Correlation effects in one- and two-dimensional electron systems in and out of equilibrium

• Applicant: Professor Dr. Christoph Karrasch
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2015 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 271732007

• Final Report Year: 2022

Final Report Abstract

The aim of the Emmy Noether proposal was to study correlation effects in low-dimensional quantum systems in and out of equilibrium. We had three distinct goals in the areas of G1) dynamical properties of 1d systems, G2) non-equilibrium time evolution in 2d, and G3) many-body localization. From a technical perspective, we wanted to approach these questions through methodological advancements of the functional renormalization group (FRG) as well as tensor networks. We made significant progress on all three goals of the proposal but also opened new research directions that we had not originally envisioned such as Floquet engineering or twisted bilayer graphene. In order to compute dynamical properties of 1d systems (G1), we developed various new FRG schemes. Our history of studying 1d transport via tensor networks was further strengthened and resulted in a review article. Novel experiments on twisted bilayer graphene triggered our interest in these systems; we calculated the phase diagram and gained significant experience in treating 2d models, which is important for G2. Towards G2, we developed novel 1d FRG schemes, which we used to study BKT transitions and phase diagrams of 1d systems out of thermal equilibrium. We identified Floquet engineering as a new direction and showed how superconductivity in 2d cuprates can be enhanced significantly by a coupling to a light field. Floquet engineering (classical, quantum) will play a major role in our future research. Important works in the area of many-body localization (G3) are a combined time-dependent FRG and tensor network study of anomalous transport, the development of new tensor network algorithms, and an analysis of MBL in two dimensions. In the Emmy Noether proposal, we had identified the study of interacting topological systems as an outlook and as a possible area for collaborations at the FU Berlin. We joined the CRC 183 ‘Entangled States of Matter’ during the first funding period 2016-2020 where we studied the interplay of topology and many-body localization and demonstrated how Floquet engineering, topology, and MBL can conspire to protect and control edge states at high energies. We took some important steps towards tackling 2d non-equilibrium such as developing FRG schemes in 1d (which turned out to be more difficult than anticipated) or implementing various FRG and tensor network applications for (quasi-) 2d systems in a different context. However, there is still much to be explored here and much work ahead in order to tackle the 2d nonequilibrium time evolution, which remains an open problem.

Publications

• “Entanglement scaling of excited states in large one-dimensional many-body localized systems”. Phys. Rev. B 93, 245129 (2016)
  D. M. Kennes, C. Karrasch
  
• “Second-order functional renormalization group approach to one-dimensional systems in real and momentum space”. Phys. Rev. B 96, 235122 (2017)
  B. Sbierski, C. Karrasch
  
• “Solvable hydrodynamics of quantum integrable systems”. Phys. Rev. Lett. 119, 220604 (2017)
  V. B. Bulchandani, R. Vasseur, C. Karrasch, J. E. Moore
  
• “Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion”. EPL 119, 37003 (2017)
  Y. Bar Lev, D. M. Kennes, C. Klöckner, D. R. Reichman, C. Karrasch
  
• “Strong correlations and d+id superconductivity in twisted bilayer graphene”. Phys. Rev. B 98, 241407(R) (2018)
  D. M. Kennes, J. Lischner, C. Karrasch
  
• “Light-induced d-wave superconductivity through Floquet-engineered Fermi surfaces in cuprates”. Phys. Rev. B 100, 075115 (2019)
  D. M. Kennes, M. Claassen, M. Sentef, C. Karrasch
  
• “Nonequilibrium properties of Berezinskii-Kosterlitz-Thouless phase transitions”. Phys. Rev. Lett. 125, 147601 (2020)
  C. Klöckner, C. Karrasch, D. M. Kennes
  
• “Phases of translation-invariant systems out of equilibrium: Iterative Green’s function techniques and renormalization group approaches”. New J. Phys. 22, 083039 (2020)
  C. Klöckner, D. M. Kennes, C. Karrasch
  
• “Finite-temperature transport in one-dimensional quantum lattice models”. Rev. Mod. Phys. 93, 025003 (2021)
  B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, M. Žnidarič
  
• “Many-body localization and the area law in two dimensions”
  K. S. C. Decker, D. M. Kennes, C. Karrasch