Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. We present derivations and descriptions of the algorithms in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied and outline prospects for future applications. 16 1. Measurement of the Green's function 16 2. Role of the parameter K -potential energy 16 V. Hybridization expansion solvers CT-HYB 16 A. The hybridization expansion representation 16 B. Density -density interactions 17 C. Formulation for general interactions

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/.

A single-site dynamical mean field study of a three band model with the rotationally invariant interactions appropriate to the t2g levels of a transition metal oxide reveals a quantum phase transition between a paramagnetic metallic phase and an incoherent metallic phase with frozen moments. The Mott transitions occurring at electron densities n = 2, 3 per site take place inside the frozen moment phase. The critical line separating the two phases is characterized by a self energy with the frequency dependence Σ(ω) ∼ √ ω and a broad quantum critical regime. The findings are discussed in the context of the power law observed in the optical conductivity of SrRuO3.PACS numbers: 71.27.+a, 71.10.Hf , 71.10.Fd, 71.28.+d, 71.30.+h The 'Mott' metal-insulator transition plays a central role in the modern conception of strongly correlated materials [1,2]. Much of our understanding of this transition comes from studies of the one-band Hubbard model. Here, the transition is generically masked by antiferromagnetism, but if this is suppressed (physically, by introducing lattice frustration or mathematically, by examining an appropriately restricted class of theories such as the paramagnetic-phase single site dynamical mean field approximation [3]) a transition from a paramagnetic metal to a paramagnetic insulator is revealed. The properties of the paramagnetic metal phase near the transition play a central role in our understanding of the physics of correlated electron compounds.While one band models are relevant to many materials including the high temperature superconductors and some organic compounds, many systems of interest involve multiple correlated orbitals for which the physics is richer and less fully understood. Multiorbital models have been studied in Refs. [4,5,6,7,8,9,10]. New physics related to the appearance of magnetic moments has been considered in the context of the orbitally selective Mott transition which may occur if the orbital degeneracy is lifted [11,12,13,14,15], but for orbitally degenerate models it seems accepted that the essential concepts of a paramagnetic metal to paramagnetic insulator transition and a strongly correlated paramagnetic metal phase can be carried over from studies of the oneband situation.In this paper we show that this assumption is not correct. We use the single-site dynamical mean field approximation to demonstrate the existence of a quantum phase transition between a paramagnetic Fermi liquid and an incoherent metallic phase characterized by frozen local moments (a spin-spin correlation function which does not decay to zero at long times). We show that for densities per site n = 2, 3 the Mott transition occurs within or at the boundary of the frozen moment phase. As Costi and Liebsch have noted in the context of an orbitally selective Mott system, the presence of frozen moments may be expected to influence the Mott transition [15].The new phase appears for multiple orbitals, a different number of electrons than orbitals and a rotationally invariant on-site exchange U/3 > J...

Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degeneracy develops amongst spirals whose propagation wavevectors reside on a continuous two-dimensional "spiral surface" in momentum space. We argue that an important ordering mechanism is entropic splitting of the degenerate ground states, an elusive phenomena called orderby-disorder. A broad "spiral spin-liquid" regime emerges at higher temperatures, where the underlying spiral surface can be directly revealed via spin correlations. We discuss the agreement between these predictions and the well characterized spinel MnSc2S4 . PACS numbers:When microscopic interactions in a material conspire to "accidentally" produce many nearly degenerate low-energy states, otherwise weak residual effects can give rise to remarkable emergent behavior. This theme recurs throughout modern condensed matter physics. Quintessential examples include the cuprates, with several competing orders including high-T c superconductivity, and exotic quantum (Hall) liquids in two-dimensional electron systems, arising from partial Landau-level occupation. Insulating magnets constitute a particularly abundant source of such phenomena, as in numerous cases frustration generated by the competition between different exchange interactions leads to large classical ground-state degeneracies. An important experimental signature of such degeneracies is an anomalously low ordering temperature T c relative to the Curie Weiss temperature Θ CW ; indeed, values of the "frustration parameter" f = |Θ CW |/T c larger than 5-10 are typically taken as empirical evidence of a highly frustrated magnet.[1] This sharp suppression of T c opens up a broad "spin-liquid" regime for temperatures T c T |Θ CW |, where the system fluctuates amongst the many low-energy configurations but evades long-range order. Highly non-trivial physics can emerge here, as attested for instance in pyrochlore antiferromagnets by the experimental observation of hexagonal loop correlations in neutron scattering on the spinel ZnCr 2 O 4 [2], and theoretically by the establishment of "dipolar" correlations. [3] Low-temperature ordering in highly frustrated magnets often displays an exquisite sensitivity to degeneracy-breaking perturbations, notably dipolar interactions and minimal disorder in the spin-ice pyrochlores,[4], spin-lattice coupling in various spinels [5], and Dzyaloshinskii-Moriya interactions in Cs 2 CuCl 4 [6]. However, the lifting of degeneracy need not require the presence of such explicit perturb...