Quantum materials and algorithms discovery framework
Theory of Quantum Materials (Erhai Zhao)
Quantum materials can be theoretically described by their effective Hamiltonians that only contain the essential (e.g. orbital, spin, and valley) degrees of freedom. The effective model Hamiltonians are written in the form of quantum many-body problems. While they may appear simple, these models are notoriously hard to solve or understand. Well-known examples include the Hubbard model, t-J model, and Heisenberg model on two dimensional lattices. A central challenge in understanding correlated quantum materials is to solve their model Hamiltonians to predict their properties, such as the phase diagram or transport characteristics, to compare with experiments.
A theoretical team at QMC, led by Erhai Zhao, builds models for quantum materials and designs new methods to solve quantum many-body problems. To make progress, they borrow ideas from quantum field theory, quantum information, and stochastic machine learning. For example, recently they have built and perfected functional renormalization group for interacting electrons and lattice spin models. The numerics are designed and benchmarked to run on Graphic Processing Units to achieve massive parallel computing. They also developed tensor network algorithms for a large class of frustrated quantum magnets. An ongoing project is to reach much larger system sizes by using the neural network representation of the many-body wave function, which has proved very recently to be mathematically equivalent to certain tensor networks.
The theory team plans to study the competing orders (density waves, superconductivity, magnetism) in 2D materials and topological quantum materials using these new numerical techniques. They will closely collaborate with experimentalists within QMC on 2D materials and their heterostructures.