Random Matrix Theory and Entanglement in Quantum Spin Chains

We compute the entropy of entanglement in the ground states of a general class of quantum spin-chain Hamiltonians - those that are related to quadratic forms of Fermi operators - between the first N spins and the rest of the system in the limit of infinite total chain length. We show that the entropy can be expressed in terms of averages over the classical compact groups and establish an explicit correspondence between the symmetries of a given Hamiltonian and those characterizing the Haar measure of the associated group. These averages are either Toeplitz determinants or determinants of combinations of Toeplitz and Hankel matrices. Recent generalizations of the Fisher-Hartwig conjecture are used to compute the leading order asymptotics of the entropy as N --> infinity . This is shown to grow logarithmically with N. The constant of proportionality is determined explicitly, as is the next (constant) term in the asymptotic expansion. The logarithmic growth of the entropy was previously predicted on the basis of numerical computations and conformal-field-theoretic calculations. In these calculations the constant of proportionality was determined in terms of the central charge of the Virasoro algebra. Our results therefore lead to an explicit formula for this charge. We also show that the entropy is related to solutions of ordinary differential equations of Painlev\'e type. In some cases these solutions can be evaluated to all orders using recurrence relations.Comment: 39 pages, 1 table, no figures. Revised version: minor correction

Entangled Light in Moving Frames

We calculate the entanglement between a pair of polarization-entangled photon beams as a function of the reference frame, in a fully relativistic framework. We find the transformation law for helicity basis states and show that, while it is frequency independent, a Lorentz transformation on a momentum-helicity eigenstate produces a momentum-dependent phase. This phase leads to changes in the reduced polarization density matrix, such that entanglement is either decreased or increased, depending on the boost direction, the rapidity, and the spread of the beam.Comment: 4 pages and 3 figures. Minor corrections, footnote on optimal basis state

Shor-Preskill Type Security-Proofs for Concatenated Bennett-Brassard 1984 Quantum Key Distribution Protocol

We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.Comment: 4 pages, RevTe

Visualizing climate change impact with ubiquitous spatial technologies

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Entanglement entropy in quantum spin chains with finite range interaction

We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L tends to infinity of the determinant of a block-Toeplitz matrix whose symbol belongs to a general class of 2 x 2 matrix functions. The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve of genus g >= 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for thes systems are characterized by the branch points of the hyperelliptic curve approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin (2004) for the XX model and Its, Jin and Korepin (2005,2006) for the XY model.Comment: 75 pages, 10 figures. Revised version with minor correction

Non-stoichiometric oxide and metal interfaces and reactions

We have employed a combination of experimental surface science techniques and density functional calculations to study the reduction of TiO2(110) surfaces through the doping with submonolayer transition metals. We concentrate on the role of Ti adatoms in self doping of rutile and contrast the behaviour to that of Cr. DFT+U calculations enable identification of probable adsorption structures and their spectroscopic characteristics. Adsorption of both metals leads to a broken symmetry and an asymmetric charge transfer localised around the defect site of a mixed localised/delocalised character. Charge transfer creates defect states with Ti 3d character in the band gap at similar to 1-eV binding energy. Cr adsorption, however, leads to a very large shift in the valence-band edge to higher binding energy and the creation of Cr 3d states at 2.8-eV binding energy. Low-temperature oxidation lifts the Ti-derived band-gap states and modifies the intensity of the Cr features, indicative of a change of oxidation state from Cr3+ to Cr4+. Higher temperature processing leads to a loss of Cr from the surface region, indicative of its substitution into the bulk

Evaluating the Relationship between Slabbing of Cr2O3/MgO Refractories Used in Steelmaking and Spalling of High Chrome Oxide Refractories Used in Gasification

Because of its excellent corrosion resistance and high temperature properties, chrome oxide refractories have been used in a number of severe service environments, including steelmaking and gasification. Refractory failure of Cr2O3/MgO or MgO/Cr2O3 refractories in steelmaking can involve a phenomena called slabbing, peeling, or chemical spalling. A similar failure mechanism exists in the high chrome oxide materials used in gasification. Gasifiers contain the reaction between a carbon feedstock, water, and oxygen under reducing conditions; producing H2 and CO used in chemicals or as fuel for power plants. A slagging gasifier typically operates between 1250- 1575°C, and with pressures between 300-1000 psi. Gasification refractory failure is by chemical dissolution and/or by spalling. Spalling is caused by slag penetration of the porous refractory surface and by expansion differences between the penetrated/non-penetrated areas, and is exacerbated by thermal cycling. Similarities between slabbing of steelmaking refractories and spalling of gasification refractories will be discussed

Microfluidic and Nanofluidic Cavities for Quantum Fluids Experiments

The union of quantum fluids research with nanoscience is rich with opportunities for new physics. The relevant length scales in quantum fluids, 3He in particular, are comparable to those possible using microfluidic and nanofluidic devices. In this article, we will briefly review how the physics of quantum fluids depends strongly on confinement on the microscale and nanoscale. Then we present devices fabricated specifically for quantum fluids research, with cavity sizes ranging from 30 nm to 11 microns deep, and the characterization of these devices for low temperature quantum fluids experiments.Comment: 12 pages, 3 figures, Accepted to Journal of Low Temperature Physic

Kahler Moduli Inflation

We show that under general conditions there is at least one natural inflationary direction for the Kahler moduli of type IIB flux compactifications. This requires a Calabi-Yau which has h^{2,1}>h^{1,1}>2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need - although these conditions may be relaxed - at least one Kahler modulus whose only non-vanishing triple-intersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the eta problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10^5-10^7) in string units, and the inflationary scale M_{infl} ~ 10^{13} GeV. We find a robust model independent prediction for the spectral index of 1 - 2/N_e = 0.960 - 0.967, depending on the number of efoldings.Comment: 17 pages, 1 figure; v2. references adde