Quantitative Determination of Temperature in the Approach to Magnetic Order of Ultracold Fermions in an Optical Lattice

We perform a quantitative simulation of the repulsive Fermi-Hubbard model using an ultracold gas trapped in an optical lattice. The entropy of the system is determined by comparing accurate measurements of the equilibrium double occupancy with theoretical calculations over a wide range of parameters. We demonstrate the applicability of both high-temperature series and dynamical mean-field theory to obtain quantitative agreement with the experimental data. The reliability of the entropy determination is confirmed by a comprehensive analysis of all systematic errors. In the center of the Mott insulating cloud we obtain an entropy per atom as low as 0.77k(B) which is about twice as large as the entropy at the Neel transition. The corresponding temperature depends on the atom number and for small fillings reaches values on the order of the tunneling energy

Luttinger Liquid in the Core of Screw Dislocation in Helium-4

On the basis of first-principle Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp He4 crystal features a superfluid core. This is the first example of a regular quasi-one-dimensional supersolid, and one of the cleanest cases of a regular Luttinger-liquid system. In contrast, the same type of screw dislocation in solid Hydrogen is insulating.Comment: replaced with revised versio

Novel Mechanism of Supersolid of Ultracold Polar Molecules in Optical Lattices

We study the checkerboard supersolid of the hard-core Bose-Hubbard model with the dipole-dipole interaction. This supersolid is different from all other supersolids found in lattice models in the sense that superflow paths through which interstitials or vacancies can hop freely are absent in the crystal. By focusing on repulsive interactions between interstitials, we reveal that the long-range tail of the dipole-dipole interaction have the role of increasing the energy cost of domain wall formations. This effect produces the supersolid by the second-order hopping process of defects. We also perform exact quantum Monte Carlo simulations and observe a novel double peak structure in the momentum distribution of bosons, which is a clear evidence for supersolid. This can be measured by the time-of-flight experiment in optical lattice systems

Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas

We present results from quantum Monte Carlo simulations of trapped bosons in optical lattices, focusing on the crossover from a gas of softcore bosons to a Tonks-Girardeau gas in a one-dimensional optical lattice. We find that depending on the quantity being measured, the behavior found in the Tonks-Girardeau regime is observed already at relatively small values of the interaction strength. A finite critical value for entering the Tonks-Girardeau regime does not exist. Furthermore, we discuss the computational efficiency of two quantum Monte Carlo methods to simulate large scale trapped bosonic systems: directed loops in stochastic series expansions and the worm algorithm.Comment: 7 pages with 9 figures;v2: improved discussion on Tonks-Girardeau ga

Quantifying the behavior of stock correlations under market stress

Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios

Going That Extra Mile: Individuals Travel Further to Maintain Face-to-Face Contact with Highly Related Kin than with Less Related Kin

The theory of inclusive fitness has transformed our understanding of cooperation and altruism. However, the proximate psychological underpinnings of altruism are less well understood, and it has been argued that emotional closeness mediates the relationship between genetic relatedness and altruism. In this study, we use a real-life costly behaviour (travel time) to dissociate the effects of genetic relatedness from emotional closeness. Participants travelled further to see more closely related kin, as compared to more distantly related kin. For distantly related kin, the level of emotional closeness mediated this relationship - when emotional closeness was controlled for, there was no effect of genetic relatedness on travel time. However, participants were willing to travel further to visit parents, children and siblings as compared to more distantly related kin, even when emotional closeness was controlled for. This suggests that the mediating effect of emotional closeness on altruism varies with levels of genetic relatednes

Experimental evidence for an intermediate phase in the multiferroic YMnO3

We have studied YMnO$_{3}$ by high-temperature synchrotron X-ray powder diffraction, and have carried out differential thermal analysis and dilatometry on a single crystal sample. These experiments show two phase transitions at about 1100K and 1350K, respectively. This demonstrates the existence of an intermediate phase between the room temperature ferroelectric and the high temperature centrosymmetric phase. This study identifies for the first time the different high-temperature phase transitions in YMnO$_{3}$.Comment: 10 pages 5 figures. New version, Additional data, Journal of Physics: Condensed Matter, in Pres

Thermometry with spin-dependent lattices

We propose a method for measuring the temperature of strongly correlated phases of ultracold atom gases confined in spin-dependent optical lattices. In this technique, a small number of "impurity" atoms--trapped in a state that does not experience the lattice potential--are in thermal contact with atoms bound to the lattice. The impurity serves as a thermometer for the system because its temperature can be straightforwardly measured using time-of-flight expansion velocity. This technique may be useful for resolving many open questions regarding thermalization in these isolated systems. We discuss the theory behind this method and demonstrate proof-of-principle experiments, including the first realization of a 3D spin-dependent lattice in the strongly correlated regime.Comment: 22 pages, 8 figures v2: Several references added; Section on heating rates updated to include dipole fluctuation terms; Section added on the limitations of the proposed method. To appear in New Journal of Physic

Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose--Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations

Variational Monte Carlo analysis of the Hubbard model with a confining potential: one-dimensional fermionic optical lattice systems

We investigate the one-dimensional Hubbard model with a confining potential, which may describe cold fermionic atoms trapped in an optical lattice. Combining the variational Monte Carlo simulations with the new stochastic reconfiguration scheme proposed by Sorella, we present an efficient method to systematically treat the ground state properties of the confined system with a site-dependent potential. By taking into account intersite correlations as well as site-dependent on-site correlations, we are able to describe the coexistence of the metallic and Mott insulating regions, which is consistent with other numerical results. Several possible improvements of the trial states are also addressed.Comment: 7 pages, 15 figures; removed unnecessary graphs (p.8-p.32 in the old version are removed