Dynamical effects and non-equilibrium in correlated quantum systems within the framework of matrix product states and renormalization group

• Antragsteller: Andreas Weichselbaum, Ph.D.
• Fachliche Zuordnung: Theoretische Physik der kondensierten Materie
• Förderung: Förderung von 2011 bis 2015
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 183054568

• Erstellungsjahr: 2015

Zusammenfassung der Projektergebnisse

The project on Dynamical effects and non-equilibrium in correlated quantum systems within the framework of matrix product states and renormalization group resulted in a range of excellent fruitful collaborations. Most prominently, this includes the collaboration with the quantum optics group of Atac Imamoglu at the ETH in Zurich on strongly correlated effects in quantum dot quenches (absorption and emission spectra) with links to Anderson orthogonality physics. The full density matrix NRG (fdm-NRG;) framework that we introduced in 2007 has attracted significant interest in the community through its elegant and transparent approach to statistical and dynamical quantities within the NRG framework. In particular, this includes the very fruitful and inspiring collaboration with the long-standing NRG expert Theo Costi. As part of my habilitation in 2012 yet also in the spirit of this project, I worked on the fdm-NRG approach to general dynamical quantities. Based on the complete basis sets of NRG in particular, it is explained in the transparent tensor network language how to compute dynamical correlation functions, absorption and emission spectra, as well as quantum quenches. This project also included a strong emphasis on the exploitation of non-abelian symmetries in the numerical simulations. By now, I am proud to be able to present significant advances in the treatment of non-abelian symmetries along the lines proposed in the work schedule to this project and also beyond. In the quest to implement non-abelian symmetries generically, i.e. beyond the simple well-known spin SU(2) symmetry, a transparent framework for general compact non-abelian symmetries has been proposed and successfully implemented through the QSpace4 tensor library. By now, this also led to several strong applications that targeted physical systems which intrinsically possess combinations of multiple SU(N≤3) symmetries together with symplectic symmetries Sp(2n≤6), with current work in progress for SU(N≤6). This is of clear interest in material science where, for example, transition metals with their partially filled d an f shells, quickly lead to SU(N) channel symmetric strongly correlated models in the crystalline three-dimensional setting. Based on the QSpace tensor library, frontier research on symmetric three-channel systems in the condensed matter setting, previously extremely challenging within the NRG context, thus already have become routine calculations. Their importance is underlined by the fact that by now these also have become the very center piece for the applied research projects of three doctoral students in the group that I have been affiliated and thus also collaborating with partly through other DFG grants. Due to lack of manpower as originally applied for, however, unfortunately some of the topics on non-equilibrium physics coult not be pursued. In particular, this concerns the topic periodic driving. Therefore it is my intention to refocus on these topics via additional funds.

Projektbezogene Publikationen (Auswahl)

• Incommensurate correlations in the anisotropic triangular heisenberg lattice, Phys. Rev. B 84, 245130 (2011)
  A. Weichselbaum and S. R. White
  
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach, Annals of Physics 327, 2972–3047 (2012)
  A. Weichselbaum
  
• Tensor networks and the numerical renormalization group, Habilitation thesis (Munich, Germany, 2012)
  A. Weichselbaum
  
• Tensor networks and the numerical renormalization group, Phys. Rev. B 86, 245124 (2012)
  A. Weichselbaum
  
• Identifying symmetry-protected topological order by entanglement entropy, Phys. Rev. B 88, 245121–245129 (2013)
  W. Li, A. Weichselbaum, and J. von Delft
  
• Non-fermi-liquid behavior in transport through co-doped au chains, Phys. Rev. Lett. 110, 196402 (2013)
  S. Di Napoli, A. Weichselbaum, P. Roura-Bas, A. A. Aligia, Y. Mokrousov, and S. Blügel
  
• Proposed Rabi-Kondo correlated state in a laser-driven semiconductor quantum dot, Phys. Rev. Lett. 111, 157402 (2013)
  B. Sbierski, M. Hanl, A. Weichselbaum, H. E. Türeci, M. Goldstein, L. I. Glazman, J. von Delft, and A. Imamoglu
  
• (2014), Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
  T. Liu, W. Li, A. Weichselbaum, J. von Delft, and G. Su
  
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet (2014)
  W. Li, A. Weichselbaum, J. von Delft, and H.-H. Tu