Ka-Ming Tam

Dept. of Physics and Astronomy, Louisiana State University

Research Directions

1. Dynamical Mean Field Theory and its Generalizations

Dynamical mean field theory has become a popular method for solving strongly correlated sys- tems, in particular, when their properties are determined by local physics, such as the Mott transi- tion. However, the dynamical mean field approximation fails in capturing the spatial fluctuations which are crucial for understanding many important characteristics of interesting materials, no- tably the cuprates and the heavy fermion compounds. The cluster generalizations of the dynamical mean field theory circumvent some of its shortcom- ing. Unfortunately, the size of the cluster is rather limited as methods such as exact diagonalization and Quantum Monte Carlo become prohibitively expensive for large cluster sizes.

2. Machine Learning Approach for Materials Science

Machine learning has seen a rapid development over the last decade. Rather sophisticated packages are readily available in various open sources packages. The time is ripe to unleash the potential of machine learning approach to gain insight from the data in scientific research. On a superficial perspective, machine learning can be regarded as a new approach to analyzing data. Conventional approaches in physics focus mostly on calculating some kind of averages. The machine learning approach tends to emphasize on looking for patterns. Recognizing patterns and categorizing data with similar patterns are strong suit of machine learning. We have used an unsupervised machine learning approach to categorize the data from molecular dynamics simulations and to further determine the phase transition. Conventional methods for detecting phase transition emphasize on the calculation of physical quantities, such as susceptibility, free energy, and heat capacity. The discontinuity or divergence of those physical quantities signals a putative phase transition. In contrast with conventional methods, machine learning approach does not rely directly on a priori knowledge of the systems. The machine learning method finds an order parameter by itself from the raw data set. The order parameter can then be used to identify the phase transition. We demonstrate this new approach by applying an unsupervised machine learning method to estimate the melting point for aluminum from the molecular dynamics data.

3. Frustrated and Disordered Classical and Quantum Spin Systems

Disordered systems have long provided challenging problems in condensed matter physics. Studies on amorphous materials have led to a completely new type of ordering–glass ordering. On the other hand, frustrated systems manifest themselves as having a macroscopic ground state degeneracy which facilitates various peculiar phenomena due to the absence of ordering. Large scale simulations both at the classical and quantum levels are essential in the study of frustrated systems.

4. Functional Renormalization Group

I have generalized renormalization group techniques to study the momentum and frequency dependence for one-dimensional systems with electron-phonon coupling. Although the standard renormalization method has been applied for more than three decades to one-dimensional quantum problems, some recent surprising discoveries have shown the limitations of the conventional implementation of this method. In particular, a bond order wave phase in the half-filled one-dimensional extended Hubbard model, whose existence is now beyond doubt, cannot be captured by the standard bosonization and renormalization method. Working with several collaborators, we developed and applied a novel functional renormalization group (FRG) method to include systematically the renormalization of the high energy scatterings that appeared irrelevant. We were able to show that this FRG approach correctly captured, and confirmed the existence of the proposed new bond order wave phase. With the advance of experimental techniques in optical lattices, notably the recent development on the mixed dimension technique, extended Hubbard models can be realized for a wide range of couplings, and thus paving the way to verify exotic phases experimentally

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