New Approaches to the Quantum Many-Body Problem in and Out of Equilibrium

Description: The exponential complexity of the quantum many-body problem makes it especially challenging to study computationally, meaning that efforts to explore new phases of quantum matter and new regimes of quantum dynamics are often limited in the insights afforded even by state-of-the-art simulations. As a result many new approaches have been devised to tackle the many-body problem, often relying on approximations or special solvable structures.

This project will explore a variety of analytical and/or numerical techniques to tackle challenging quantum problems both in and out of equilibrium that arise in a range of settings. Examples could include new fractionalized and broken-symmetry phases of matter in moiré and crystallographic 2D materials, new types of "glassy" phenomena in quantum systems with quenched disorder of various kinds, and new forms of dynamics linked to constraints of various types.

Techniques deployed will range from state-of-the art variational techniques, tensor-network and other quantum information-based algorithms, novel characterizations of ground states using the "many body bootstrap", and the arsenal of field-theoretic and diagrammatic approaches that are standard in the field.

This falls under the following EPSRC Research areas: cold atoms and molecules condensed matter: electronic structure condensed matter: magnetism and materials quantum devices, components, and systems quantum optics and information