Slave spin cluster mean field theory away from half-filling: Application to the Hubbard and the extended Hubbard Model

A new slave-spin representation of fermion operators has recently been proposed for the half-filled Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. The resulting spin problem can be solved using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength $U$ is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical $U$ for the Mott transition as a function of a frustrating second-neighbor interaction on lattices relevant for various correlated systems, namely the cobaltites, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In additionto a uniform metallic state, we find a $\sqrt(3) \times \sqrt(3)$ charge density wave in a broad doping regime, including commensurate ones. We find that in the large $U$ limit, intersite Coulomb repulsion $V$ strongly suppresses the single-particle weight of the metallic state.Comment: 10 pages, 11 figures, submitted to PR

Scale-free network topology and multifractality in weighted planar stochastic lattice

We propose a weighted planar stochastic lattice (WPSL) formed by the random sequential partition of a plane into contiguous and non-overlapping blocks and find that it evolves following several non-trivial conservation laws, namely $\sum_i^N x_i^{n-1} y_i^{4/n-1}$ is independent of time $\forall \ n$, where $x_i$ and $y_i$ are the length and width of the $i$th block. Its dual on the other hand, obtained by replacing each block with a node at its center and common border between blocks with an edge joining the two vertices, emerges as a network with a power-law degree distribution $P(k)\sim k^{-\gamma}$ where $\gamma=5.66$ revealing scale-free coordination number disorder since $P(k)$ also describes the fraction of blocks having $k$ neighbours. To quantify the size disorder, we show that if the $i$th block is populated with $p_i\sim x_i^3$ then its distribution in the WPSL exhibits multifractality.Comment: 7 pages, 8 figures, To appear in New Journal of Physics (NJP

Emergence of fractal behavior in condensation-driven aggregation

We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision. We solved the model exactly by using scaling theory for the case whereby a particle, say of size $x$, grows by an amount $\alpha x$ over the time it takes to collide with another particle of any size. It is shown that the particle size spectra of such system exhibit transition to dynamic scaling $c(x,t)\sim t^{-\beta}\phi(x/t^z)$ accompanied by the emergence of fractal of dimension $d_f={{1}\over{1+2\alpha}}$. One of the remarkable feature of this model is that it is governed by a non-trivial conservation law, namely, the $d_f^{th}$ moment of $c(x,t)$ is time invariant regardless of the choice of the initial conditions. The reason why it remains conserved is explained by using a simple dimensional analysis. We show that the scaling exponents $\beta$ and $z$ are locked with the fractal dimension $d_f$ via a generalized scaling relation $\beta=(1+d_f)z$.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

Fractal dimension and degree of order in sequential deposition of mixture

We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the case of random sequential adsorption (RSA) and show that the pattern created in the long time limit becomes scale invariant. This pattern can be described by an unique exponent, the fractal dimension. In addition, we introduce an external tuning parameter beta to describe the correlated sequential deposition of a mixture of particles where the degree of correlation is determined by beta, while beta=0 corresponds to random sequential deposition of mixture. We show that the fractal dimension of the resulting pattern increases as beta increases and reaches a constant non-zero value in the limit $\beta \to \infty$ when the pattern becomes perfectly ordered or non-random fractals.Comment: 16 pages Latex, Submitted to Phys. Rev.

Non-Linear Massive Gravity with Additional Primary Constraint and Absence of Ghosts

We complete the Hamiltonian analysis of specific model of non-linear massive gravity that was started in arXiv:1112.5267. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism invariant theory. Finally we determine the number of physical degrees of freedom and we show that it corresponds to the number of physical modes of massive gravity.Comment: 13 page

Supersolidity, entropy and frustration

We study the properties of t-t'-V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t-V model where the supersolid characterized by the ordering pattern (x,x,-2x') ("ferrimagnetic" or SS A) is a ground state for chemical potential \mu >3V. By turning on either temperature or t' at half-filling \mu =3V, we find a first order transition from SS A to the elusive supersolid characterized by the (x,-x,0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a large region where a superfluid phase becomes a solid upon raising temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.Comment: 4 pages, igures, LaTe

Modulation of NKG2D expression in human CD8(+) T cells corresponding with tuberculosis drug cure.

BACKGROUND: Biomarkers predicting tuberculosis treatment response and cure would facilitate drug development. This study investigated expression patterns of the co-stimulation molecule NKG2D in human tuberculosis and treatment to determine its potential usefulness as a host biomarker of tuberculosis drug efficacy. METHODS: Tuberculosis patients (n = 26) were recruited in Lahore, Pakistan, at diagnosis and followed up during treatment. Household contacts (n = 24) were also recruited. NKG2D expression was measured by qRT-PCR in RNA samples both ex vivo and following overnight mycobacterial stimulation in vitro. Protein expression of NKG2D and granzyme B was measured by flow cytometry. RESULTS: NKG2D expression in newly diagnosed tuberculosis patients was similar to household contacts in ex vivo RNA, but was higher following in vitro stimulation. The NKG2D expression was dramatically reduced by intensive phase chemotherapy, in both ex vivo blood RNA and CD8(+) T cell protein expression, but then reverted to higher levels after the continuation phase in successfully treated patients. CONCLUSION: The changes in NKG2D expression through successful treatment reflect modulation of the peripheral cytotoxic T cell response. This likely reflects firstly in vivo stimulation by live Mycobacterium tuberculosis, followed by the response to dead bacilli, antigen-release and finally immunopathology resolution. Such changes in host peripheral gene expression, alongside clinical and microbiological indices, could be developed into a biosignature of tuberculosis drug-induced cure to be used in future clinical trials

Rearrangements and Dilatancy for Sheared Dense Materials

Constitutive equations are proposed for dense materials, based on the identification of two types of free-volume activated rearrangements associated to shear and compaction. Two situations are studied: the case of an amorphous solid in a stress-strain test, and the case of a lubricant in tribology test. Varying parameters, strain softening, shear thinning, and stick-slip motion can be observed.Comment: 4 pages, 3 figure

Aero-acoustic oscillations inside large deep cavities

This investigation focuses on the pressure amplitude response, within two deep cavities characterized by their length over depth ratios (L/H = 0.2 and 0.41), under varying free stream velocity in a large wind tunnel. Experiments have shown that for deep rectangular cavities at low Mach number, oscillations of discrete frequencies can be produced. These oscillations appear when the free stream velocity becomes higher than a minimum value. In addition, as flow velocity is increased, upward jumps in oscillation frequency are observed in the two cavity configurations. Convection velocity of instabilities along the shear layer was measured using velocity cross-correlations. This study shows that the hydrodynamic modes of the cavity shear layer are correctly predicted by the Rossiter model when the convection velocity is determined and the empirical time delay is neglected. For L/H = 0.2 the first oscillation mode is observed on the spectrogram. For L/H = 0.41, both the first and the second mode have approximately the same amplitude. Time-resolved Particle image velocimetry measurements were performed to obtain the vorticity distribution during the oscillation cycle along the cavity shear layer. It is found that the number of structures in the cavity shear layer depends on the mode order of cavity oscillation