Prof. Dr. Alejandro Muramatsu
 |
|
|||||||
Research Highlights
 | Strongly interacting electronsAlthough metals are known to mankind for thousands of years, the understanding of their physical properties was only possible with the advent of quantum mechanics. Indeed, the fact that electrons obey the Fermi-Dirac statistics is crucial to correctly describe the low temperature behavior of metals, like their linear specific heat. Even in the presence of interactions, fermions present universal characteristics encompassed under the name of Fermi-liquids, where the low energy behavior can be mapped to that of non-interacting fermions with a renormalized mass. Recently, departures from Fermi-liquid behavior was found in condensed matter systems like high temperature superconductors, due to the dominance of interactions. Such strongly correlated systems may develop unexpected states of matter like spin liquids, where the electronic magnetic moments are spatially correlated on short distances but, as in a liquid, they appear as disordered on long distances. We recently found based on large-scale numerical simulations of strongly interacting fermions on a graphene-like structure (shown in the picture on the left), one such spin-liquid, with short range correlations closely described by a resonating valence bond liquid as proposed long ago for benzene rings and more recently for cuprate high temperature superconductors.more |
|
 | Many-body quantum systems out of equilibriumWhile the theoretical description of many-body systems in equilibrium is a well established subject in statistical mechanics, the counterpart for systems out of equilibrium is much less developed. However, recent advances in the control and manipulation of ultra-cold quantum gases call for the treatment of quantum systems out of equilibrium. At least, for one-dimensional systems, a new method called time-dependent density matrix renormalization group (t-DMRG) allows now to calculate the time evolution of a many-body state, such that quantum quenches caused by a sudden change of the parameters of the system can be readily simulated. We investigated recently the time evolution of strongly correlated fermions after a sudden change of the interaction strength. The animation on the left shows the collapse and revival of the Fermi edge of interacting fermions for an initial metallic state after an increase of the interaction strength that in equilibrium would lead to an insulator. We found also, that for certain parameter values, two different initial states lead to observables that become indistinguishable after relaxation. However, the quasi-stationary state is nonthermal.more |
|
 | Correlated quantum gasesSince the experimental achievement of Bose-Einstein condensation with rubidium atoms, ultra-cold quantum gases became a new playground for investigating many-body quantum systems. Placing ultra-cold quantum gases in an optical lattice opened furthermore the possibility of creating strongly correlated systems with either bosonic or fermionic atoms, that may be implemented as quantum simulators of solid-state materials in those cases where deep insights are still necessary, as for e.g. high temperature superconductors. We performed in recent years numerical simulations of both bosonic and fermionic atoms trapped in optical lattices both in equilibrium and out of it. The animation on the left shows the expansion on an optical lattice of strongly interacting bosons out of a quasi Bose-Einstein condensate forming a Fermi edge at long times, a state of matter not generally achievable in equilibrium.more |