# Research

We are a group that is primarily interested in correlated quantum phenomena in chemistry and physics. Over time, we have helped develop a wide variety of new simulation tools. See the research page for topics and methods of current interest.

## Phenomena

### Electronic Structure of Metalloenzymes

Metalloenzymes catalyze the most remarkable reactions in Nature, including photosynthesis and nitrogen fixation. The active sites of most enzymes are composed of intricate metallocluster cores. At a fundamental level, the interplay between the electronic structure of the transition metals and that of the substrates and products determines the underlying reaction pathways. In recent work, we carried out the first many-particle quantum mechanical simulations that helped fully unveil the low-energy states existing in complex metallocluster cores [1,2]. We are currently extending our techniques to tackle the most challenging problems of metalloenzyme quantum chemistry, namely, to resolve the detailed electronic structure of the M and P factors of nitrogenase, and the Mn$_4$Ca cofactor of the oxygen evolving complex.

### Numerical Theory of High Temperature Superconductivity

While high temperature superconductors were discovered more than three decades ago, little is known about their microscopic properties, and this is not for a lack of trying! In recent years, new simulation tools have emerged that promise to provide an unambiguous characterization of the microscopic physics. We have been working to design, and more recently apply, such tools to compute the phase diagram of high temperature superconductors. In recent work, we have helped produce accurate ground-state phase diagrams of microscopic lattice models of superconductivity [3,4], and to definitively resolve the long-standing mystery of the ground-state order in the underdoped region [5]. We are currently working to extend these techniques to an ab initio setting, so we can address the long-standing goal of determining the properties of high temperature superconductors directly from the material composition.

### Precision Condensed Phase Chemistry and Physics

The traditional hierarchy of molecular quantum chemistry provides a well-trodden path to theoretical simulations of small molecule properties and spectra with accuracies that can rival and replace high resolution experiments. The same systematic approach, however, has long been absent for materials, where simulations provide more of a rough guide than definitive, quantitative answers. We are working to build the capability for “precision” simulations of condensed phase theoretical chemistry and physics. We have recently shown that we can compute crystalline lattice energies on the very small polymorph energy scale [6], and have also demonstrated a systematically improvable many-body framework for accurate band structures, spectra, and gaps [7]. We are currently working to extend our methods to benchmark quality simulations of surface spectroscopy, surface reaction chemistry, and bulk spectroscopy in two- and three-dimensional materials.

## Theoretical Methods

### Tensor Network Methods

Our group developed much of the machinery behind the use of the density matrix renormalization group and matrix product states in quantum chemistry [8-12]. Our current work focuses on numerical algorithms for higher dimensional tensor networks, as well as the use of matrix product states in new quantum chemical settings [13-15].

### Quantum Embedding Methods and Local Correlation

We helped to introduce quantum chemistry to dynamical mean-field theory [16-17], and more recently devised the density matrix embedding theory for strongly correlated quantum embeddings [3,18-20]. In local correlation, we developed the orbital specific virtual ansatz [21-23]. We are currently interested in the connection between quantum embedding methods and traditional local correlation techniques, particularly for spectroscopy and condensed phase problems.

### Quantum Monte Carlo

From time to time, we have fun working at the interface between quantum Monte Carlo and other numerical techniques. In the past, this has led to new variational and trial states in QMC wavefunctions [24-25], as well as optimization methods and ways to target excited states [26-27]. Recently, we have been interested in using diffusion Monte Carlo to simulate the master equations appearing in classical non-equilibrium statistical mechanics.

### Multireference Dynamic Correlation Methods

We maintain a long-standing interest in dynamical correlation methods within multireference settings [28-29]. We are currently interested in efficient formulations of multireference perturbation theory that can handle large active spaces, where we have recently shown that the long-standing paradigm of internal contraction can be entirely avoided [14,30].

### Quantum Chemistry with Periodic Boundary Conditions

We are developing a rich infrastructure for systematic quantum chemistry, such as coupled cluster theory, in periodic systems. We recently demonstrated the first spectral simulations with coupled cluster theory in three-dimensional materials [7,31]. We are currently extending this framework to local methods and dynamics in semiconducting and metallic materials.

### Time-dependent Simulations

We are developing time-dependent electronic structure methods as a route to efficient spectroscopy simulations. Recently, we have been working with time-dependent methods for electronic spectroscopy on surfaces, including molecular junctions and adsorbates [32,33].

### Miscellaneous Interests

As a large group with different perspectives and expertise, we maintain interests across a wide variety of different topics. Some particular recent projects have looked into designing new quantum algorithms for short-term quantum computers, as well as the emerging connections between machine learning and tensor networks.

### Software

We maintain several different pieces of open-source software that provide access to the methods that we develop. PySCF, the Python-based simulations of chemistry framework, is a leading open-source implementation of many different quantum chemistry methods for molecules and solids [34]. BLOCK provides access to different types of density matrix renormalization group and matrix product state algorithms, with a focus on quantum chemistry Hamiltonians [35]. For further details, see our software page.