Mutual information in interacting spin systems
arXiv:1303.4356
Abstract
This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting spins. Quantum information theory often focuses on the ground state of such systems; we will however be interested in what happens at finite temperature. Using mutual information, which can be seen as a generalization of entanglement entropy to the finite-temperature case, we can study the different phases occurring in these models, and in particular the phase transitions between those. We examine broadly two different classes of models: classical spins on two-dimensional lattices, and fully-connected models of quantum-mechanical spin-1/2 particles. (Abstract abridged.)
Doctoral thesis, University of Vienna
References in corpus (16)
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Matrix product states represent ground states faithfully
- Area laws in quantum systems: mutual information and correlations
- Entanglement spectrum in one-dimensional systems
- Entanglement in a second order quantum phase transition
- Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
- Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
- Strings, Projected Entangled Pair States, and variational Monte Carlo methods
- Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
- Finite Size Scaling of Mutual Information: A Scalable Simulation
- Rényi entropy of a line in two-dimensional Ising models
- Finite Temperature Critical Behavior of Mutual Information
- Quantum Fidelity and Thermal Phase Transitions
- Circuit QED scheme for realization of the Lipkin-Meshkov-Glick model
- Quantum phase transitions in fully connected spin models: an entanglement perspective
- Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions