Entanglement in Strongly Correlated Quantum Many-body Systems
Scaling Behavior of Entanglement
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In this thesis, the scaling behavior of entanglement is investigated in quantum systems with strongly fluctuating ground states. We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way, and calculate exactly the scaling of the entanglement entropy of finite systems in an infinite universe. Our study shows that although in one dimension there is a unique relation between the quantum phase transition and the scaling behavior of entanglement, this is not necessarily true in higher dimensions. By exactly solving a spinles...
In this thesis, the scaling behavior of entanglement is investigated in quantum systems with strongly fluctuating ground states. We relate the reduced density matrices of quadratic fermionic and bosonic models to their Green's function matrices in a unified way, and calculate exactly the scaling of the entanglement entropy of finite systems in an infinite universe. Our study shows that although in one dimension there is a unique relation between the quantum phase transition and the scaling behavior of entanglement, this is not necessarily true in higher dimensions. By exactly solving a spinless fermionic system in two and three dimensions, we find that the scaling behavior of the block entropy is not exclusively controlled by the decay of the correlation function. We identify two regimes of scaling. The scaling of the block entropy crucially depends on the nature of the excitation spectrum of the system and on the topology of the Fermi surface. In free bosons systems with a generic quadratic Hamiltonian, we verify that the scaling behavior of the block entropy in higher dimensions always follows the area law.
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