Entanglement signatures of correlated electron systems

Patra, Siddhartha (2022) Entanglement signatures of correlated electron systems. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Siddhartha Patra (14IP022)) 14IP022.pdf - Submitted Version Restricted to Repository staff only Download (14MB)

Abstract

This thesis reports the study of entanglement signatures of various correlated electronic systems. Strong interparticle interactions and quantum fluctuations can lead to the formation of exotic phases that lie beyond the Landau-Ginzburg-Wilson (LGW) paradigm and the regime of validity of approaches that are perturbative in nature. Such phases can be broadly classified into two classes: gapped and gapless. We have studied the entanglement properties of both types of systems in this thesis, and briefly present the main results here. Topologically ordered phases are a special class of gapped phases of quantum liquids that show fractional statistics, nontrivial dependence of ground state degeneracy on the underlying manifold, etc. Long-range entanglement and a ground state configuration that is robust against local perturbations make these topologically ordered systems very useful for proposals for the implementation of topological quantum computing. Various spin liquids and mathematical models like the toric code have been studied to show long-range entanglement and topological order. Staring with the generalized reduced BCS model, we have used the unitary renormalization group (URG) method to show the emergence of a Cooper pair insulating (CPI) phase which has Cooper pairs but no long-range phase coherence among them (i.e., a vanishing off-diagonal long-range order (ODLRO)). A non-local gauge theoretical structure of the effective Hamiltonian and degenerate ground-state manifold are some of the important properties of this phase. Apart from a degenerate entanglement spectrum, topological entanglement entropy (TEE) is another special feature of a topologically ordered system. TEE indicates a geometry-independent term in the von-Neumann entanglement measure, and arises purely from the topological properties of the topologically ordered system.

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