Superfluid-Insulator Transition in an Optical Lattice

Having considered several examples of magnetic quantum phase transitions, we now turn to the superfluid-insulator transition in many-boson systems. In the section on Classical Monte Carlo Approaches we discussed how the universal critical behavior of this transition can be determined by mapping the Bose-Hubbard model, Eq. [32], onto the classical (d -I-1)-dimensional link current Hamiltonian, Eq. [35], which can then be simulated using classical Monte Carlo methods. 

To provide quantitative predictions about how to detect the superfluid-insulator transition in these experiments, Kashurnikov, Prokofev and Svistunov performed quantum Monte Carlo simulations of the singleparticle density matrix p,y = (I I /). They used the Bose-Hubbard model with harmonic confining potential and carried out world-line Monte Carlo simulations with the continuous-time Worm algorithm. The diagonal elements of the density matrix provide the real-space particle density, and 

System (f) again displays the fine structure associate with the appearance of an insulating domain in the second shell. These quantitative results can be used to identify the superfluid-insulator transition in experiments. 

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Figure 15 Superfluid-insulator transition in an optical lattice Single-particle momentum distribution. Panels (a)-(f) correspond to the systems shown in Figure 14. (Taken with permission from Ref. 111.)...

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