We apply the quantum renormalization group to construct a holographic dual for the U(N) vector model for complex bosons defined on a lattice. The bulk geometry becomes dynamical as the hopping amplitudes which determine connectivity of space are prom
oted to quantum variables. In the large N limit, the full bulk equations of motion for the dynamical hopping fields are numerically solved for finite systems. From finite size scaling, we show that different phases exhibit distinct geometric features in the bulk. In the insulating phase, the space gets fragmented into isolated islands deep inside the bulk, exhibiting ultra-locality. In the superfluid phase, the bulk exhibits a horizon beyond which the geometry becomes non-local. Right at the horizon, the hopping fields decay with a universal power-law in coordinate distance between sites, while they decay in slower power-laws with continuously varying exponents inside the horizon. At the critical point, the bulk exhibits a local geometry whose characteristic length scale diverges asymptotically in the IR limit.
Temperature and magnetic field studies of the elastic constants of the chromium spinel CdCr_2O_4 show pronounced anomalies related to strong spin-phonon coupling in this frustrated antiferromagnet. A detailed comparison of the longitudinal acoustic m
ode propagating along the [111] direction with theory based on an exchange-striction mechanism leads to an estimate of the strength of the magneto-elastic interaction. The derived spin-phonon coupling constant is in good agreement with previous determinations based on infrared absorption. Further insight is gained from intermediate and high magnetic field experiments in the field regime of the magnetization plateau. The role of the antisymmetric Dzyaloshinskii-Moriya interaction discussed and we compare the spin-phonon coupling in CdCr_2O_4 in both the ordered and disordered states.
We calculate the tunneling conductance of a graphene normal metal-insulator-superconductor (NIS) junction with a barrier of thickness $d$ and with an arbitrary voltage $V_0$ applied across the barrier region. We demonstrate that the tunneling conduct
ance of such a NIS junction is an oscillatory function of both $d$ and $V_0$. We also show that the periodicity and amplitude of such oscillations deviate from their universal values in the thin barrier limit as obtained in earlier work [Phys. Rev. Lett. {bf 97}, 217001 (2006)] and become a function of the applied voltage $V_0$. Our results reproduces the earlier results on tunneling conductance of such junctions in the thin [Phys. Rev. Lett. {bf 97}, 217001 (2006)] and zero [Phys. Rev. Lett. {bf 97}, 067007 (2006)] barrier limits as special limiting cases. We discuss experimental relevance of our results.
