Entanglement Entropy in Many-Fermion System

Abstract

In this four-part prospectus, we first give a brief introduction to the motivation for studying entanglement entropy and some recent development. Then follows a summary of our recent work about entanglement entropy in states with traditional long-range order. After that we demonstrate calculation of entanglement entropy in both one-dimensional spin-less fermionic systems as well as bosonic systems via different approaches, and connect them using one-dimensional bosonization. In the last part, we briefly sketch the idea of bosonization in high-dimensions, and discuss the possibility and advantage of approaching the scaling behavior of entanglement entropy of fermions in arbitrary dimensions via bosonization.

Dissertation tentative prospectus submitted to dissertation committee on 8/20/08; successfully defended on 8/21/08

References in corpus (27)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entropy and Area
• Calculation of reduced density matrices from correlation functions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Bosonization for Beginners --- Refermionization for Experts
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Violation of the entropic area law for Fermions
• Interacting anyons in topological quantum liquids: The golden chain
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement and alpha entropies for a massive Dirac field in two dimensions
• Entanglement in XY Spin Chain
• An entanglement-area law for general bosonic harmonic lattice systems
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Scaling Behavior of Entanglement in Two- and Three-Dimensional Free Fermions
• Entanglement Entropy beyond the Free Case
• Entanglement entropy in collective models
• Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
• Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
• Multidimensional Bosonization
• Luttinger's Theorem and Bosonization of the Fermi Surface
• Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Block Entanglement Entropy of Ground States with Long-Range Magnetic Order