Block Spin Ground State and 3-Dimensionality of (K,Tl)Fe1.6_{1.6}Se2_2

The magnetic properties and electronic structure of (K,Tl)y Fe1.6 Se2 is studied using first-principles calculations. The ground state is checkerboard antiferromagnetically coupled blocks of the minimal Fe4 squares, with a large block spin moment ~11.2{\mu}B . The magnetic interactions could be modelled with a simple spin model involving both the inter- and intra-block, as well as the n.n. and n.n.n. couplings. The calculations also suggest a metallic ground state except for y = 0.8 where a band gap ~400 - 550 meV opens, showing an antiferromagnetic insulator ground state for (K,Tl)0.8 Fe1.6 Se2 . The electronic structure of the metallic (K,Tl)y Fe1.6 Se2 is highly 3-dimensional with unique Fermi surface structure and topology. These features indicate that the Fe-vacancy ordering is crucial to the physical properties of (K,Tl)y Fe2-x Se2 .Comment: Magnetic coupling constants double checked, journal ref. adde

Holographic entropy inequalities and gapped phases of matter

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the "cyclic inequalities" derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.Comment: 20 pages, 4 figures. v2: section 4 rewritten, where all linear entropy (in)equalities satisfied by area-law systems are derived and an error in their relations to graph theory is correcte

Towards Bulk Metric Reconstruction from Extremal Area Variations

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension $d \geq 4$, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.Comment: 33+4 pages, 7 figures; v2: addressed referee comment

Quantum Circuit Cosmology: The Expansion of the Universe Since the First Qubit

We consider cosmological evolution from the perspective of quantum information. We present a quantum circuit model for the expansion of a comoving region of space, in which initially-unentangled ancilla qubits become entangled as expansion proceeds. We apply this model to the comoving region that now coincides with our Hubble volume, taking the number of entangled degrees of freedom in this region to be proportional to the de Sitter entropy. The quantum circuit model is applicable for at most 140 $e$-folds of inflationary and post-inflationary expansion: we argue that no geometric description was possible before the time $t_1$ when our comoving region was one Planck length across, and contained one pair of entangled degrees of freedom. This approach could provide a framework for modeling the initial state of inflationary perturbations.Comment: v2, minor correction

De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity

We investigate the proposed connection between de Sitter spacetime and the MERA (Multiscale Entanglement Renormalization Ansatz) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite-dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). We also suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti-de Sitter space.Comment: 24 pages, 12 figures. Updated to be consistent with PRD versio

Dielectric modelling of human skin and breast tissue in terahertz frequencies : potential application to cancer detection

University of Technology Sydney. Faculty of Engineering and Information Technology.Growing developments in the generation and detection of terahertz (THz) radiation over more than two decades have created a strong incentive for researchers to study the biomedical applications of terahertz imaging. Contrasts in the THz images of various types of cancer, especially skin and breast cancer, are associated with changes in the dielectric properties of cancerous tissues. In fact, dielectric models can explain the interaction between terahertz radiation and human tissue at a molecular level just as their parameters have the potential for becoming indicators of cancer. However, dielectric modelling of various forms of human tissue remains limited due to a number of factors, especially suboptimal fitting algorithms and tissue heterogeneity. Thanks to the high water content of human skin, its dielectric response to terahertz radiation can be described by the double Debye model. The existing fitting method using a nonlinear least square algorithm can extract the model parameters which track their measurements accurately at frequencies higher than one THz but poorly at lower frequencies. However, the majority of dielectric contrast between normal and cancerous skin tissues has been observed in the low THz range. Accordingly, this research has developed two global optimization algorithms which are capable of globally accurate tracking thereby supporting the full validity of the double Debye model in simulating the dielectric spectra of human skin in the THz frequencies. Numerical results confirm their superiority over the conventional methods. Furthermore, the next goal of the study is to apply statistical analysis to the parameters of the double Debye model in order to test their discrimination capability of skin cancer from normal tissue. Linear programming and support vector machine algorithms have also been employed using these parameters to classify normal skin tissue and basal cell carcinoma. By combining the double Debye parameters, the classification accuracy has shown significant improvement. The encouraging outcomes confirm the classification potential of the double Debye parameters. The double Debye model, however, has been shown to be not suitable for simulating human breast tissue due to its low water content and heterogeneous structure, thus limiting the understanding of the THz dielectric response of breast tissue. To overcome this problem, this study proposes a new non-Debye dielectric model to fit the dielectric spectra of human breast tissue. Due to the mathematical complexity of the fitting procedure, a sampling gradient algorithm of non-smooth optimization is used to optimize the fitting solution. Simulation results confirm applicability of the non-Debye model through its exceptional ability to fit the examined data. Statistical measures have also been used to analyse the possibility of using the parameters of this model to differentiate breast tumours from healthy breast tissue. Based on the statistical analysis, popular classification methods such as support vector machines and Bayesian neural network have also been applied to examine these parameters and their combinations for breast cancer classification. The obtained classification accuracies indicate the classification potential of the model parameters as well as highlighting several valuable features of the parameter combinations