QUANTUM MECHANICS + MANY-BODY PHYSICS
I am interested in the quantum many-body problem: given a large number of quantum mechanical degrees of freedom and a detailed description of their interactions, can we predict their emergent, collective behavior? This question is relevant to a number of research areas, including condensed matter, statistical mechanics, quantum information/computation, quantum chemistry, string theory and quantum gravity.
THE RENORMALIZATION GROUP AND ENTANGLEMENT.-- A particular route to addressing this problem is the renormalization group (RG). The goal of the RG is to produce a sequence of effective descriptions of the system, corresponding to increasing length scales, and see how these effective descriptions eventually converge to some fixed point that can be properly characterized. On the other hand, in recent years our understanding of many-body wave-functions has been significantly enriched by the study of their entanglement. For instance, we have learned that in most ground states of local Hamiltonians, entanglement entropy obeys a boundary law (with, at most, logarithmic corrections).
TENSOR NETWORKS.--The multi-scale entanglement renormalization ansatz (MERA) is a modern realization of the RG ideas for quantum systems on a lattice. The MERA is a tensor network that exploits the spatial structure of entanglement to produce an efficient (i.e., computationally tractable) description of ground states. Thanks to its in-built RG flow, the MERA also produces effective descriptions that explicitly identify the degrees of freedom of a many-body system relevant at low energies. Thus, it provides both a computational tool to solve specific many-body problems as well as a natural framework to investigate emergence in quantum systems. More generally, I am interested in other tensor network states, such as matrix product states (MPS) and projected entangled-pair states (PEPS), and their use to classify possible phases of matter.
COLLECTIVE PHENOMENA.--In addition, I also apply tensor network algorithms to learn about new physics. Specifically, I study lattice models (e.g. of frustrated antiferromagnets, interacting fermions, quantum critical system) and aim at characterizing their emergent quantum phenomena (e.g. topological order, high-Tc superconductivity, quantum phase transitions, etc). More broadly, I am also interested in the potential application of these non-perturbative tools to quantum field theories and to quantum gravity.