At sufficiently low temperatures, condensed-matter systems tend to develop order. A notable exception to this behaviour is the case of quantum spin liquids, in which quantum fluctuations prevent a transition to an ordered state down to the lowest temperatures. There have now been tentative observations of such states in some two-dimensional organic compounds, yet quantum spin liquids remain elusive in microscopic two-dimensional models that are relevant to experiments. Here we show, by means of large-scale quantum Monte Carlo simulations of correlated fermions on a honeycomb lattice (a structure realized in, for example, graphene), that a quantum spin liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence-bond liquid, akin to the one proposed for high-temperature superconductors: the possibility of unconventional superconductivity through doping therefore arises in our system. We foresee the experimental realization of this model system using ultra-cold atoms, or group IV elements arranged in honeycomb lattices.

We present release 2.0 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. The code development is centered on common XML and HDF5 data formats, libraries to simplify and speed up code development, common evaluation and plotting tools, and simulation programs. The programs enable non-experts to start carrying out serial or parallel numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), the density matrix renormalization group (DMRG) both in a static version and a dynamic time-evolving block decimation (TEBD) code, and quantum Monte Carlo solvers for dynamical mean field theory (DMFT). The ALPS libraries provide a powerful framework for programers to develop their own applications, which, for instance, greatly simplify the steps of porting a serial code onto a parallel, distributed memory machine. Major changes in release 2.0 include the use of HDF5 for binary data, evaluation tools in Python, support for the Windows operating system, the use of CMake as build system and binary installation packages for Mac OS X and Windows, and integration with the VisTrails workflow provenance tool. The software is available from our web server at http://alps.comp-phys.org/.

We determine the phase diagram of hardcore bosons on a triangular lattice with nearest neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities ρ < 1/3 or ρ > 2/3 a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings 1/3 < ρ < 2/3 we find an extended supersolid phase even at half filling ρ = 1/2. PACS numbers:Next to the widely observed superfluid and Bosecondensed phases with broken U (1) symmetry and "crystalline" density wave ordered phases with broken translational symmetry, the supersolid phase, breaking both the U (1) symmetry and translational symmetry has been a widely discussed phase that is hard to find both in experiments and in theoretical models. Experimentally, evidence for a possible supersolid phase in bulk 4 He has recently been presented [1], but the question of whether a true supersolid has been observed is far from being settled [2,3], leaving the old question of supersolid behavior in translation invariant systems [4,5] unsettled for now.More precise statements for a supersolid phase can be made for bosons on regular lattices. It has been proposed that such bosonic lattice models can be realized by loading ultracold bosonic atoms into an optical lattice, where the required longer range interaction between the bosons could be induced by using the dipolar interaction in chromium condensates [6], or an interaction mediated by fermionic atoms in a mixture of bosonic and fermionic atoms [7]. With the recent realization of a Bose-Einstein condensate (BEC) in Chromium atoms [8], these experiments have now become feasible, raising the interest in phase diagrams of lattice boson model, and particularly in the stability of supersolids on lattices.The question if a supersolid phase is a stable thermodynamic phase for lattice boson models has been controversial for many years. Analytical calculations using mean-field and renormalization group methods [9,10,11,12] have predicted supersolid phases for many models, including for the simplest model of hardcore bosons with nearest neighbor repulsion on a square lattice with Hamiltonianwhere a † i (a i ) creates (destroys) a particle on site i, t denotes the nearest-neighbor hopping, V a nearestneighbor repulsion, and µ the chemical potential. Subsequent numerical investigations using exact diagonalization and quantum Monte Carlo (QMC) algorithms [13,14,15,16,17]

We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/.