New States: A focus of the Ultra Quantum Matter (UQM) Collaboration is the search for new states of matter which are effectively described by gauge theories. Although gauge theories have been studied, beginning with Maxwell’s electrodynamics and more recently in particle physics, new realization in condensed matter systems opens, quite literally, a new dimension. Quantum matter motivates the study of entirely new kinds of gauge theories, not previously considered by particle theorists. A prime example are fractons, originally conceived to engineer robust quantum memories, which are not readily described by conventional quantum field theory. Fractons are a major thrust within the UQM Collaboration and PIs with different backgrounds have launched an attack utilizing complementary tools, while remaining committed to achieving a few overarching goals. We have now achieved a deeper understanding of the underlying mathematical classification of these phases (which incorporates foliated QFTs), progress in field theory and even string theory (d-brane) approaches to describing fractons, and preliminary progress in realizations of these exotic states in coupled Quantum Hall layers.
Gapless UQM: Another focus area of the Collaboration is gapless ultra-quantum matter (UQM) with a Fermi surface of low-energy excitations. While such UQM may play an important role in strongly correlated metals, it presents numerous challenges for theoretical descriptions. However, a number of key developments within the Collaboration over the last year – some closely tied to ongoing work at the Flatiron Institute – are opening the way for new progress. These developments include extensions of the Sachdev-Ye-Kitaev model to include “Mottness,” the localization of electrons by strong repulsive interactions, and applications to cuprate superconductors. At the same time, progress in solving Einstein’s equations for general relativity in large space-time dimension D has led to a new understanding of non-Fermi liquids at large-D, via gauge-gravity duality. Results thus obtained are closely related to those arising from dynamical mean-field theory (DMFT), a quite different large-D approach to correlated materials. These advances in understanding the dynamics of gapless UQM are complemented by significant progress on kinematic constraints – related to anomalies – imposed on low-energy effective theories. For instance, it has been shown that compressible systems – those with continuously tunable electron density – must have a very large low-energy symmetry group, larger than any compact Lie group.
Physical Realizations: A major breakthrough in the creation of synthetic quantum matter was recently achieved. When two sheets of graphene are twisted relative to one another to a precise magic angle close to one degree, dramatic phenomena have been reported as a result of the moiré patterns appearing between the sheets. These `moiré’ materials are important settings to realize new forms of UQM. Our collaboration is actively contributing to this exciting area, developing the theory of magnetism and superconductivity in these devices as well as proposals for realizing new forms of UQM.
Probes of UQM: A growing realization has been that even if exotic states are created in quantum materials, a new generation of tools will be needed to identify and to properly characterize them. This is because existing probes are biased towards classical order parameters, and lack the ability to discern subtle forms of quantum order. Here too significant progress has been achieved – one example worth highlighting is utilizing random rotations of quantum states followed by measurements to identify exotic forms of order. While this may appear to be the equivalent of adding noise to a measurement, in fact subtle correlations in the noise turn out to be the signal.
New Directions in UQM: How is quantum matter affected by measurement? While measurement is fundamental to quantum mechanics, it had not been discussed much in the context of many quantum particles, i.e. quantum matter. In few particle quantum theory, measurement is known to lead to the quantum “Zeno effect” which prevents time evolution, the reference being to Zeno’s paradox for a continuously monitored system. Is there a quantum many-body Zeno effect? This was answered in a flurry of activity in the recent past with important contributions from the UQM collaboration. Remarkably, a finite measurement threshold was shown to exist separating two distinct phases. Deep connections to the theory of quantum error correcting codes have emerged and a surprising fact – conformal invariance at the phase transition – has also been established.
Public Lecture (Wednesday, January 20)
Xie Chen, Ph.D.
Professor, Division of Physics, Mathematics and Astronomy, California Institute of Technology
Fracton: From Quantum Hard Drive to Foliated Manifold
Wednesday, January 20, 2021
4:45 – 5:00 PM ET Webinar waiting room opens
5:00 – 6:15 PM ET Talk + Q&A
Quantum systems are weird. A large quantum system where all the constituent quantum particles strongly interact with each other is even weirder. The recently discovered fracton systems are excellent examples of this. The constituent particles interact so strongly that single-particle features are obscured, and the low energy dynamics of the system is dominated by local defects that look completely different. They can have different charge, different statistics, and more surprisingly, they can be completely immobile, rendering even simple notions like momentum and mass inadequate.
In this lecture, Xie Chen will tell the story of how such an unexpected discovery made in the quest for a quantum hard drive led to surprising developments. Such developments include the redefinition of fundamental concepts like phase and universality based on foliation in manifolds and the re-formulation of field theory. Along the way, the quest connected researchers in quantum information, condensed matter and high-energy theory, all inspired by the endless weirdness of strongly interacting quantum many-body systems.