E-mail: mrigol [at] physics [dot] georgetown [dot] edu
Marcos Rigol received his B.Sc. (summa cum laude) and M.Sc. in Nuclear Physics at the Institute of Nuclear Sciences and Technologies in Havana, Cuba, in 1999 and 2000, respectively. He completed his Ph.D. in Physics (summa cum laude) under the supervision of Prof. Alejandro Muramatsu at the University of Stuttgart, Germany, in 2004. Before joining Georgetown University as an Assistant Professor in 2008, Marcos Rigol did postdoctoral fellowships with Prof. Richard T. Scalettar and Prof. Rajiv R. P. Singh at the University of California at Davis (2004-2006), with Prof. Maxim Olshanii at the University of Southern California (2006-2007), and with Prof. B. Sriram Shastry at the University of California at Santa Cruz (2007-2008). Prof. Rigol was awarded the 2011 Young Scientist Prize by the International Union of Pure and Applied Physics (Commission 10: Structure and Dynamics of Condensed Matter).
Prof. Rigol's 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 very important role in many materials, like high-Tc superconductors, and some recently realized ultracold atomics gases. Prof. Rigol follows different theoretical approaches, which combine computational and analytical tools. The beauty and challenges of his area of research rely on the fact that even though the constituents of those systems 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, Prof. Rigol's 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, he and his collaborators use exact diagonalization and time-dependent density matrix renormalization group algorithms. Prof. Rigol has also applied exact techniques derived from analytical insights to study one-dimensional integrable systems.
Dynamics and thermalization in isolated quantum many-body systems
We are interested in understanding the behavior of generic isolated quantum systems when they are taken out of equilibrium. During the transient regime, in which the system is trying to equilibrate, we are investigating metastable states that have special properties which may never occur in equilibrium. Given that quantum dynamics is unitary, we are also interested in understanding how equilibration takes place in an isolated many-body system and how to describe thermodynamic observables after relaxation.
Ultracold gases in optical lattices
These systems have emerged as almost ideal experimental realizations of model Hamiltonians that are used to study complicated condensed matter materials. We are looking at the different quantum phases and phase transitions that occur when ultracold atoms (bosons, fermions, or their mixtures) are loaded in optical lattices. Since inhomogeneities play a very important role in most experiments, we are also studying the effects of the confining potential and how experimental observables are affected by it.
Frustrated quantum magnets
Frustrated quantum magnets are fascinating systems in which exotic states of matter, like quantum spin liquids, could be realized. We are studying the ground state and finite temperature properties of some of those systems. We are particularly excited by some kagome lattice materials, like the recently synthesized Herbertsmithite, which can be described by the Heisenberg model. In relation to experiments, we would like to identify the effects that perturbations like impurities and symmetry breaking Dzyaloshinsky-Moriya interactions have on the ideal magnet properties.
We are working on the development of computational tools that, while being exact, allow one to study generic quantum systems in and out of equilibrium. In equilibrium, we have introduced, in collaboration with Rajiv R. P. Singh at UC Davis, a numerical linked cluster approach (NLC) that provides unique opportunities to study thermodynamic properties of strongly correlated systems at finite temperatures. Among the most prominent models that can be studied using NLC that cannot be treated with more standard quantum Monte-Carlo techniques are frustrated quantum magnets, the t-J model, and the fermionic Hubbard model.
Recent invited talks
- Physics 155: Mathematical & Computational Methods (Spring 2010, 2011, 2012)
- Physics 211: Relativity and Quantum Physics [Tutorials] (Fall 2008, 2009)
- Physics 505: Quantum Mechanics I (Fall 2011)
- Physics 511: Electromagnetic Radiation [Module 2] (Fall 2009)
- Physics 513: Semiconductors & Insulators [Module 1] (Spring 2009)
- M. Rigol and M. Srednicki, Alternatives to Eigenstate Thermalization, Phys. Rev. Lett. 108, 110601 (2012).
- C. N. Varney, K. Sun, V. Galitski, and M. Rigol, Kaleidoscope of Exotic Quantum Phases in a Frustrated XY Model, Phys. Rev. Lett. 107, 077201 (2011).
- L. F. Santos, A. Polkovnikov, and M. Rigol, Entropy of Isolated Quantum Systems after a Quench, Phys. Rev. Lett. 107, 040601 (2011).
- A. C. Cassidy, C. W. Clark, and M. Rigol, Generalized Thermalization in an Integrable Lattice System, Phys. Rev. Lett. 106, 140405 (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, G. G. Batrouni, V. G. Rousseau, and R. T. Scalettar, State diagrams for harmonically trapped bosons in optical lattices, Phys. Rev. A 79, 053605 (2009).
- M. Rigol, V. Dunjko, and M. Olshanii,Thermalization and its mechanism for generic isolated quantum systems, Nature 452, 854 (2008).
- M. Rigol and B. S. Shastry, Drude weight in systems with open boundary conditions, Phys. Rev. B 77, 161101(R) (2008).
- M. Rigol and R. R. P. 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 Lattice Hard-Core Bosons, Phys. Rev. Lett. 98, 050405 (2007).