Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size $N$ is partitioned into two subclusters. At each iteration the Lanczos vector is projected into two sets of $n_{{\rm svd}}$ smaller subcluster vectors using singular value decomposition. For low entanglement entropy $S_{ee}$, (satisfied by short range Hamiltonians), the truncation error is expected to vanish as $\exp(-n_{{\rm svd}}^{1/S_{ee}})$. Convergence is tested for the Heisenberg model on Kagom\'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given.Comment: 7 pages, 8 figure

Even-odd correlations in capacitance fluctuations of quantum dots

We investigate effects of short range interactions on the addition spectra of quantum dots using a disordered Hubbard model. A correlation function \cS(q) is defined on the inverse compressibility versus filling data, and computed numerically for small lattices. Two regimes of interaction strength are identified: the even/odd fluctuations regime typical of Fermi liquid ground states, and a regime of structureless \cS(q) at strong interactions. We propose to understand the latter regime in terms of magnetically correlated localized spins.Comment: 3 pages, Revtex, Without figure

Atomic Quantum Simulation of Dynamical Gauge Fields coupled to Fermionic Matter: From String Breaking to Evolution after a Quench

Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.Comment: 14 pages, 5 figures. Main text plus one general supplementary material and one basic introduction to the topic. Published versio

QCD as a Quantum Link Model

QCD is constructed as a lattice gauge theory in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. The resulting quantum link model for QCD is formulated with a fifth Euclidean dimension, whose extent resembles the inverse gauge coupling of the resulting four-dimensional theory after dimensional reduction. The inclusion of quarks is natural in Shamir's variant of Kaplan's fermion method, which does not require fine-tuning to approach the chiral limit. A rishon representation in terms of fermionic constituents of the gluons is derived and the quantum link Hamiltonian for QCD with a U(N) gauge symmetry is expressed in terms of glueball, meson and constituent quark operators. The new formulation of QCD is promising both from an analytic and from a computational point of view.Comment: 27 pages, including three figures. ordinary LaTeX; Submitted to Nucl. Phys.

Elucidating the structural composition of a Fe-N-C catalyst by nuclear and electron resonance techniques

Fe–N–C catalysts are very promising materials for fuel cells and metal–air batteries. This work gives fundamental insights into the structural composition of an Fe–N–C catalyst and highlights the importance of an in‐depth characterization. By nuclear‐ and electron‐resonance techniques, we are able to show that even after mild pyrolysis and acid leaching, the catalyst contains considerable fractions of α‐iron and, surprisingly, iron oxide. Our work makes it questionable to what extent FeN4 sites can be present in Fe–N–C catalysts prepared by pyrolysis at 900 °C and above. The simulation of the iron partial density of phonon states enables the identification of three FeN4 species in our catalyst, one of them comprising a sixfold coordination with end‐on bonded oxygen as one of the axial ligands

Quantum simulation of spin ordering with nuclear spins in a solid state lattice

An experiment demonstrating the quantum simulation of a spin-lattice Hamiltonian is proposed. Dipolar interactions between nuclear spins in a solid state lattice can be modulated by rapid radio-frequency pulses. In this way, the effective Hamiltonian of the system can be brought to the form of an antiferromagnetic Heisenberg model with long range interactions. Using a semiconducting material with strong optical properties such as InP, cooling of nuclear spins could be achieved by means of optical pumping. An additional cooling stage is provided by adiabatic demagnetization in the rotating frame (ADRF) down to a nuclear spin temperature at which we expect a phase transition from a paramagnetic to antiferromagnetic phase. This phase transition could be observed by probing the magnetic susceptibility of the spin-lattice. Our calculations suggest that employing current optical pumping technology, observation of this phase transition is within experimental reach.Comment: 11 pages, 3 figues; Published versio

Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C5H12N)2CuBr4 (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.Comment: 35 pages, 26 figure

Trapdoor Memory-Hard Functions

Memory-hard functions (MHF) are functions whose evaluation provably requires a lot of memory. While MHFs are an unkeyed primitive, it is natural to consider the notion of trapdoor MHFs (TMHFs). A TMHF is like an MHF, but when sampling the public parameters one also samples a trapdoor which allows evaluating the function much cheaper. Biryukov and Perrin (Asiacrypt\u2717) were the first to consider TMHFs and put forth a candidate TMHF construction called Diodon that is based on the Scrypt MHF (Percival, BSDCan\u2709). To allow for a trapdoor, Scrypt\u27s initial hash chain is replaced by a sequence of squares in a group of unknown order where the order of the group is the trapdoor. For a length $n$ sequence of squares and a group of order $N$, Diodon\u27s cumulative memory complexity (CMC) is $O(n^2\log N)$ without the trapdoor and $O(n \log(n) \log(N)^2)$ with knowledge of it. While Scrypt is proven to be optimally memory-hard in the random oracle model (Alwen et al., Eurocrypt\u2717), Diodon\u27s memory-hardness has not been proven so far. In this work, we fill this gap by rigorously analyzing a specific instantiation of Diodon. We show that its CMC is lower bounded by $\Omega(\frac{n^2}{\log n} \log N)$ which almost matches the upper bound. Our proof is based Alwen et al.\u27s lower bound on Scrypt\u27s CMC but requires non-trivial modifications due to the algebraic structure of Diodon. Most importantly, our analysis involves a more elaborate compression argument and a solvability criterion for certain systems of Diophantine equations

Quantum and classical thermal correlations in the XY spin-1/2 chain

We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic XY spin-1/2 chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second-neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the XX limit, the thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit

Hydrophilic intraocular lens opacification after posterior lamellar keratoplasty - a material analysis with special reference to optical quality assessment

Background: Laboratory analysis and optical quality assessment of explanted hydrophilic intraocular lenses (IOLs) with clinically significant opacification after posterior lamellar keratoplasty (DMEK and DSAEK). Methods: Thirteen opacified IOLs after posterior lamellar keratoplasty, 8 after descemet stripping automated endothelial keratoplasty (DSAEK), 3 after descemet membrane endothelial keratoplasty (DMEK) and 2 after both DSAEK and DMEK were analysed in our laboratory. Analyses included optical bench assessment for optical quality, light microscopy, scanning electron microscopy (SEM) and energy dispersive X-Ray spectroscopy (EDS). Results: In all IOLs the opacification was caused by a thin layer of calciumphosphate that had accumulated underneath the anterior optical surface of the IOLs in the area spared by the pupil/anterior capsulorhexis. The calcifications lead to a significant deterioration of the modulation transfer function across all spatial frequencies of the affected IOLs. Conclusions: The instillation of exogenous material such as air or gas into the anterior chamber increases the risk for opacification of hydrophilic IOLs irrespective of the manufacturer or the exact composition of the hydrophilic lens material. It is recommended to avoid the use of hydrophilic acrylic IOLs in patients with endothelial dystrophy that will likely require procedures involving the intracameral instillation of air or gas, such as DMEK or DS(A)EK