Quantum Metals Meet Gravity

Theoretical breakthroughs often take time to reach fruition. Our Fall 2018 KITP program “Chaos and Order: from Strongly Correlated Systems to Black Holes” was triggered by progress that occurred in two distinct steps over a period of more than twenty years. A paper in 1993 and a series of talks at KITP in 2015! These remarkable insights are now referred to as the SYK (Sachdev-Ye-Kitaev) model.

Click to play A simple model of quantum holography; part 1 and 2

L to R: Subir Sachdev, Jinwu Ye and Alexei Kitaev at a program at KITP. Photo by Subir Sachdev.

This research thread was first introduced and studied by Subir Sachdev, at Yale at the time, and his first PhD student Jinwu Ye. Most analytical methods of many-body systems assume that the interactions between the particles are weak, only slightly perturbing their motion. In that case the calculations are relatively simple. Quantum many-body systems with much stronger interactions are, in contrast, notoriously difficult to deal with. In their landmark 1993 paper published in Physical Review Letters, Sachdev and Ye sought to understand the possible phases of strongly interacting quantum metals or magnets (a system of spins). Remarkably, they found a transition from a glassy-like phase to a fluid-like phase that is not possible with weak interactions.

In 2015 Alexei Kitaev, then a Permanent Member at KITP, gave a series of talks that showed that the Sachdev and Ye model was both chaotic and exactly solvable. He also showed that its unique properties allowed it to be recast as a two-dimensional model of gravity! Deep insights into strongly-coupled condensed matter systems may now be gained by exploiting our understanding of the corresponding gravitational theories, even though the elementary degrees of freedom look completely different. This has sparked a large amount of research, motivated our program and also led to convening all three physicists at the KITP: S, Y and K!

- Mark Bowick
KITP Deputy Director

KITP Newsletter, Spring 2019