Research Highlights
Dynamical mean-field theory (DMFT) and its nonlocal extensions
DMFT is a go-to method for theoretically studying strongly correlated electrons. It maps a lattice system onto a quantum impurity model to be solved by an "impurity solver." The availability and accuracy of DMFT calculations thus depend on the choice of the solver. The numerical renormalization group (NRG) is a tensor network method specialized for solving impurity problems, which can provide accurate dynamical properties for arbitrary (real or imaginary) frequencies and temperatures [S.-S. B. Lee and A. Weichselbaum, Phys. Rev. B 94, 235127 (2016); S.-S. B. Lee et al., Phys. Rev. Lett. 119, 236402 (2017); S.-S. B. Lee et al., Phys. Rev. X 11, 041007 (2021)] (see "Strongly correlated electrons" below).
Recently we accomplished the first steps (see "Multipoint correlation functions" below) towards a nonlocal extension of DMFT+NRG, which is a promising approach for treating nonlocal strong correlations. Here we compute the multipoint correlation functions of DMFT solutions and use them to solve a set of field-theoretical equations, called parquet equations. Such a "tensor networks meet quantum field theory" approach will be able to provide accurate correlation functions for strong interactions and low temperatures, which is a holy grail of quantum many-body theory.
Multipoint correlation functions
Many observables in quantum many-body systems, such as the conductivity and inelastic scattering spectra, are theoretically described as multipoint correlation functions. Also, the multipoint functions are key ingredients of the DMFT extensions. Recently, we made several breakthroughs in the theory of multipoint functions and their non-perturbative computation [F. B. Kugler et al., Phys. Rev. X 11, 041006 (2021); S.-S. B. Lee et al., Phys. Rev. X 11, 041007 (2021); J.-M. Lihm et al., arXiv:2310.12098; A. Ge et al., arXiv:2311.11389]. We are currently pursuing multiple projects, including several international collaborations, on this topic.
Note: The two 2021 PRX papers are the first back-to-back publications written by the same team of authors, throughout the history of PRX!
Strongly correlated electrons
DMFT+NRG and its cluster extension are powerful methods for studying strongly correlated metals—especially non-Fermi liquids that are genuinely many-body quantum matter—since they can yield correlation functions for arbitrary low frequency and temperature with high accuracy.
With these, we study various strongly correlated systems, including Hund metals (e.g., iron-based superconductors, transition metal oxides) [E. Walter et al., Phys. Rev. X 10, 031052 (2020); Y. Wang et al., Phys. Rev. Lett. 124, 136406 (2020); F. B. Kugler et al., Phys. Rev. Lett. 124, 016401 (2020)], heavy fermions (e.g., Ce and Yb compounds) [A. Gleis et al., arXiv:2310.12672], Moiré materials (e.g., twisted bilayer graphene), etc.
Tensor networks for strong correlations and quantum information
Many powerful quantum many-body methods use tensor networks as the efficient representation of many-body wave functions and operators. For example, NRG and density matrix renormalization group (DMRG), which are the gold standards for solving quantum impurity models and one-dimensional systems, respectively, employ matrix product states (MPS) that are one-dimensional tensor networks. They can be generalized to higher dimensions, such as projected entangled pair states (PEPS) for two dimensions. (Refer to the course materials for "Tensor Networks" for details.)
We apply tensor networks not only for studying strongly correlated systems but also quantum processors; indeed, tensor networks can effectively emulate the states of noisy intermediate-scale quantum (NISQ) devices. Such quantum emulation will be used to design benchmarks for quantum advantages and to develop useful quantum-classical algorithms.