Ab initio holography
Abstract
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 promoted 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 ultralocality. In the superfluid phase, the bulk exhibits a horizon beyond which the geometry becomes nonlocal. Right at the horizon, the hopping fields decay with a universal powerlaw in coordinate distance between sites, while they decay in slower powerlaws 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2015
 DOI:
 10.1007/JHEP08(2015)107
 arXiv:
 arXiv:1503.06474
 Bibcode:
 2015JHEP...08..107L
 Keywords:

 AdSCFT Correspondence;
 Holography and condensed matter physics (AdS/ CMT);
 Spontaneous Symmetry Breaking;
 Renormalization Group;
 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 44+11 pages, many figures, added how to extract critical exponent from bulk (Fig. 13), other minor changes