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 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/.

The Néel temperature, TN, of quasi-one-and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (interlayer) to intra-chain (intra-layer) coupling J ′ /J down to J ′ /J ≃ 10 −3 . We find that TN obeys a modified random-phase approximation-like relation for small J ′ /J with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing TN for a wide range of J ′ and useful for the analysis of experimental measurements are presented.While genuinely one-dimensional (1D) and two-dimensional (2D) antiferromagnetic Heisenberg (AFH) models cannot display long-range order (LRO) except at zero temperature [1], weak inter-chain or inter-layer couplings, J ′ , which always exist in real materials, lead to a finite Néel temperature T N . So far, the J ′ -dependence of T N was calculated by exactly treating effects of the strong interaction J in the 1D or 2D system, but using mean-field approximations for the inter-chain and interlayer coupling. Recently, more advanced theories of the latter effects have been proposed for quasi-1D (Q1D) [3,4] and quasi-2D (Q2D) [5] systems, and the results have been compared with the experimental observations on Q1D antiferromagnets, e.g., Sr 2 CuO 3 [6], and Q2D antiferromagnets, e.g., La 2 CuO 4 [7]. In view of the importance of experimentally well-studied Q2D antiferromagnets as undoped parent compounds of the high-temperature superconductors, accurate and unbiased numerical results for Q1D and Q2D AFH models are strongly desired. In a recent work along this line, Sengupta et al. [8] have demonstrated peculiar temperature dependences of the specific heat in the quantum Q2D AFH model.Here we calculate the Néel temperature T N as a function of J ′ in fully three-dimensional (3D) classical and quantum Monte Carlo (MC) simulations of coupledchains and coupled-layers. Our MC results on the quantum spin-S and classical S = ∞ AFH models are analyzed by a modified random-phase approximation (RPA) with a renormalized coordination number defined bywhere χ s (T ) is the staggered susceptibility of the 1D or 2D model at temperature T . In a simple RPA calculation [2], this quantity is just the coordination number z d in the inter-chain or inter-layer directions: z 1 = 4 and z 2 = 2 for the Q1D and Q2D systems, respectively. Our main result is that ζ(J ′ ) evaluated by Eq. (1) with our numerically obtained T N (J ′ ) and χ s (T ) becomes constant, with the constants k 1 = 0.695 and k 2 = 0.65. These constants k d differ from the simple RPA result k d = 1, but the value of k 1 is consistent with the modified self-consistent RPA theory for the quantum Q1D (q-Q1D) model of Irkhin and Katanin (IK) [3]. Furthermore we find, that, within our numerical accuracy, the value of k d is the same for the S = 1/2, S = 1, S = 3/2 and S = ∞, and we conjecture that k d is universal and independent of the spin S for small J ′ /J. We also propose empirical formulae ...

The S = 1/2 and S = 1 two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S = 1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchaincoupling, case.