Ab initio holography

TL;DR

This paper constructs a holographic dual for a lattice U(N) vector model using quantum renormalization group techniques, revealing phase-dependent geometric features and critical behavior in the bulk geometry.

Contribution

It introduces a novel approach to derive a dynamical bulk geometry from a lattice vector model, highlighting phase-specific geometric structures and critical phenomena.

Findings

Insulating phase shows fragmented, ultra-local bulk geometry.

Superfluid phase exhibits a horizon with non-local geometry.

Critical point features diverging characteristic length scale.

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 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.