The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation In a spherical geometry. It is shown that Laughlin`s mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.The ground and the excited states of a two-dimensional anyon system are studied via finite-size numerical calculations and single-mode approximation In a spherical geometry. It is shown that Laughlin`s mean field theory gives an accurate description of the ground state properties. We find, consistent with earlier analytic theories, that the collective mode of the system exhibits a linear dispersion in the long wavelength limit, and predict a novel roton minimum at a finite value of the wavenumber q. We also discuss the consequences on the anyon spectrum of having a model repulsive interaction between the particles.

Dec 31, 19910 citations

Mutual information in interacting spin systems

Johannes Wilms

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.)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.)

arXiv:1303.4356Mar 18, 20130 citations

Fundamentals of Information Theory

Elloá B. Guedes, Francisco de Assis, Rex A. C. Medeiros

Springer eBooksJan 1, 20166 citations

Quantum Information Theory

János A. Bergou, Mark S. Hillery, Mark E. Saffman

Graduate texts in physicsJan 1, 20211 citation

Quantum information approach to a Bose–Einstein condensate in a tilted double-well system

Zhao Liu, Hongli Guo, Shu Chen +1 more

We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$ ), two transitions are found. For a moderate tilt (for example $10^{-3}$ ), only one transition is found. For a large tilt (for example $10^{-1}$ ), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$ . This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large- $N$ limit it can be.We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitions are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.

arXiv:1111.4879Journal of Physics B Atomic Molecular and Optical PhysicsFeb 14, 20122 citations

10^{-10}

), two transitions are found. For a moderate tilt (for example

10^{-3}

), only one transition is found. For a large tilt (for example

10^{-1}

), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number

N

. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-

N

limit it can be.