Holographic duality or the “AdS/CMT”
The exploration of the meaning of the Anti-de-Sitter/Conformal Field Theory duality (AdS/CFT), also known as the “gauge gravity duality” or “holographic duality” mainly in the context of physics that is measurable on our planet has been the central subject of our group since more than a decade. In 2007 the first alarm went off when Sachdev, Hartnoll, Son and their coworkers realized that this exquisitely string theoretical mathematical machinery may have dealings with the condensed matter affair called quantum criticality. Among the empirically oriented “Bell labs style” condensed matter theorists, Zaanen was the only one who had learned string theory a bit and understood what AdS/CFT was about. Schalm who was back then in Amsterdam working on string cosmology was on the outlook for an empirical theatre to apply AdS/CFT. A couple of weeks after the first announcement they bumped into each other and started talking, in fact figuring out immediately the ploy that later turned into the now seminal “Leiden-MIT fermions”. During the explosion of theoretical results that followed they trained each other in their quite different disciplines with the outcome that arguably the Leiden group is presently the most truly interdisciplinary think tank in this area. This climaxed in their writing of a book: Holographic duality in condensed matter physics, together with their Chinese partners Yan and Ya-Wen, which is now a standard text in this area.
AdS/CFT started its life in the string theory community, as a remarkable mathematical machine relating quantum field theory in D space-time dimensions to quantum-gravity in a space with one higher dimension: the “holography” aspect. In 2002 it was discovered that AdS/CFT has something to say about measurable properties of matter: the famous “minimal viscosity” of the hydrodynamical fluid realized in the finite temperature boundary, linked to universal properties of the black hole in the bulk. Condensed matter physics with its focus on the quantum physics of electrons in solids is ruled by finite density. The study of what holography has to say regarding finite density systems was taken up around 2008 and groundbreaking results followed in rapid succession. The subject of “Anti-de-Sitter/Condensed matter theory” (AdS/CMT) was born. The greatest surprise was perhaps that the bulk gravity appears to encode for a condensed matter universe that is in crucial regards similar to the traditional canon. There is a metallic state that may be characterized by a Drude-type transport, undergoing a superconducting transition being BCS like for instance in the sense that a gap opens. But looking more closely unfamiliar things are going on and these are quite suggestive regarding the empirical observations at the heart of the mystery of high Tc superconductivity – collective properties are disjoint from the single fermion ones and governed by the “Planckian dissipation”, Tc is per default high, while scaling behavior is realized that is completely different from anything known from the textbooks such as the local quantum criticality. This intrigue was the state of the art when the book was written.
Since the book appeared it has become better understood what is going on and this is very exciting: AdS/CMT has an intimate relation to quantum computation. Conventional condensed matter- and high energy physics implicitly assumes that the vacuum state is of the short ranged entangled tensor product kind. The many body entanglement which is the exquisite property of quantum physics is irrelevant and matter in the thermodynamic limit is thereby ruled by the principles of classical physics. Semiclassical quantum field theory organized around the notion of particles suffices to dress the classical saddle with perturbation theory, wiring in short ranged entanglement. However, given the sign problem strongly interacting fermions may well realize states of matter where the ground state is delocalized in the “NP hard” gigantic many body Hilbert space. Inspired by the bench marking of the quantum computer prototypes we call these now “quantum supreme matter”. Besides the strongly interacting “bosonic” quantum critical states (CFT’s, which are of this kind) literally nothing is known regarding the physical properties of such matter. These may be governed by general principles of a new kind, different from classical matter that is governed by the elementary excitations (the “particle principle”), spontaneous symmetry breaking and so forth. We now understand that holography describes a certain kind of “maximally” quantum supreme matter. Universal traits of the GR in the bulk translate in a variety of universal properties in the boundary and the open question is whether the electrons in copper oxides are close enough to this holographic “quantum supremacy” limit for these general principles to apply.
This perspective determines the present research effort in Leiden. This consist of two parts. On the one hand, we are exploring theoretically the relation between dense many body entanglement and holography theoretically. This revolves around themes like eigenstate thermalization, quantum chaos and so forth to shed light on holographic results. Recent progress on the computational side is also encouraging. The quantum information inspired tensor networks demonstrate that even in the case of simple Hubbard models one has to cope with dense entanglement, changing the physics dramatically from conventional semi-classical expectations (article submitted in arXiv). We are starting up a numerical tensor network effort to further explore this connection. On the other hand, the highest priority is the use of nature itself as analogue quantum computer to devise experiments that will deliver unambiguous (counter) evidence for the existence of quantum supreme matter. Our favorite theatre is formed by the high Tc superconductors for no other reason than that so much can be done in the laboratory. We have in the mean-time already identified a collection of such test, which are all non-standard involving substantial investments in the condensed matter laboratories.
Diffusion and quantum chaos: the pole skipping (to be updated)
The operator thermalization hypothesis (to be updated)