Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations

We present an adaptive algorithm which optimizes the statistical-mechanical ensemble in a generalized broad-histogram Monte Carlo simulation to maximize the system's rate of round trips in total energy. The scaling of the mean round-trip time from the ground state to the maximum entropy state for this local-update method is found to be O([N log N]^2) for both the ferromagnetic and the fully frustrated 2D Ising model with N spins. Our new algorithm thereby substantially outperforms flat-histogram methods such as the Wang-Landau algorithm.Comment: 6 pages, 5 figure

Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.Comment: 12 pages, 10 figure

Mechanisms for Spin-Supersolidity in S=1/2 Spin-Dimer Antiferromagnets

Using perturbative expansions and the contractor renormalization (CORE) algorithm, we obtain effective hard-core bosonic Hamiltonians describing the low-energy physics of $S=1/2$ spin-dimer antiferromagnets known to display supersolid phases under an applied magnetic field. The resulting effective models are investigated by means of mean-field analysis and quantum Monte Carlo simulations. A "leapfrog mechanism", through means of which extra singlets delocalize in a checkerboard-solid environment via correlated hoppings, is unveiled that accounts for the supersolid behavior.Comment: 12 pages, 10 figure

The fate of vacancy-induced supersolidity in 4He

The supersolid state of matter, exhibiting non-dissipative flow in solids, has been elusive for thirty five years. The recent discovery of a non-classical moment of inertia in solid 4He by Kim and Chan provided the first experimental evidence, although the interpretation in terms of supersolidity of the ideal crystal phase remains subject to debate. Using quantum Monte Carlo methods we investigate the long-standing question of vacancy-induced superflow and find that vacancies in a 4He crystal phase separate instead of forming a supersolid. On the other hand, non-equilibrium vacancies relaxing on defects of poly-crystalline samples could provide an explanation for the experimental observations.Comment: 4 pages,4 figures. Replaced with published versio

Two-dimensional quantum liquids from interacting non-Abelian anyons

A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y superconductor or quasiholes in certain quantum Hall states - gives rise to a macroscopic degeneracy. Such a degeneracy is split in the presence of interactions between the anyons. Here we show that in two spatial dimensions this splitting selects a unique collective state as ground state of the interacting many-body system. This collective state can be a novel gapped quantum liquid nucleated inside the original parent liquid (of which the anyons are excitations). This physics is of relevance for any quantum Hall plateau realizing a non-Abelian quantum Hall state when moving off the center of the plateau.Comment: 5 pages, 6 figure

On possible superconductivity in the doped ladder compound La_(1-x)Sr_xCuO_2.5

LaCuO_2.5 is a system of coupled, two-chain, cuprate ladders which may be doped systematically by Sr substitution. Motivated by the recent synthesis of single crystals, we investigate theoretically the possibility of superconductivity in this compound. We use a model of spin fluctuation-mediated superconductivity, where the pairing potential is strongly peaked at \pi in the ladder direction. We solve the coupled gap equations on the bonding and antibonding ladder bands to find superconducting solutions across the range of doping, and discuss their relevance to the real material.Comment: RevTex, 4 pages, 7 figure

Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder: a quantum Monte Carlo study

We consider a spin-1/2 ladder with a ferromagnetic rung coupling J_\perp and inequivalent chains. This model is obtained by a twist (\theta) deformation of the ladder and interpolates between the isotropic ladder (\theta=0) and the SU(2) ferromagnetic Kondo necklace model (\theta=\pi). We show that the ground state in the (\theta,J_\perp) plane has a finite string order parameter characterising the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from \Delta/J_\| \propto J_\perp/J_\| for \theta < \theta_c \simeq 8\pi/9 to \Delta/J_\| \propto (J_\perp/J_\|)^2 for \theta > \theta_c. Those results are obtained on the basis of large scale Quantum Monte Carlo calculations.Comment: 4 page

Switcher-random-walks: a cognitive-inspired mechanism for network exploration

Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the concepts (nodes) are associated (linked) to others depending on perceptions, similarities, etc. Lexical access is the complementary part of this system and allows the retrieval of such organized knowledge. While conceptual information is stored under certain underlying organization (and thus gives rise to a specific topology), it is crucial to have an accurate access to any of the information units, e.g. the concepts, for efficiently retrieving semantic information for real-time needings. An example of an information retrieval process occurs in verbal fluency tasks, and it is known to involve two different mechanisms: -clustering-, or generating words within a subcategory, and, when a subcategory is exhausted, -switching- to a new subcategory. We extended this approach to random-walking on a network (clustering) in combination to jumping (switching) to any node with certain probability and derived its analytical expression based on Markov chains. Results show that this dual mechanism contributes to optimize the exploration of different network models in terms of the mean first passage time. Additionally, this cognitive inspired dual mechanism opens a new framework to better understand and evaluate exploration, propagation and transport phenomena in other complex systems where switching-like phenomena are feasible.Comment: 9 pages, 3 figures. Accepted in "International Journal of Bifurcations and Chaos": Special issue on "Modelling and Computation on Complex Networks