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The ALPS project release 2.0: open source software for strongly correlated systems

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 programmers 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/.

Cluster Algorithms for General-S Quantum Spin Systems

We present a general strategy to extend quantum cluster algorithms for S = 1 / 2 spin systems, such as the loop algorithm, to those with an arbitrary size of spins. The partition function of a high- S spin system is generally represented by the path integral of a S = 1 / 2 model with special boundary conditions in the imaginary-time direction. We introduce additional graphs for the boundary part and give the labeling probability explicitly, which completes the algorithm together with an existing S = 1 / 2 algorithm. As a demonstration, we simulate the integer-spin antiferromagnetic Heisenberg chains. The magnitude of the first excitation gap is estimated to be 0.41048(6), 0.08917(4), and 0.01002(3) for S = 1, 2, and 3, respectively.

Markov Chain Monte Carlo Method without Detailed Balance

We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.

Finite-temperature phase diagram of hard-core bosons in two dimensions.

We determine the finite-temperature phase diagram of the square lattice hard-core boson Hubbard model with nearest neighbor repulsion using quantum Monte Carlo simulations. This model is equivalent to an anisotropic spin-1/2 XXZ model in a magnetic field. We present the rich phase diagram with a first order transition between a solid and superfluid phase, instead of a previously conjectured supersolid and a tricritical end point to phase separation. Unusual reentrant behavior with ordering upon increasing the temperature is found, similar to the Pomeranchuk effect in 3He.

Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

The S = ½ and S= I 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-interchain-coupling, case.

Order parameter to characterize valence-bond-solid states in quantum spin chains

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method.

Order-N cluster Monte Carlo method for spin systems with long-range interactions

An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The realized stochastic dynamics is equivalent to that of the conventional Swendsen-Wang algorithm, which requires O(N^2) operations per Monte Carlo sweep if applied to long-range interacting models. In addition, it is shown that the total energy and the specific heat can also be measured in O(N) time. We demonstrate the efficiency of our algorithm over the conventional method and the O(NlogN) algorithm by Luijten and Blote. We also apply our algorithm to the classical and quantum Ising chains with inverse-square ferromagnetic interactions, and confirm in a high accuracy that a Kosterlitz-Thouless phase transition, associated with a universal jump in the magnetization, occurs in both cases.

Quantum phase transition of the randomly diluted Heisenberg antiferromagnet on a square lattice

Ground-state magnetic properties of the diluted Heisenberg antiferromagnet on a square lattice are investigated by means of the quantum Monte Carlo method with the continuous-time loop algorithm. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the two-dimensional percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. Furthermore, we found that the transition is not universal, i.e., the critical exponents significantly depend on S.

Bond-dilution effects on two-dimensional spin-gapped Heisenberg antiferromagnets

Abstract Bond-dilution effects on spin-1/2 spin-gapped Heisenberg antiferromagnets of coupled alternating chains on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that, in contrast with the site-diluted system having an infinitesimal critical concentration, the bond-diluted system has a finite critical concentration of diluted bonds, xc, above which the system is in an antiferromagnetic (AF) long-range ordered phase. In the disordered phase below xc, plausibly in the concentration region significantly less than xc, the system has a spin-gap due to singlet pairs of induced magnetic moments reformed by the AF interactions through the two-dimensional shortest paths.

Site-dilution-induced antiferromagnetic long-range order in a two-dimensional spin-gapped Heisenberg antiferromagnet

Effects of the site dilution on spin-gapped Heisenberg antiferromagnets with