Entanglement Entropy in Quantum Mechanics, Field Theory and Gravity

Mukherjee, Arkaprava (2021) Entanglement Entropy in Quantum Mechanics, Field Theory and Gravity. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Arkaprava Mukherjee (16MS058)) 16MS058_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

This thesis is mainly divided into four parts. At first, we have reviewed Entanglement Entropy for the harmonic oscillator, Area law for scalar fields in three dimensions, Rényi Entropy from replica method for bosonic, fermionic fields. Then we have revisited XY spin chains and entanglement entropy in the ground state. In the second part, we have reviewed the recent developments in the algebraic definition of Target Space entanglement entropy. In the context of target space entanglement for the matrix quantum mechanical model, we have developed a straightforward approach for N = 2, 3 matrix cases by constraints on eigenvalues. We have tried to generalize it for any finite N case. In the third part, we have reviewed non-commutative geometry for gauge fields on fuzzy sphere, bosonic three matrix models. We then compute entanglement entropy for free fields on fuzzy sphere and for fluctuations on fuzzy sphere states. We have studied geometric and area law behaviour. Finally, in the fourth part, we have reviewed topological recursion relation for correlation of resolvents in genus expansion of Hermitian matrix model and choose a double scaled limit for explicit derivation of first few cases. iv

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