Abstract:
Motivated by a recent adsorption experiment [M.O. Blunt et al., Science 322, 1077 (2008)], we study tilings of the plane with three different types of rhombi. An interaction disfavors pairs of adjacent rhombi of the same type. This is shown to be a special case of a model of fully-packed loops with interactions between monomers at distance two along a loop. We solve the latter model using Coulomb gas techniques and show that its critical exponents vary continuously with the interaction strenght. At low temperature it undergoes a Kosterlitz-Thouless transition to an ordered phase, which is predicted from numerics to occur at a temperature T \sim 110K in the experiments.

Abstract:
We discuss the implementation of a directed geometrical worm algorithm for the study of quantum link-current models. In this algorithm Monte Carlo updates are made through the biased reptation of a worm through the lattice. A directed algorithm is an algorithm where, during the construction of the worm, the probability for erasing the immediately preceding part of the worm, when adding a new part,is minimal. We introduce a simple numerical procedure for minimizing this probability. The procedure only depends on appropriately defined local probabilities and should be generally applicable. Furthermore we show how correlation functions, C(r,tau) can be straightforwardly obtained from the probability of a worm to reach a site (r,tau) away from its starting point independent of whether or not a directed version of the algorithm is used. Detailed analytical proofs of the validity of the Monte Carlo algorithms are presented for both the directed and un-directed geometrical worm algorithms. Results for auto-correlation times and Green functions are presented for the quantum rotor model.

Abstract:
We propose a highly efficient "worm" like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the new algorithm even in the presence of disorder. For the pure quantum rotor model with $\mu=0$ the new algorithm yields high precision estimates for the critical point $K_c=0.33305(5)$ and the correlation length exponent $\nu=0.670(3)$. For the disordered case, $\mu=1/2 \pm 1/2$, we find $\nu=1.15(10)$.

Abstract:
We investigate the arguably simplest $SU(2)$-invariant wave functions capable of accounting for spin-liquid behavior, expressed in terms of nearest-neighbor valence-bond states on the square lattice and characterized by different topological invariants. While such wave-functions are known to exhibit short-range spin correlations, we perform Monte Carlo simulations and show that four-point correlations decay algebraically with an exponent $1.16(4)$. This is reminiscent of the {\it classical} dimer problem, albeit with a slower decay. Furthermore, these correlators are found to be spatially modulated according to a wave-vector related to the topological invariants. We conclude that a recently proposed spin Hamiltonian that stabilizes the here considered wave-function(s) as its (degenerate) ground-state(s) should exhibit gapped spin and gapless non-magnetic excitations.

Abstract:
The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multi-peak structure in the energy distribution for finite lattices, usually indicative of a first order phase transition. However, this multi-peak structure is shown to disappear in the thermodynamic limit revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.

Abstract:
we discuss how reweighting and histogram methods for classical systems can be generalized to quantum models for discrete and continuous time world line simulations, and the stochastic series expansion (sse) method. our approach allows to apply all classical reweighting and histogram techniques for classical systems, as well as multicanonical or wang-landau sampling to the quantum case.

Abstract:
The spin texture surrounding a non-magnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a Neel ordered phase and a valence bond solid phase in square lattice S=1/2 antiferromagnets. Using a newly developed T=0 Quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.

Abstract:
When a system undergoes a quantum phase transition, the ground-state wave-function shows a change of nature, which can be monitored using the fidelity concept. We introduce two Quantum Monte Carlo schemes that allow the computation of fidelity and its susceptibility for large interacting many-body systems. These methods are illustrated on a two-dimensional Heisenberg model, where fidelity estimators show marked behaviours at two successive quantum phase transitions. We also develop a scaling theory which relates the divergence of the fidelity susceptibility to the critical exponent of the correlation length. A good agreement is found with the numerical results.

Abstract:
Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce-free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the non-uniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest.

Abstract:
In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant amount of) two-site entanglement, whereas they possess multi-body entanglement. Two examples ("RVB gas and liquid") are given to illustrate this claim, which essentially comes from a lower bound derived for spin correlators in VB states. We show in this Comment that (i) for the "RVB liquid" on the square lattice, the calculations and conclusions of Chandran et al. are incorrect. (ii) A simple analytical calculation gives the exact value of the correlator for the "RVB gas", showing that the bound found by Chandran et al. is tight. (iii) The lower bound for spin correlators in VB states is equivalent to a celebrated result of Anderson dating from more than 50 years ago.