Research Projects

This project aims to study paradigmatic lattice models of topological phases such as Haldane model and of topological orders such as Kitaev honeycomb and Toric code models, undergoing dissipative evolution, using analytic methods and large scale numerical simulations. Topological phases have brought about a revolution in our understanding of quantum aspects of matter and they are known to be suitable platforms for quantum computation due to their robustness property. Recently, dissipation due to coupling with environment has been shown to reveal novel phases and phenomena, than act as a hinderance. In fact, new emergent topological features have been discovered in the dynamics modelled by a quantum master equation, which includes some of PIs recent works. We discovered that in certain models, protected edge localisation of dissipation, a 'topological quantum channel', emerges during the evolution towards the steady state, even though the initial state does not have any topological information. Quantum channels describe the most general transformations applied to a quantum state in quantum information processing. The consequences of topology on such quantum channels have been largely unexplored, but has been gaining attention. Therefore, this project plans to address this important issue in breadth and depth. Lattice models have direct relevance for the experimental realisation in quantum materials and photonics. Though recent years have seen much exchange of ideas between condensed matter and quantum information, extensive study of dissipative lattice models have been possible recently with the advent of so-called “third-quantisation” formalism. The PIs experience in working with this formalism and collaborations with expert groups in Germany provides an advantage of immediately attacking some of the open problems in the field. We will study the dynamically emergent topological features such as winding, exceptional points, edge states and anomalies and at the same time, these features will be characterised using quantum information concepts such as relative entropy, capacity, error correction and recovery maps etc., which has not been achieved before. Such a cross disciplinary study is rewarding in two ways: It reveals novel phases and phenomena such as exceptional spin liquids, dissipative abelian and non-Abelian topological states with exotic Majorana modes etc. At the same time, it also leads to application of quantum information theory to realistic condensed matter systems. This would be of immense significance in expanding our understanding of dynamical phases of matter beyond closed systems. It would also pioneer novel ways of characterising quantum channels and quantum information in terms of topology. The program also entails training young scientists thus pushing India further to the frontiers of quantum sciences and technology.