Prof. Victor Kagalovsky

In my research, I study various applications of network models, starting with the original Chalker-Coddington (CC) network model, proposed to describe the inter-plateaux transition in the integer quantum Hall effect (QHE) and based on its semiclassical picture. Different symmetries of the transfer matrices corresponding to novel symmetry classes allow the study of the spin QHE, thermal QHE, and quantum spin Hall effect with a very nontrivial phase diagram. Two recently introduced network models, a weakly chiral network model on the square lattices and a triangular network model, describe the levitation of extended states at low magnetic fields. The exact analytical expression for the spin-dependent transmission coefficients is derived to study the effect of magnetic impurities on the QHE. A fictitious nonunitary scattering matrix S is introduced for electrons that reproduces the precisely calculated scattering probabilities, with decoherence identified by the deviation of S from unitarity. My research is also devoted to a phenomenological description of topological insulators. Two of its main results are the explanation of the experiment with asymmetric current electrodes and the prediction of new quantum Hall effects in systems with ferromagnetic electrodes. In recent years, I have studied various facets of Luttinger liquids to model metal-insulator transitions in quasi-one-dimensional systems, investigate the stability of edge states in topological insulators, and explain disorder-enhanced superconductivity in one-dimensional superconductors. My most recent research topics include fractional conductance in one-dimensional conductors, quantum phase transitions in two-dimensional strongly interacting electron systems, and machine learning in condensed matter physics

I organized conferences in Dresden, Trieste, Loughborough, UK, and Pohang, South Korea. Together with German and US collaborators, we organized the program “Recent progress and perspectives in topological insulators: quantum Hall effects, ballistic vs. diffusive regimes and Anderson transitions” at  Kavli Institute for Theoretical Physics, China in April 2016. I have also been a Convener of the Advanced Study Group (August 24 - September 21, 2016) and Coordinator of the Workshop “Anderson Localization in Topological Insulators” at the Center for Theoretical Physics of Complex Systems, Institute of Basic Research, Daejeon, South Korea (September 5 – 9, 2016)

In September 2017, I participated in the Advanced Study Group on Topological Phases in Arrays of Luttinger Liquid Wires at the Center for Theoretical Physics of Complex Systems, Institute of Basic Research, Daejeon, South Korea

In June–July 2018, I participated in the Advanced Study Group: Edge Reconstruction in Quantum Hall Systems and Topological Insulators, and served as Coordinator of the International Workshop on Edge Reconstruction: Topology and Quantum Phase Transitions on the Edge

I participated as a Visiting Professor in the project "Superconducting edges of the topological insulator" at the Center for Theoretical Physics of Complex Systems, Institute of Basic Research, Daejeon, South Korea, in June 2019. The primary objective of this project was to investigate the emergence of superconductivity at the edge of topological insulators. We predicted its existence even for typical repulsive interactions

In September 2019, I visited Sophia University in Tokyo under the “Japan Society for the Promotion of Science Invitational Fellowships for Research in Japan”. The main subject of the research was the Machine Learning of the metal-insulator transition

In 2022, I returned to the Max-Planck-Institut für Physik komplexer Systeme in Dresden, Germany, as a Visiting Professor for my annual two-month research stay, and we began working on a project studying the conductance of many-channel, strongly interacting one-dimensional systems

                  I was the Convener of the Advanced Study Group on Deep Learning in Quantum Phase Transition at the Center for Theoretical Physics of Complex Systems, Institute of Basic Research, Daejeon, South Korea, held at the PCS from mid–June to mid–July 2022. I was also an Organizer of the Workshop on Recent Advances in the Physics of Strongly Correlated 2D Electron Systems at Northeastern University, Boston, USA, September 16-19. In the last three years (2023, 2024, 2025), I was a Visiting Professor at the PCS and the MPI PKS

http://www.mpipks-dresden.mpg.de/~cormag08/

http://indico.ictp.it/event/a09147/

http://www.mpipks-dresden.mpg.de/~rpsat14/

https://www.apctp.org/plan.php/Delocalisation2015

https://pcs.ibs.re.kr/PCS_Workshops/PCS_ASG_ALTI.html

http://pcs.ibs.re.kr/PCS_Workshops/PCS_Anderson_Localization_in_Topological_Insulators.html

https://pcs.ibs.re.kr/PCS_Workshops/PCS_EdgeRec.html