NSF Award
2316598
NONTECHNICAL SUMMARY<br/><br/>This award supports theoretical research on complex quantum systems that are in a highly excited or nonequilibrium state. One of the main challenges of such systems is that they heat to a high temperature, a situation which is detrimental to observing any non-trivial quantum phenomena. Nevertheless, if the system has some symmetries, this can limit heating. The award will explore how symmetries, and generalizing the notion of symmetries, can lead to phenomena out of equilibrium that are immune to heating. The project will bring together methods from mathematical physics, statistical mechanics, and condensed matter physics with the common goal being to study generalized symmetries, out of equilibrium. One consequence of generalized symmetries is that the quantum system can host objects known as "non-abelian anyons". These objects can be used to store memory that is stable for long times. The project will explore how non-abelian anyons can be realized in experimental platforms such as the so-called "Noisy Intermediate Scale Quantum" devices. <br/><br/>The project has a strong educational component as it will involve the active participation of a graduate student, an undergraduate student, and a postdoctoral research scientist. Recent developments in generalized symmetries have brought together concepts from mathematical physics, statistical mechanics, condensed matter, and high energy physics. The PI will adapt her course on theoretical condensed matter physics to introduce students to these recent developments. In addition, the PI and the junior research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program. <br/><br/>TECHNICAL SUMMARY<br/><br/>This award supports theoretical research on nonequilibrium phenomena in strongly correlated quantum systems. The focus will be twofold. One is to develop methods to study non-abelian excitations, essential for quantum computing, in a highly non-equilibrium setting, realizable in current Noisy Intermediate Scale Quantum (NISQ) devices. The second is to develop methods to study information theoretic measures that quantify how an initial decoherence grows, and entanglement spreads. <br/><br/>In the first major thrust, the PI will study Floquet models built out of a fusion category. In these models, the role of topological defects, operators that can be deformed in the space and time direction without changing the physics, will be explored. When the topological defects are invertible, these are unitary symmetries. When the topological defects are non-invertible, these act as projectors, are non-abelian, and are examples of non-invertible symmetries. The latter are also examples of generalized symmetries, and their effect on quantum dynamics will be explored. The Floquet circuits to be studied will include unitary circuits, non-unitary circuits, and dual-unitary circuits, without integrability being a key requirement. When several topological defects are applied to the circuit, creating junctions, its effect on the dynamics will be studied. The implementation of topological defects in NISQ devices will be explored. In the second thrust, the PI will employ an augmented Schwinger-Keldysh formalism to study the space-time propagation of information theoretic measures such as out of time ordered correlators. The goal will be to understand how intrinsic noise can affect propagation of the butterfly front. In addition, how proximity to localization-delocalization transitions affects information propagation will be explored.<br/><br/>The project has a strong educational component as it will involve the active participation of a graduate student, an undergraduate student, and a postdoctoral research scientist. Recent developments in generalized symmetries have brought together concepts from mathematical physics, statistical mechanics, condensed matter, and high energy physics. The PI will adapt her course on theoretical condensed matter physics to introduce students to these recent developments. In addition, the PI and the junior research scientists will broaden participation by mentoring high school students through the NYU-GSTEM program.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
