Penn State Science
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My research interest is in many-body quantum systems in and out of equilibrium, with a focus in cases where particles interact strongly. Strong correlations play a fundamental role in many solid-state materials as well as in ultracold gases in optical lattices. We follow different theoretical approaches to study those systems, which combine computational and analytical tools. The beauty and challenges of this area of research rely on the fact that, even though the system constituents and the interactions among them are well known, their collective behavior can lead to the emergence of unexpected and fascinating properties.

Among the wide range of computational techniques available to study many-body quantum systems in equilibrium, my expertize focuses on those that are unbiased (exact within statistical errors and/or finite size effects), such as quantum Monte-Carlo algorithms, Lanczos and full diagonalization techniques, and linked cluster expansions. In systems far from equilibrium, we have utilized exact diagonalization and time-dependent density matrix renormalization group algorithms. We have also applied exact techniques derived from analytical insights to study one-dimensional integrable systems.

Complete List of Peer-Reviewed Publications (ResearcherID)

Publications

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M. Rigol and M. Srednicki, "Alternatives to Eigenstate Thermalization," Phys. Rev. Lett. 108, 110601 (2012)
M. Olshanii, K. Jacobs, M. Rigol, V. Dunjko, H. Kennard and V. Yurovsky, "An exactly solvable model for the integrability-chaos transition in rough quantum billiards," Nature Comm. 3, 641 (2012)
L. Santos, A. Polkovnikov and M. Rigol, "Entropy of Isolated Quantum Systems after a Quench," Phys. Rev. Lett. 107, 040601 (2011)
M. Cazalilla, R. Citro, T. Giamarchi, E. Orignac and M. Rigol, "One dimensional bosons: From condensed matter systems to ultracold gases," Rev. Mod. Phys. 83, 1405 – 1466 (2011)
I. Hen and M. Rigol, "Strongly Interacting Atom Lasers in Three Dimensional Optical Lattices," Phys. Rev. Lett. 105, 180401 (2010)
M. Rigol, "Breakdown of Thermalization in Finite One-Dimensional Systems," Phys. Rev. Lett. 103, 100403 (2009)
M. Rigol, V. Dunjko and M. Olshanii, "Thermalization and its mechanism for generic isolated quantum systems," Nature 452, 845 (2008)
M. Rigol and R. Singh, "Magnetic Susceptibility of the Kagome Antiferromagnet ZnCu3(OH)6Cl2," Phys. Rev. Lett. 98, 207204 (2007)
M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii, "Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons," Phys. Rev. Lett. 98, 050405 (2007)
M. Rigol, T. Bryant and R. Singh, "Numerical Linked-Cluster Approach to Quantum Lattice Models," Phys. Rev. Lett. 97, 187202 (2006)
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M. Rigol : Research