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 a new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons with Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a selfconsistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

We use nonequilibrium dynamical mean-field theory to study the time evolution of the fermionic Hubbard model after an interaction quench. Both in the weak-coupling and in the strong-coupling regime the system is trapped in quasistationary states on intermediate time scales. These two regimes are separated by a sharp crossover at U(c)dyn=0.8 in units of the bandwidth, where fast thermalization occurs. Our results indicate a dynamical phase transition which should be observable in experiments on trapped fermionic atoms.

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/.

A recently developed continuous time solver based on an expansion in hybridization about an exactly solved local limit is reformulated in a manner appropriate for general classes of quantum impurity models including spin exchange and pair hopping terms. The utility of the approach is demonstrated via applications to the dynamical mean field theory of the Kondo lattice and two-orbital models. The algorithm can handle low temperatures and strong couplings without encountering a sign problem. I. INTRODUCTIONOne of the fundamental challenges of theoretical condensed matter physics is the accurate solution of quantum impurity models. These, in general terms, consist of a Hamiltonian involving a finite number of states and a hybridization process which allows particle exchange with one or more "reservoirs" of particles. They are important both in their own right and as a crucial ingredient in the dynamical mean field (DMFT) [1] method of approximating the properties of interacting fermions on a lattice. Examples include the familiar Kondo and Anderson Hamiltonians and their generalization to multi-spin and multi-orbital cases, as well as to the "embedded plaquettes" used in the recently developed cluster extensions of dynamical mean field theory [2,3,4].Quantum impurity models may be formulated as quantum field theories in zero space and one time dimension, and the reduced dimensionality suggests that numerical approaches should be feasible. However, up to now general quantum impurity models have to a large degree resisted numerical attack. A special but conceptually crucial model, the one-orbital Anderson impurity model, has been studied in detail but the techniques (the Hirsch-Fye discrete Hubbard-Stratonovich transformation [5] and exact diagonalization [6]) which work relatively well in this case have proven difficult to extend to wider classes of models of physical interest.One issue is that the Hirsch-Fye method cannot easily be applied to models with interactions other than direct density-density couplings. In particular, there is no good decoupling for the exchange and "pair hopping" terms which are important to the physics of partially filled d-levels. A scheme proposed by Sakai et al. [9] has been used in some DMFT studies [10,11], but the method has a severe sign problem which prevents calculations at low temperatures. Another issue with Hirsch-Fye and similar methods is time discretization, and in particular the fine grid spacing required to capture the short time behavior of the Green function. The computational burden in Hirsch-Fye type methods grows as the cube of the (large) grid size, which must be increased linearly with interaction strength and inverse temperature. This severely restricts the accessible parameter range.The exact diagonalization method [6] represents the continuous density of states of the reservoir by a small number of levels-but the number of levels required scales linearly with the number of orbitals included while the computational burden grows exponentially with the number of lev...

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...