happens first at astronomic system sizes because of the suppressed instanton fugacity. We illustrate our result by first-principles simulations.

Comment on Direct Mapping of the Finite Temperature Phase Diagram of Strongly Correlated Quantum Models by Q. Zhou, Y. Kato, N. Kawashima, and N. Trivedi, Phys. Rev. Lett. 103, 085701 (2009)

In their Letter, Zhou, Kato, Kawashima, and Trivedi claim that finite-temperature critical points of strongly correlated quantum models emulated by optical lattice experiments can generically be deduced from kinks in the derivative of the density profile of atoms in the trap with respect to the external potential, $kappa = -dn(r)/dV(r)$. In this comment we demonstrate that the authors failed to achieve their goal: to show that under realistic experimental conditions critical densities $n_c(T,U)$ can be extracted from density profiles with controllable accuracy.

Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {it theorem of inclusions} which states that for any transition in a disordered system one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: The critical disorder bound, $Delta_c$, corresponding to the onset of disorder-induced superfluidity, satisfies the relation $Delta_c > E_{rm g/2}$, with $E_{rm g/2}$ the half-width of the Mott gap in the pure system.