Research interests

  • efficient simulation of strongly correlated quantum many-body systems based on tensor network states
  • symmeries and multi-channel/orbital/flavor systems in lattice models from 1D to 2D to infinite dimensional systems [cf. dynamical meanfield theory (DMFT)]
  • QSpace tensor libarary for general abelian and non-abelian symmetries (maintenance and development towards open source)
  • strongly correlated systems in and out of equilibrium (transport, quantum quenches, Anderson orthogonality, driven systems, ...)
  • quantum information aspects of strongly correlated quantum many-body states
  • quantum measurement through environment, cat states, etc.

Research highlights

  • Exponential thermal tensor network approach for quantum lattice models (2018) — We speed up thermal simulations of quantum many-body systems in both 1D and 2D models in an exponential way by iteratively projecting the thermal density matrix $\rho=e^{−{\beta}H}$ onto itself. We refer to this scheme of doubling $\beta$ in each step of the imaginary time evolution as the exponential tensor renormalization group (XTRG). Is is attractive because of its conceptual and algorithmic simplicity that sidesteps several common hurdles of Trotter-like approaches. As a consequence, it represents a highly competitive efficient and accurate approach to thermal simulations that naturally generalizes (2D-)DMRG simulations for ground state calculations to thermal simulations.
     
  • Unified phase diagram of antiferromagnetic SU(N) spin ladders (2018) — This work features large scale DMRG simulations that fully exploit SU(N) symmetries on the specific model system of Heisenberg ladders with N symmetric flavors (up to $N\leq6$). This allows us to keep beyond a million of states [equivalent to about 8,000 SU(N) multiplets] in our DMRG simulations. The simulations are based on the QSpace tensor library.
     
  • Application of non-abelian symmetries to 2D tensor networks (2015) — We show that the spin-1 Kagome Heisenberg lattice develops spontaneous symmetry breaking (trimerization) in its ground state. This demonstrates that the QSpace tensor library provides a unique tool that can be efficiently applied to two-dimensional (2D) tensor network states!
     
  • DMFT+NRG study of spin-orbital separation in a three-band Hund's metal (2015) — Here we demonstrate that the Numerical Renormalization Group (NRG) provides a highly competitive quantum impurity solver for dynamical mean field theory (DMFT) calculations. Besides an accurate self-consistent spectral treatment of the underlying hybridization function (Zitko et al), the major ingredient in this work is the explicit exploitation of the SU(3) channel symmetry based on the QSpace tensor library.
     
  • General framework for non-abelian symmetries in tensor networks (2012) — Over the past couple of years, I have developed from scratch a generic tensor library, dubbed QSpace, short for quantum symmetry spaces. It can deal with tensors of arbitrary rank and was initially designed for abelian symmetires only (v1, 2006). Since QSpace v2 (2012; this work) it can also deal with general non-abelian symmetry settings with and without outer multiplicity in a transparent and efficient setup. It represents a fully self-contained numerical approach to non-abelian symmetries, in that it is solely based on the specific individual Lie algebras. It is coded in C++ embedded through mex-files into MatLab, which provides an excellent setting for the developement of algorithms based on tensor networks. Successfully implemented symmetries so far w.r.t. the (fdm-)NRG include multiple combinations of SU(N\(\leq\)3), symplectic Sp(2n\(\leq\)6), together with simple abelian U(1) symmetries.
     
  • Tensor networks and the numerical renormalization group (2012) — By construction, the NRG generates matrix-product-states. This therefore allows a direkt link to the flourishing recent field of tensor network states as well as quantum information. In particular, the underlying diagramatical approach proved a very convenient setting in describing and developing the aforementioned NRG algorithms.
     
  • Full-density-matrix approach to the numerical renormalization group at arbitrary temperatures (fdm-NRG, 2007) — based on the complete basis sets of Anders and Schiller (2005), this proved extremely useful in devising clean black-box algrithms (2012) for the calculation of dynamical quantities within the NRG. Traditionally, these had been calculated through carefully tailored patching schemes for an essentially discrete set of temperatures. The resulting algorithms for spectral functions (fdm-NRG), quantum quenches (tdm-NRG), as well as absorption and emission spectra based on Fermi's Golden rule (fgr-NRG) in the meantime have been applied in excellent collaborations.
     

Research grants

  • DOE Grant No. DE-SC0012704 (Brookhaven National Lab, Upton, New York, USA)
  • WE-4819/3-1 (DFG) 2-year postdoc position with focus on pushing the frontier of simulations of two-dimensional multi-orbital fermionic lattice and Heisenberg models by fully exploiting non-abelian symmetries in tensor network states (2018-2019)
  • WE-4819/2-1 (DFG) Heisenberg fellowship raised for three years, and extendable by another two years, with the Ludwig Maximilians University the hosting institution. Focus is on the efficient simulation of multi-dimensional tensor networks by direct exploitation of generic non-abelian symmetries (2015-2018).
  • I-1259-303.10/2014 (German-Israeli Foundation for Scientific Research and Development, GIF, 3 years) Theory of Strongly-Correlated Optically-Driven Nanoelectronic Systems, together with Moshe Goldstein (Israel) and Jan von Delft (Munich).
  • DPG WE-4819/1-1, raised for a period of three years, to foster my own independent research (2011-2014).
  • SFB631 (DFG), principal investigator in subproject B7, Real Time Dynamics of Driven Dissipative Quantum Systems, together with Jan von Delft (Munich) and Stefan Kehrein (Göttingen) (2011-2015).
  • TR12 (DFG), investigator in subproject A8, Nonabelian symmetries in tensor network models, together with Ulrich Schollwöck, Jan von Delft (Munich), and Peter Littelmann (Cologne) (2011-2015).

Collaborations, ongoing or recent

  • Alexei Tsvelik and Robert Konik (Brookhaven National Lab, New York) on quasi-1D ladder SU(N) spin models
  • Wei Li (LMU Munich) on simulation of 2D quantum systems using tensor networks
  • Jan von Delft (LMU Munich) on quantum impurity models
  • Ireneusz Weymann (Poznan, Poland) on stochastic treatment of impurity models
  • Thomas Quella (Cologne, Germany) on SU(N) Heisenberg models
  • Armando Aligia (Bariloche, Argentina) on non-Fermi liquid break junctions
  • Theo Costi (Forschungszentrum Julich, Germany) on NRG related topics
  • Mikhail Kiselev (ICTP, Trieste, Italy) on NRG and DMRG related topics

Current (co)supervised students

Doctoral students

  • Katharina Stadler (NRG+DMFT)

Visiting doctoral students

  • Bin-Bin Chen (2018-19; in collaboration with Prof. Wei Li, Beihang University, Beijing) on project WE-4819/3-1 (DFG) above

Diploma students

Former (co)supervised students

Doctoral students

  • Frauke Schwarz (nonequilibrium steady-state transport in quantum impurity models; 2017)
  • Benedikt Bruognolo (tensor network techniques for strongly correlated systems simulating the many-body wavefunction in zero, one, and two dimensions; 2017)
  • Markus Hanl (multi-channel Kondo systems; 2014)
  • Arne Alex (SU(N) symmetries; multi-level impurity systems; 2012)
  • Cheng Guo, Using Density Matrix Renormalization Group to Study Open Quantum Systems (2012)
  • Andreas Holzner, DMRG studies of Chebychev-expanded spectral functions and quantum impurity models (2012)
  • Wolfgang Münder, Matrix product state calculations for one-dimensional quantum chains and quantum impurity models (2011)
  • Hamed Saberi, Matrix-product states for strongly correlated systems and quantum information processing (2009)
  • Theresa Hecht, Numerical Renormalization Group studies of Correlation effects in Phase Coherent Transport through Quantum Dots (2008)

Diploma students

  • Katharina Stadler, Towards exploiting non-abelian symmetries in the Dynamical Mean-Field Theory using the Numerical Renormalization Group (2013)
  • Francesco Alaimo, On the Effects of Spin Orbit Interaction on the Conductance through a Quantum Dot in the presence of Kondo Correlations (2012)
  • Arne Alex, Non-Abelian Symmetries in the Numerical Renormalization Group (2009)
  • Wael Chibani, Analysis of the anisotropic Kondo effect using the numerical renormalization group (2011)
  • Markus Hanl, The Kondo exciton: non-equilibrium dynamics after a quantum quench in the Anderson impurity model (2009)
  • Wolfgang Münder, Matrix Product Calculation of Correlation Density Matrices for 1-Dimensional Quantum Chains (2008)
  • Andreas Holzner, Matrix product state approach for a multi-lead Anderson model (2006)

Bachelor students

  • Marc Ritter, Conductance Simulations of Transport through a Quantum Dot in the Presence of a Sharp Drop in the Hybridization Function (2017).
PDF's of theses resulting out of the above projects can be found here.