Quantum states in ultracold fermionic gases in optical lattices:Supersolid and dynamically generated antiferromagnetic states
Final Report Abstract
Progress in understanding the electrical and magnetic properties of different materials is not only fundamentally important for condensed matter physics, it is also extremely relevant for numerous technological applications. These include semi-conductor based electronics, magnetic memories, solid state lasers and photovoltaic cells. Many of these applications employ doped semi-conductors, which are well understood by approaches based on density functional theory. A different class of materials, known as strongly correlated systems, show a remarkable diversity in their electronic and magnetic behavior encompassing metal-to-insulator transitions, different types of charge and magnetic order, and unusual forms of superconductivity. Examples include transition metal oxide compounds, such as the cuprate high temperature superconductors, manganites or heavy fermion systems. It is conceivable that a new generation of applications, such as ultrafast transistors or energy applications, emerges from strongly correlated materials. In contrast to the group of weakly-correlated materials, it is still very challenging to reliably predict the behavior of their strongly correlated counterparts. The objective of the carried out research was to develop and apply theoretical techniques contributing to a better understanding of phases and dynamics of strongly correlated systems. There were two major research lines. The first (P1) research line dealt with the analysis of unconventional phases such as supersolidity and charge order for lattice models in equilibrium. The second (P2) one was about accessing those phases under non-equilibrium conditions. Additional research included the development of a novel scheme (DMF2RG). The study of a supersolid phase for attractive fermion turned out to be not promising. However, a replacement project on a concrete proposal of how to realize Kondo physics with cold atoms attracted a lot of attention. I hope that an experimental realization can be achieved in the near future. Another fruitful research direction was that of unconventional charge order in the cuprate superconductors. The second major research direction was that of non-equilibrium dynamic phase transitions for correlated systems. This was a technically difficult and relatively unpredictable research direction. However, we managed to carry out the project successfully and answer most of the questions posed in the original research proposal. In particular, we have been developing a general non-equilibrium framework in the Keldysh formalism for one- and two-particle quantities which allows us to analyze the behavior of a system after a fast interaction ramp. We observe the onset of growing magnetic instability modes from a pre-thermalized non-equilibrium state and map out a dynamic phase diagram for the appearance of transient ordered states. These are novel and exciting results and they should play a role in future investigations of realizing magnetic phases with ultracold atoms.
Publications
- Realizing a Kondo-correlated state with ultracold atoms, Phys. Rev. Lett. 111 (2013), 215304
J Bauer, C Salomon, E Demler
- Dynamical instabilities and transient short-range order in the fermionic Hubbard model, Phys. Rev. B 92 (2015), 024305
J Bauer, M Babadi, E Demler
(See online at https://doi.org/10.1103/PhysRevB.92.024305) - Local origin of the pseudogap in the attractive Hubbard model, Phys. Rev. B 92 (2015), 014511
R Peters and J Bauer
(See online at https://doi.org/10.1103/PhysRevB.92.014511)
