Tharnier Puel de Oliveira - Academia.edu (original) (raw)
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Papers by Tharnier Puel de Oliveira
Physical Review E, 2012
We employ a mean-field approximation to study the Ising model with aperiodic modulation of its in... more We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, JA and JB, are present, according to the Fibonacci sequence. We calculated the pseudo-critical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents β, δ, and γ and, from the usual scaling relations for anisotropic models at the upper critical dimension (assumed to be 4 for the model we treat), we calculate α, ν, ν / / , η, and η / /. Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents which depend on the ratio r ≡ JB/JA, as expected. But the scaling relation γ = β (δ − 1) is obeyed for all values of r we studied. We characterize some thermodynamic functions as log-periodic functions of their arguments, as expected for aperiodic-modulated models, and obtain precise values for the exponents from this characterization.
Physical Review B, 2014
Topological insulators and topological superconductors (TSC) display various topological phases t... more Topological insulators and topological superconductors (TSC) display various topological phases that are characterized by different Chern numbers or by gapless edge states. In this work we show that various quantum information methods such as the von Neumann entropy, entanglement spectrum, fidelity and fidelity spectrum, may be used to detect and distinguish topological phases and their transitions. As an example we consider a two-dimensional p-wave superconductor, with Rashba spin-orbit coupling and a Zeeman term. The nature of the phases and their changes are clarified by the eigenvectors of the k-space reduced density matrix. We show that in the topologically non-trivial phases the highest weight eigenvector is fully aligned with the triplet pairing state. A signature of the various phase transitions between two points on the parameter space is encoded in the k-space fidelity operator.
We analyse the entanglement entropy properties of a two-dimensional p-wave superconductor with Ra... more We analyse the entanglement entropy properties of a two-dimensional p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and provides a sensible signature of each topological phase. We separately analyse the contributions to the entanglement entropy that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the subsystem. We conclude that both contributions are generically non-universal depending on the specific Hamiltonian parameters and on the particular geometry. Nevertheless, contributions to the entanglement entropy due to different kinds of boundaries or edges simply add up. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state.
Physical Review E, 2012
We employ a mean-field approximation to study the Ising model with aperiodic modulation of its in... more We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, JA and JB, are present, according to the Fibonacci sequence. We calculated the pseudo-critical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents β, δ, and γ and, from the usual scaling relations for anisotropic models at the upper critical dimension (assumed to be 4 for the model we treat), we calculate α, ν, ν / / , η, and η / /. Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents which depend on the ratio r ≡ JB/JA, as expected. But the scaling relation γ = β (δ − 1) is obeyed for all values of r we studied. We characterize some thermodynamic functions as log-periodic functions of their arguments, as expected for aperiodic-modulated models, and obtain precise values for the exponents from this characterization.
Physical Review B, 2014
Topological insulators and topological superconductors (TSC) display various topological phases t... more Topological insulators and topological superconductors (TSC) display various topological phases that are characterized by different Chern numbers or by gapless edge states. In this work we show that various quantum information methods such as the von Neumann entropy, entanglement spectrum, fidelity and fidelity spectrum, may be used to detect and distinguish topological phases and their transitions. As an example we consider a two-dimensional p-wave superconductor, with Rashba spin-orbit coupling and a Zeeman term. The nature of the phases and their changes are clarified by the eigenvectors of the k-space reduced density matrix. We show that in the topologically non-trivial phases the highest weight eigenvector is fully aligned with the triplet pairing state. A signature of the various phase transitions between two points on the parameter space is encoded in the k-space fidelity operator.
We analyse the entanglement entropy properties of a two-dimensional p-wave superconductor with Ra... more We analyse the entanglement entropy properties of a two-dimensional p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and provides a sensible signature of each topological phase. We separately analyse the contributions to the entanglement entropy that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the subsystem. We conclude that both contributions are generically non-universal depending on the specific Hamiltonian parameters and on the particular geometry. Nevertheless, contributions to the entanglement entropy due to different kinds of boundaries or edges simply add up. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state.