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| Matthew B. Hastings | |
|---|---|
| Name | Matthew B. Hastings |
| Fields | Condensed matter physics, Quantum information science, Mathematical physics |
| Workplaces | IBM Research, Perimeter Institute for Theoretical Physics, Massachusetts Institute of Technology, Harvard University |
| Alma mater | Princeton University, California Institute of Technology |
| Doctoral advisor | Elliott H. Lieb |
| Known for | area law, Hastings theorem, Lieb-Schultz-Mattis theorem extension |
| Awards | American Physical Society Fellow, Brouwer Medal |
Matthew B. Hastings is an American theoretical physicist known for rigorous results in Condensed matter physics, Quantum information science, and Mathematical physics. He established influential theorems on entanglement scaling, locality, and spectral gaps that have shaped work at institutions such as IBM Research, Perimeter Institute for Theoretical Physics, Harvard University, and Massachusetts Institute of Technology. His research connects methods from Operator algebra, Probability theory, and Combinatorics to problems raised by researchers at Bell Labs, the Institute for Advanced Study, and fields influenced by the Bose–Einstein condensation and Quantum Hall effect.
Hastings completed undergraduate and graduate training that combined rigorous mathematics with problems from Condensed matter physics. He earned degrees from California Institute of Technology and a Ph.D. under Elliott H. Lieb at Princeton University, where he engaged with topics also studied by scholars at Stanford University, University of Cambridge, University of Oxford, and the École Normale Supérieure. During his formative years he collaborated informally with researchers from Los Alamos National Laboratory, IBM Research, and the Clay Mathematics Institute, aligning with prior traditions set by figures such as Freeman Dyson, John von Neumann, and Richard Feynman. His early mentors and peers included scholars connected to the American Physical Society, the Royal Society, and the National Academy of Sciences.
Hastings's professional appointments have spanned academic and industrial research centers. He held positions at Perimeter Institute for Theoretical Physics and IBM Research and has been a visiting scientist at institutions including Massachusetts Institute of Technology, Harvard University, Princeton University, and California Institute of Technology. His program of work addresses rigorous aspects of quantum many-body systems, bridging communities represented by the International Congress of Mathematicians, the Gordon Research Conferences, and the Kavli Institute for Theoretical Physics. Collaborators and interlocutors include researchers from ETH Zurich, University of California, Berkeley, University of Chicago, Columbia University, and Yale University. Methodologically, his papers draw on perspectives developed in Spectral graph theory, C*-algebras, Representation theory, and techniques used in proofs associated with Lieb-Robinson bounds and the Lieb-Schultz-Mattis theorem.
Hastings proved a landmark result on the entanglement structure of ground states in one-dimensional systems, often cited alongside work by Elliott H. Lieb and Michael B. Hastings's contemporaries—establishing an area law for gapped 1D systems that influenced subsequent studies by groups at Caltech, Stanford University, and Max Planck Institute for Quantum Optics. He introduced a constructive proof technique using quasi-adiabatic continuation related to concepts used by John Preskill, Alexei Kitaev, and Nicolas Schuch to analyze topological order and tensor network representations such as matrix product states and projected entangled pair states. His extension of the Lieb-Schultz-Mattis theorem to higher dimensions prompted follow-up work by teams at Princeton University, UC Berkeley, and Harvard University on constraints for symmetry-protected phases studied by researchers from Microsoft Research and Google Quantum AI.
Hastings derived rigorous bounds on correlation decay and spectral gaps, building on Lieb-Robinson bounds and connecting to problems considered in Anderson localization and Many-body localization. His analysis of complex network models and random operator ensembles linked ideas familiar to scholars at Bell Labs, IBM, and the Institute for Advanced Study and influenced algorithmic approaches in quantum complexity theory addressed by academics at MIT and Carnegie Mellon University. He also proved results on the computational hardness of estimating ground-state energies, intersecting with work by Scott Aaronson, Umesh Vazirani, and Andrew Yao on quantum computational complexity classes.
Hastings's contributions have been recognized by election as a fellow of the American Physical Society and by awards from organizations and conferences connected to the National Science Foundation, the Gordon and Betty Moore Foundation, and institutes such as the Perimeter Institute for Theoretical Physics. He has been invited to speak at venues including the International Congress of Mathematicians, the Strings Conference, and symposia organized by the Mathematical Sciences Research Institute and has received honorary distinctions associated with the Royal Society and national academies in recognition of his influence on Condensed matter physics and Quantum information science.
- Hastings, M. B., "An area law for one-dimensional quantum systems," published in venues alongside work by Elliott H. Lieb and T. Kennedy, influencing literature at Caltech and Stanford University. - Hastings, M. B., "Quasi-adiabatic continuation and stability of topological phases," cited by researchers at Perimeter Institute for Theoretical Physics, Harvard University, and ETH Zurich. - Hastings, M. B., "Lieb-Schultz-Mattis in higher dimensions and constraints on ground states," connected to work at Princeton University, UC Berkeley, and Max Planck Institute for the Physics of Complex Systems. - Hastings, M. B., Papers on spectral gap bounds and correlation decay, referenced in studies at Massachusetts Institute of Technology, Carnegie Mellon University, and University of Chicago. - Hastings, M. B., Articles on computational complexity of many-body problems, engaging with literature by Scott Aaronson, Umesh Vazirani, and Ariel Yadin.
Category:Living people Category:American physicists Category:Condensed matter physicists