Continuous-time Quantum Monte Carlo Method Research Articles

Dynamical properties of ultracold fermions with attractive interactions in an optical lattice

We study dynamical properties of ultracold fermions with attractive interactions by means of dynamical mean-field theory and a continuous-time quantum Monte Carlo method. By calculating the pair potential and the density of states, we discuss the stability of the superfluid state. We also show that when holes are doped into the fermionic optical lattice system with intermediate interaction strength, the quasi-particle peak smears and a gap structure instead appears in the dilute system.

Mott Insulator in Two-Channel Kondo Lattice

The Mott insulator is found in the two-channel Kondo lattice by using the dynamical mean-field theory combined with continuous-time quantum Monte Carlo method. At quarter filling of two conduction bands, the paramagnetic state shows metal-insulator crossover with increasing the coupling constant at low temperatures. The insulating state is explained by the strong coupling limit, where the system is effectively interpreted as the half-filled Hubbard model. It is shown that the present Mott insulating state is well described by the Hubbard I approximation.

Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension

We demonstrate that fermion-boson models with nonlocal interactions can be simulated at finite band filling with the continuous-time quantum Monte Carlo method. We apply this method to explore the influence of the electron-phonon interaction range for a half-filled band in one dimension, covering the full range from the Holstein to the Fröhlich regime. The phase diagram contains metallic, Peierls, and phase-separated regions. Nonlocal interactions suppress the Peierls instability, and thereby lead to almost degenerate power-law exponents for charge and pairing correlations.

Strong Coupling Superconductivity, Pseudogap, and Mott Transition

An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.

Efficient treatment of the high-frequency tail of the self-energy function and its relevance for multiorbital models

In this paper, we present an efficient and stable method to determine the one-particle Green's function in the hybridization-expansion continuous-time (CT-HYB) quantum Monte Carlo method within the framework of the dynamical mean-field theory. The high-frequency tail of the impurity self-energy is replaced with a noise-free function determined by a dual-expansion around the atomic limit. This method does not depend on the explicit form of the interaction term. More advantageous, it does not introduce any additional numerical cost to the CT-HYB simulation. We discuss the symmetries of the two-particle vertex, which can be used to optimize the simulation of the four-point correlation functions in the CT-HYB. Here, we adopt it to accelerate the dual-expansion calculation, which turns out to be especially suitable for the study of material systems with complicated band structures. As an application, a two-orbital Anderson impurity model with a general on-site interaction form is studied. The phase diagram is extracted as a function of the Coulomb interactions for two different Hund's coupling strengths. In the presence of the hybridization between different orbitals, for smaller interaction strengths, this model shows a transition from metal to band-insulator. Increasing the interaction strengths, this transition is replaced by a crossover from Mott-insulator to band-insulator behavior.

Cluster-size dependence in cellular dynamical mean-field theory

We examine the cluster-size dependence of the cellular dynamical mean-field theory (CDMFT) applied to the two-dimensional Hubbard model. Employing the continuous-time quantum Monte Carlo method as the solver for the effective cluster model, we obtain CDMFT solutions for 4-, 8-, 12-, and 16-site clusters at a low temperature. Comparing various periodization schemes, which are used to construct the infinite-lattice quantities from the cluster results, we find that the cumulant periodization yields the fastest convergence for the hole-doped Mott insulator where the most severe size dependence is expected. We also find that the convergence is much faster around (0,0) and (pi/2,pi/2) than around (pi,0) and (pi,pi). The cumulant-periodized self-energy seems to be close to its thermodynamic limit already for a 16-site cluster in the range of parameters studied. The 4-site results remarkably agree well with the 16-site results, indicating that the previous studies based on the 4-site cluster capture the essence of the physics of doped Mott insulators.

Numerical study of Kondo impurity models with strong potential scattering: Reverse Kondo effect and antiresonance

Accurate numerical results are derived for transport properties of Kondo impurity systems with potential scattering and orbital degeneracy. Using the continuous-time quantum Monte Carlo (CT-QMC) method, static and dynamic physical quantities are derived in a wide temperature range across the Kondo temperature T_K. With strong potential scattering, the resistivity tends to decrease with decreasing temperature, in contrast to the ordinary Kondo effect. Correspondingly, the quasi-particle density of states obtains the antiresonance around the Fermi level. Thermopower also shows characteristic deviation from the standard Kondo behavior, while magnetic susceptibility follows the universal temperature dependence even with strong potential scattering. It is found that the t-matrix in the presence of potential scattering is not a relevant quantity for the Friedel sum rule, for which a proper limit of the f-electron Green's function is introduced. The optical theorem is also discussed in the context of Kondo impurity models with potential scattering. It is shown that optical theorem holds not only in the Fermi-liquid range but also for large energies, and therefore is less restrictive than the Friedel sum rule.

Low-temperature properties of the infinite-dimensional attractive Hubbard model

We investigate the attractive Hubbard model in infinite spatial dimensions by combining dynamical mean-field theory with a strong-coupling continuous-time quantum Monte Carlo method. By calculating the superfluid order parameter and the density of states, we discuss the stability of the superfluid state. In the intermediate-coupling region above the critical temperature, the density of states exhibits a heavy fermion behavior with a quasiparticle peak in the dense system, while a dip structure appears in the dilute system. The formation of the superfluid gap is also addressed.

Mott physics and first-order transition between two metals in the normal-state phase diagram of the two-dimensional Hubbard model

For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength $U$, temperature $T$, and filling $n$ shows that, upon increasing $n$ toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T $=$ 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.

Critical Kondo Destruction in a Pseudogap Anderson Model: Scaling and Relaxational Dynamics

We study the pseudogap Anderson model as a prototype system for critical Kondo destruction. We obtain finite-temperature (T) scaling functions near its quantum-critical point, by using a continuous-time quantum Monte Carlo method and also considering a dynamical large-N limit. We are able to determine the behavior of the scaling functions in the typically difficult to access quantum-relaxational regime (ℏω<k(B)T) and conclude that the relaxation rates for both the spin and single-particle excitations are linear in temperature. We discuss the implications of these results for the quantum-critical phenomena in heavy-fermion metals.

Effects of Conduction Electron Correlation on Heavy-Fermion Systems

We study the effects of Hubbard-type electron correlation on the periodic Anderson model. From the analysis based on dynamical mean field theory and continuous-time quantum Monte Carlo method, we obtain the high-precision phase diagrams where a crossover within the magnetically ordered phase as well as another intriguing crossover between the Mott and Kondo insulating phases are observed with increasing c – f hybridization. We further address the effects of c – f Coulomb repulsion and elucidate that the charge-density-wave (CDW) phase with alternating c - and f -rich sites is stabilized in the strong correlation region. The above conclusions are drawn via the extensive calculations of the order parameter, the double occupancy, the spin correlation function and the spectral function.

Dynamical Band Flipping in Fermionic Lattice Systems: An ac-Field-Driven Change of the Interaction from Repulsive to Attractive

We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.

Continuous-time quantum Monte Carlo impurity solvers

Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summary Program title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: • Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) • MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) • IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers • Compaq Tru64 UNIX with Compq C++ Compiler (cxx) • SGI IRIX with MIPSpro C++ Compiler (CC) • HP-UX with HP C++ Compiler (aCC) • Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB–1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) 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. Solution method: Quantum impurity models 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 for which we present implementations here meet this challenge. Continuous-time quantum impurity methods are based on partition function expansions of quantum impurity models that are stochastically sampled to all orders using diagrammatic quantum Monte Carlo techniques. For a review of quantum impurity models and their applications and of continuous-time quantum Monte Carlo methods for impurity models we refer the reader to [2]. Additional comments: Use of dmft requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. Running time: 60 s–8 h per iteration.

Continuous-Time Quantum Monte Carlo Study of Local Non-Fermi Liquid State in the Multichannel Anderson Model

The impurity Green's function Gf in the local non-Fermi liquid state is evaluated by means of the continuous-time quantum Monte Carlo method extended to the multichannel Anderson model. For N=M (where N and M are numbers of spin components and channels, respectively), Gf is expressed as -Im Gf(w+i0) = c - b |w|^{1/2}, and the zero-frequency value c depends only on N (=M). A corresponding impurity self-energy at low frequencies is composed of two parts: a resonance term related to c, and a non-Fermi liquid term proportional to |w|^{1/2}. The characteristic energy scale is discussed in terms of the non-Fermi liquid term in the self-energy.

Continuous-Time Monte Carlo study of the pseudogap Bose-Fermi Kondo model

We study the pseudogap Bose–Fermi Anderson model with a continuous-time quantum Monte Carlo (CT-QMC) method. We discuss some delicate aspects of the transformation from this model to the Bose–Fermi Kondo model. We show that the CT-QMC method can be used at sufficiently low temperatures to access the quantum critical properties of these models.

Staggered Order with Itinerant and Localized Singlets in Generalized Kondo Lattice

The generalized Kondo lattice where even number of localized electrons are coupled with two conduction bands is investigated using the dynamical mean-field theory combined with continuous-time quantum Monte Carlo method. The crystalline electric field (CEF) singlet-triplet states are taken for localized states. With one conduction electron per site, a staggered order with Kondo and CEF singlets arises. Nature of the electronic order is studied in terms of the local susceptibility. The effective CEF splitting in one sublattice remains almost the same as the original CEF splitting, while the other sublattice looks like Kondo singlets. Hence, this electronic order is interpreted as alternating sites of itinerant and localized singlet states.

Cold atoms in a two-dimensional triangular optical lattice as an artificial frustrated system

We investigate the strongly correlated effect of cold atoms in a triangular optical lattice using the dynamical cluster approximation combined with the continuous-time quantum Monte Carlo method. When the interaction increases, the Fermi surface evolves from a circular ring into a flat plane, and the system transitions from a Fermi liquid into a Mott insulator. The transition between the Fermi liquid and a pseudogap shows a reentrant behavior due to the Kondo effect. We give an experimental protocol to observe these phenomena in future experiments by varying the lattice depth and the atomic interaction via the Feshbach resonance.

Electronic Order with Staggered Kondo and Crystalline Electric Field Singlets

Novel electronic order is found theoretically for a system where even number of localized electrons per site are coupled with conduction electrons. For precise quantitative study, a variant of the Kondo lattice model is taken with crystalline electric field (CEF) singlet and triplet states for each site. Using the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method, a staggered order with alternating Kondo and CEF singlets is identified for a case with one conduction electron per site being distributed in two conduction bands each of which is quarter-filled. This electronic order accompanies a charge density wave (CDW) of conduction electrons that accumulate more on Kondo-singlet sites than on CEF-singlet sites. Possible relevance of the present order to the scalar order in PrFe$_4$P$_{12}$ is discussed.

Itinerant antiferromagnetism in infinite dimensional Kondo lattice

Highly accurate numerical results for single-particle spectrum and order parameter are obtained for the magnetically ordered Kondo lattice by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. Hybridized energy bands involving local spins are identified in the N\'{e}el state as a hallmark of itinerant antiferromagnetism. At the boundary of the reduced Brillouin zone, the two-fold degeneracy remains in spite of the doubled unit cell. This degeneracy results if the molecular field felt by localized spins has identical magnitude and reversed direction with that of conduction electrons. The persistent Kondo effect is responsible for the behavior. The antiferromagnetic quantum transition occurs inside the itinerant regime, and does not accompany the itinerant-localized transition.

Quantum criticality and non-Fermi-liquid behavior in a two-level two-lead quantum dot

Analytical and continuous-time quantum Monte Carlo methods are used to investigate the possibility of occupation switching and quantum criticality in a model of two quantum impurities coupled to two leads. A general discussion of potential occupancy-switching related quantum critical points is given, and a detailed analysis is made of a specific model which has been recently discussed. For spinless electrons, no phase transition is found. For electrons with spin, a critical value of the interaction strength separates a weak coupling regime in which all properties vary smoothly with parameters from a strong coupling phase in which occupation numbers vary discontinuously as level energies are changed. The discontinuity point is characterized by non-Fermi-liquid behavior. Results for self-energies and correlation functions are given. Phase diagrams are presented.