The structure of spinful quantum Hall states: a squeezing perspective

We provide a set of rules to define several spinful quantum Hall model states. The method extends the one known for spin polarized states. It is achieved by specifying an undressed root partition, a squeezing procedure and rules to dress the configurations with spin. It applies to both the excitation-less state and the quasihole states. In particular, we show that the naive generalization where one preserves the spin information during the squeezing sequence, may fail. We give numerous examples such as the Halperin states, the non-abelian spin-singlet states or the spin-charge separated states. The squeezing procedure for the series (k=2,r) of spinless quantum Hall states, which vanish as r powers when k+1 particles coincide, is generalized to the spinful case. As an application of our method, we show that the counting observed in the particle entanglement spectrum of several spinful states matches the one obtained through the root partitions and our rules. This counting also matches the counting of quasihole states of the corresponding model Hamiltonians, when the latter is available.Comment: 19 pages, 7 figures; v2: minor changes, and added references. Mathematica packages are available for downloa

Valence Bond Entanglement and Fluctuations in Random Singlet Phases

The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain can be viewed as a strongly fluctuating liquid of valence bonds, while in disordered chains these bonds lock into random singlet states on long length scales. We show that this phenomenon can be studied numerically, even in the case of weak disorder, by calculating the mean value of the number of valence bonds leaving a block of $L$ contiguous spins (the valence-bond entanglement entropy) as well as the fluctuations in this number. These fluctuations show a clear crossover from a small $L$ regime, in which they behave similar to those of the uniform model, to a large $L$ regime in which they saturate in a way consistent with the formation of a random singlet state on long length scales. A scaling analysis of these fluctuations is used to study the dependence on disorder strength of the length scale characterizing the crossover between these two regimes. Results are obtained for a class of models which include, in addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical 1D transverse-field Ising model and chains of interacting non-Abelian anyons.Comment: 8 pages, 6 figure

Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles

One-dimensional chains of non-Abelian quasiparticles described by $SU(2)_k$ Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to $k \to \infty$). For $k=2$ this phase provides a random singlet description of the infinite randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size $L$ in these phases scales as $S_L \simeq \frac{\ln d}{3} \log_2 L$ for large $L$, where $d$ is the quantum dimension of the particles.Comment: 4 pages, 4 figure

From the Mendeleev periodic table to particle physics and back to the periodic table

We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry (special issue to commemorate the one hundredth anniversary of the death of Mendeleev who died in 1907); version 2: 16 pages; some sentences added; acknowledgment and references added; misprints correcte

Computation of Casimir forces for dielectrics or intrinsic semiconductors based on the Boltzmann transport equation

The interaction between drifting carriers and traveling electromagnetic waves is considered within the context of the classical Boltzmann transport equation to compute the Casimir-Lifshitz force between media with small density of charge carriers, including dielectrics and intrinsic semiconductors. We expand upon our previous work [Phys. Rev. Lett. {\bf 101}, 163203 (2008)] and derive in some detail the frequency-dependent reflection amplitudes in this theory and compute the corresponding Casimir free energy for a parallel plate configuration. We critically discuss the the issue of verification of the Nernst theorem of thermodynamics in Casimir physics, and explicity show that our theory satisfies that theorem. Finally, we show how the theory of drifting carriers connects to previous computations of Casimir forces using spatial dispersion for the material boundaries.Comment: 9 pages, 2 figures; Contribution to Proceedings of "60 Years of the Casimir Effect", Brasilia, June 200

The fundamental problem of command : plan and compliance in a partially centralised economy

When a principal gives an order to an agent and advances resources for its implementation, the temptations for the agent to shirk or steal from the principal rather than comply constitute the fundamental problem of command. Historically, partially centralised command economies enforced compliance in various ways, assisted by nesting the fundamental problem of exchange within that of command. The Soviet economy provides some relevant data. The Soviet command system combined several enforcement mechanisms in an equilibrium that shifted as agents learned and each mechanism's comparative costs and benefits changed. When the conditions for an equilibrium disappeared, the system collapsed.Comparative Economic Studies (2005) 47, 296–314. doi:10.1057/palgrave.ces.810011

Renormalization, duality, and phase transitions in two- and three-dimensional quantum dimer models

We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of $Z_N$ models in the $N\to\infty$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.Comment: 16 pages, 3 figure

High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets

The ground states of Klein type spin models on the pyrochlore and checkerboard lattice are spanned by the set of singlet dimer coverings, and thus possess an extensive ground--state degeneracy. Among the many exotic consequences is the presence of deconfined fractional excitations (spinons) which propagate through the entire system. While a realistic electronic model on the pyrochlore lattice is close to the Klein point, this point is in fact inherently unstable because any perturbation $\epsilon$ restores spinon confinement at $T = 0$. We demonstrate that deconfinement is recovered in the finite--temperature region $\epsilon \ll T \ll J$, where the deconfined phase can be characterized as a dilute Coulomb gas of thermally excited spinons. We investigate the zero--temperature phase diagram away from the Klein point by means of a variational approach based on the singlet dimer coverings of the pyrochlore lattices and taking into account their non--orthogonality. We find that in these systems, nearest neighbor exchange interactions do not lead to Rokhsar-Kivelson type processes.Comment: 19 page

A q-deformed Aufbau Prinzip

A building principle working for both atoms and monoatomic ions is proposed in this Letter. This principle relies on the q-deformed chain SO(4) > G where G = SO(3)_q

Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment

The low-temperature behavior of the Casimir-Polder free energy and entropy for an atom near a dielectric plate are found on the basis of the Lifshitz theory. The obtained results are shown to be thermodynamically consistent if the dc conductivity of the plate material is disregarded. With inclusion of dc conductivity, both the standard Lifshitz theory (for all dielectrics) and its generalization taking into account screening effects (for a wide range of dielectrics) violate the Nernst heat theorem. The inclusion of the screening effects is also shown to be inconsistent with experimental data of Casimir force measurements. The physical reasons for this inconsistency are elucidated.Comment: 10 pages, 1 figure; improved discussion; to appear in J. Phys. A: Math. Theor. (Fast Track Communications