The Joint Condensed Matter Seminar (JCMS) series is organised by KTH Royal Insitute of Technology, Nordita, and Stockholm University.
On Monday, May 22nd, 2023 from 11 am to 12 am we will host a seminar by Sthitadhi Roy from International Centre for Theoretical Sciences, Tata Institue of Fundamental Research, Bengaluru.
Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
The dynamics of non-Hermitian quantum systems have taken on an increasing relevance in light of quantum devices which are not perfectly isolated from their environment. The interest in them also stems from their fundamental differences from their Hermitian counterparts, particularly with regard to their spectral and eigenvector correlations. These correlations form the fundamental building block for understanding the dynamics of quantum systems as almost all other correlations can be reconstructed from it. In this work, we study such correlations across a localisation transition in non-Hermitian quantum systems. As a concrete setting, we consider non-Hermitian power-law banded random matrices which have emerged as a promising platform for studying localisation in disordered, non-Hermitian systems. We show that eigenvector correlations show marked differences between the delocalised and localised phases. In the delocalised phase, the eigenvectors are strongly correlated as evinced by divergent correlations in the limit of vanishingly small complex eigenvalue spacings. On the contrary, in the localised phase, the correlations are independent of the eigenvalue spacings. We explain our results in the delocalised phase by appealing to the Ginibre random matrix ensemble. On the other hand, in the localised phase, an analytical treatment sheds light on the suppressed correlations, relative to the delocalised phase. I will briefly touch upon some aspects in the non-Hermitian Rosenzweig-Porter ensemble as well.
Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices, S. Ghosh, M. Kulkarni, and S. Roy, arXiv:2304.09892.