Continuous-Time Solver for Quantum Impurity Models

Werner, Philipp; Comanac, Armin; Medici, Luca de’; Troyer, Matthias; Millis, Andrew J.

doi:10.1103/physrevlett.97.076405

Cited by 1,054 publications

(1,242 citation statements)

References 15 publications

(25 reference statements)

Supporting

Mentioning

1,232

Contrasting

Order By: Relevance

“…To solve the self-consistency equations different techniques ("impurity solvers") have been developed which are either fully numerical and "numerically exact", or semi-analytic and approximate. The numerical solvers can be divided into renormalization group techniques such as the numerical renormalization group (NRG) [37,38] and the density-matrix renormalization group (DMRG) [39], exact diagonalization (ED) [40][41][42], and methods based on the stochastic sampling of quantum and thermal averages, i.e., quantum Monte-Carlo (QMC) techniques such as the Hirsch-Fye QMC algorithm [32,43,44,33] and continuous-time (CT) QMC [45][46][47].…”

Section: Solution Of the Self-consistency Equations Of The Dmftmentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

View full text Add to dashboard Cite

Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter. Motivation Electronic CorrelationsAlready in 1937, at the outset of modern solid state physics, de Boer and Verwey [1] drew attention to the surprising properties of materials with incompletely filled 3d-bands. This observation prompted Mott and Peierls [2] to discuss the interaction between the electrons. Ever since transition metal oxides (TMOs) were investigated intensively [3]. It is now well-known that in many materials with partially filled electron shells, such as the 3d transition metals V and Ni and their oxides, or 4f rare-earth metals such as Ce, electrons occupy narrow orbitals. The spatial confinement enhances the effect of the Coulomb interaction between the electrons, making them "strongly correlated". Correlation effects can lead to profound quantitative and qualitative changes of the physical properties of electronic systems as compared to non-interacting particles. In particular, they often respond very strongly to changes in external parameters. This is expressed by large renormalizations of the response functions of the system, e.g., of the spin susceptibility and the charge compressibility. In particular, the interplay between the spin, charge and orbital degrees of freedom of the correlated d and f electrons and with the lattice degrees of freedom leads to an amazing multitude of ordering phenomena and other fascinating properties, including high temperature superconductivity, colossal magnetoresistance and Mott metal-insulator transitions [3].arXiv:1109.4833v1 [cond-mat.str-el]

show abstract

Section: Solution Of the Self-consistency Equations Of The Dmftmentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

View full text Add to dashboard Cite

show abstract

“…Since the occupation number n f of the f state is conserved by H c + H f , the "segment picture" 22 can be used for evaluation of the trace for f operators. The f state |f (τ ) fluctuates between the empty state |0 and the occupied state |1 by the hybridization term H hyb as shown in Fig.…”

Section: A Treatment Of the Coulomb Interactionmentioning

confidence: 99%

“…(25). In order to fulfill ergodicity, we need to perform two types of updates: (i) the segment addition/removal as in the ordinary Anderson model 22 , and (ii) a U f c addition/removal update. For update (i), we perform random choice for a new segment in the same way as in Ref.…”

Section: B Monte Carlo Proceduresmentioning

confidence: 99%

“…For update (i), we perform random choice for a new segment in the same way as in Ref. 22: a position of the segment is chosen from the interval [0 : β) and its length L from (0 : ℓ max ). In the present case, the update probability R for the segment addition is given by…”

Section: B Monte Carlo Proceduresmentioning

confidence: 99%

“…The function ∆ is defined in Ref. 22. After the Fourier transform, F γγ ′ (iω n ) yields the Green's functions by…”

Section: Green's Functionsmentioning

confidence: 99%

See 2 more Smart Citations

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

2013

View full text Add to dashboard Cite

The continuous-time quantum Monte Carlo method is applied to the interacting resonant level model (IRLM) using double expansion with respect to Coulomb interaction U f c and hybridization V . Thermodynamics of the IRLM without spin is equivalent to the anisotropic Kondo model in the low-energy limit. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of U f c with a given value of V . For negative U f c , excellent agreement including a quantum critical point is found with a simple scaling formula that deals with V in the lowest-order, and U f c up to infinite order. As U f c becomes positive and large, lower order scaling results deviate from exact numerical results. Possible relevance of the results is discussed to certain Samarium compounds with unusual heavy-fermion behavior.

show abstract

QuantumMonteCarlo Methods

Assaad

Troyer

2007

Handbook of Magnetism and Advanced Magnetic Materials

View full text Add to dashboard Cite

We present a review of quantum Monte Carlo algorithms for the simulation of quantum magnets. A general introduction to Monte Carlo sampling is followed by an overview of local updates, cluster updates, and generalized ensemble techniques such as multicanonical and Wang‐Landau sampling for classical magnets. For quantum systems we present two complementary approaches: world‐line methods in (i) a path‐integral and (ii) a stochastic series expansion (SSE) representation, which are best suited for pure spin Hamiltonians. Determinental quantum Monte Carlo algorithms are the methods of choice for the simulation of fermionic Hamiltonians, such as the Hubbard model. An overview of the methods is followed by a selection of typical applications.

show abstract

Continuous-Time Solver for Quantum Impurity Models

Cited by 1,054 publications

References 15 publications

Dynamical Mean-Field Theory

Dynamical Mean-Field Theory

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

QuantumMonteCarlo Methods

Contact Info

Product

Resources

About