Matthew B. Hastings

Condensed Matter Physics and Quantum Information. Nonequilibrium Statistical Physics. Soft Matter Physics.

For a full list of publications, see the arXiv. Specific research topics include:


Entanglement in Many-Body Quantum Systems

The locality of interactions in physical quantum systems imposes several constraints on the form of the ground state, especially in systems with a spectral gap. Examples include exponential decay of correlations and a higher dimensional Lieb-Schultz-Mattis theorem and area laws for the entanglement entropy. I am trying to understand more about the structure of the ground state in these systems, with applications to developing novel algorithms. One of the main methods for doing this is the use of Lieb-Robinson bounds. This research combines mathematical physics, condensed matter physics, and quantum information theory.



Statistical Mechanics of Systems on Networks

When standard systems of statistical mechanics, such as an Ising model or a free Gaussian field, are placed on a network, a general graph, the properties are often very different from the same system on a regular lattice. Examples of this include mean-field critical behavior with anomalous critical amplitudes on a small-world network and new scaling behavior in power-law networks. I am also interested in developing algorithms for problems such as community detection using statistical mechanics techniques. Recently, with Misha Chertkov and other collaborators, I have begun to study application of statistical mechanics techniques to inference and optimization problems.



Statistical Mechanics in Non-Equilibrium and Glassy Systems

I have been considering a number of problems in statistical mechanics applied to non-equilibrium and glassy systems. Some examples are: Diffusion-Limited Aggregation ; vortex entanglement with Cynthia Olson Reichhardt , featured in Nature News and Views; two-dimensional spin glasses with Carlo Amoruso, Alexander Hartmann , and Michael Moore .




Office Map

Contact

Technical Staff Member
Complex systems group T-13

Affiliate
Center for Nonlinear Studies

TA-3, Bldg. 0123, Rm. 136
Mail Stop:B213
Los Alamos National Laboratory
Los Alamos, NM 87545
hastings at lanl dot gov
(505) 665-9730