Emanuel Gull

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/.

Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Numerically exact long-time magnetization dynamics at the nonequilibrium Kondo crossover of the Anderson impurity model

We investigate the dynamical and steady-state spin response of the nonequilibrium Anderson model to magnetic fields, bias voltage, and temperature using a numerically exact method combining a bold-line quantum Monte Carlo technique with the memory function formalism. We obtain converged results in a range of previously inaccessible regimes, in particular the crossover to the Kondo domain. We provide detailed predictions for novel nonequilibrium phenomena, including non-monotonic temperature dependence of observables at high bias voltage and oscillatory quench dynamics at high magnetic fields.

Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model

Cluster dynamical mean field calculations based on 2, 4, 8 and 16 site clusters are used to analyze the doping-driven metal-insulator transition in the two dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole doped side than on the electron doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-

Thermodynamics of the 3D Hubbard Model on Approaching the Neel Transition

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Diagrammatic Monte Carlo for correlated fermions

cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi liquid renormalizations are larger and the electron self energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap in some regions of the Fermi surface but gapless behavior in other regions. On the electron doped side the partially gapped regime does not occur, and the momentum dependence of the electron self energy is less pronounced. Implications for the high-

Systematically improvable multiscale solver for correlated electron systems

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Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods

cuprates and for the use of cluster dynamical mean field methods in wider classes of problems are discussed.

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.