Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in J_xy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order J^2_xy/J_z on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six--vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes - a phase with long range Neel order and confined spinon excitations, a non-magnetic state of resonating square plaquettes, and a quasi-collinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square--lattice quantum dimer model is also discussed.Comment: 4 pages, 5 figure

Equivalence of Bose-Einstein condensation and symmetry breaking

Based on a classic paper by Ginibre [Commun. Math. Phys. {\bf 8} 26 (1968)] it is shown that whenever Bogoliubov's approximation, that is, the replacement of a_0 and a_0^* by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of ||^2/V and /V in symmetry breaking fields, irrespective of the existence or absence of Bose-Einstein condensation. Because the former was proved by Ginibre to hold for absolutely integrable superstable pair interactions, the latter is equally valid in this case. Apart from Ginibre's work, our proof uses only a simple convexity inequality due to Griffiths.Comment: An error in my summary of previous results (the definition of F') is corrected. The correction is to be done also in the PR

Shift in critical temperature for random spatial permutations with cycle weights

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of permutations. The critical temperature of the transition to long cycles depends on an interaction-strength parameter $\alpha$. For weak interactions, the shift in critical temperature is expected to be linear in $\alpha$ with constant of linearity $c$. Using Markov chain Monte Carlo methods and finite-size scaling, we find $c = 0.618 \pm 0.086$. This finding matches a similar analytical result of Ueltschi and Betz. We also examine the mean longest cycle length as a fraction of the number of sites in long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures which appeared at the end of the PDF

Ground state at high density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superposed on the sites of a close-packed lattice.Comment: Note adde

The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as $\lambda \to \infty$, $\dim (\sigma(H_\lambda)) \cdot \log \lambda$ converges to an explicit constant ($\approx 0.88137$). We also discuss consequences of these results for the rate of propagation of a wavepacket that evolves according to Schr\"odinger dynamics generated by the Fibonacci Hamiltonian.Comment: 23 page

Spectra of Discrete Schr\"odinger Operators with Primitive Invertible Substitution Potentials

We study the spectral properties of discrete Schr\"odinger operators with potentials given by primitive invertible substitution sequences (or by Sturmian sequences whose rotation angle has an eventually periodic continued fraction expansion, a strictly larger class than primitive invertible substitution sequences). It is known that operators from this family have spectra which are Cantor sets of zero Lebesgue measure. We show that the Hausdorff dimension of this set tends to $1$ as coupling constant $\lambda$ tends to $0$. Moreover, we also show that at small coupling constant, all gaps allowed by the gap labeling theorem are open and furthermore open linearly with respect to $\lambda$. Additionally, we show that, in the small coupling regime, the density of states measure for an operator in this family is exact dimensional. The dimension of the density of states measure is strictly smaller than the Hausdorff dimension of the spectrum and tends to $1$ as $\lambda$ tends to $0$

H\"older Continuity of the Integrated Density of States for the Fibonacci Hamiltonian

We prove H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian for any positive coupling, and obtain the asymptotics of the H\"older exponents for large and small couplings.Comment: 18 page

Effect of genotype and hens' starting body fat content on the changes in the body fat content of the hens and on the weight and composition of the eggs produced in the first egg laying period

The aim of this study was to examine the effect of genotype and hens’ starting body fat content on the changes in the body fat content of the hens and on the weight and composition of the eggs produced in the first egg laying period. The experiment was carried out with altogether 30 hens (15 TETRA SL brown egg layers and 15 TETRA BLANCA white egg layers), which were chosen from altogether 45 TETRA SL and 45 TETRA BLANCA hens based on their CT (computer tomography) predicted body fat content at 20 weeks of age (hens with the highest (n=5), hens with the lowest (n=5) and hens with average (n=5) body fat content in both genotype). For the in vivo determination of changes in the body composition of these hens, computer tomography (CT) measurements were carried out at every fourth week between the 20th and 72nd week of age. During the CT measurements hens were fixed with belts in a special plexiglass container without using any anaesthetics. The measurements covered the whole body of the hens using overlapping 10 mm slice thickness on a Siemens Somatom Emotion 6 multislice CT scanner. After collecting, weighing and breaking the eggs produced by the experimental birds on the days of the CT measurements their yolk ratio was determined. Based on the results, it was established that the body fat content of the hens increased continuously in both of the genotypes in the first phase of the experimental period, while it did not change further in the second phase of the experiment. It was also observed at all examination days, that the body fat content of the white egg layers was higher than that of the brown egg layers. Hens with the highest starting body fat content had the highest body fat content in both genotypes during the whole egg laying period. The egg production of the hens was not influenced by the body fat content of the birds, but it was affected by the genotype. The TETRA SL hens produced significantly more eggs than the TETRA BLANCA hens. The hens with average body fat content produced lighter eggs than the hens with low or high body fat content

Justification of c-Number Substitutions in Bosonic Hamiltonians

The validity of substituting a c-number $z$ for the $k=0$ mode operator $a_0$ is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities like the pressure or ground state energy, but also the value of $|z|^2$ that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry breaking term -- a point that had previously been elusive.Comment: RevTeX4, 4pages; minor modifications in the text; final version, to appear in Phys. Rev. Let

A mechanical model of normal and anomalous diffusion

The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are presented. These show that above a threshold value of the field normal diffusion is superimposed to ballistic motion. The diffusion constant can be given explicitly. At the threshold field the transition between conduction and localization is accompanied by an anomalous diffusion. Our results exemplify that, even in the absence of time-dependent stochastic forces, a purely mechanical model equipped with a quenched disorder can exhibit normal as well as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure