Ab initio holography

作者：Lunts Peter^*; Bhattacharjee Subhro; Miller Jonah; Schnetter Erik; Kim Yong Baek; Lee Sung Sik

来源：The Journal of High Energy Physics, 2015, 2015(8): 107.

DOI：10.1007/JHEP08(2015)107

• AdS-CFT Correspondence
• Holography and condensed matter physics (AdS/CMT)
• Spontaneous Symmetry Breaking
• Renormalization Group

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.

• 出版日期2015-8-21