Continuous-time quantum Monte Carlo method for fermions

Abstract

We present a numerically exact continuous-time Quantum Monte Carlo algorithm for fermions with a general interaction non-local in space-time. The new determinantal grand-canonical scheme is based on a stochastic series expansion for the partition function in the interaction representation. The method is particularly applicable for multi-band, time-dependent correlations since it does not invoke the Hubbard-Stratonovich transformation. The test calculations for exactly solvable models, as well results for the Green function and for the time-dependent susceptibility of the multi-band super-symmetric model with a spin-flip interaction are discussed.

DMFT Study on the Electron–hole Asymmetry of the Electron Correlation Strength in the High Tc Cuprates

“…Among the several algorithms of CT-QMC, here we adopt CT-INT in this study. This algorithm, developed by Rubtsov et al, 31,32) is based on the Monte Carlo summation of all diagrams obtained from the expansion of the partition function in powers of the interaction U . We describe only a brief outline of CT-INT in this section.…”

“…Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using dynamical mean field theory (DMFT) 21) with two kinds of impurity solvers : iterated perturbation theory (IPT) [22][23][24][25][26][27][28][29] and continuous time quantum Monte Carlo (CT-QMC) [30][31][32][33][34][35] We find that the electron-hole asymmetry can exist even under common interaction strengths between the hole-and the electron-doped systems. The asymmetry of the spectrum already exists in the non-interacting case, but it is drastically enhanced, especially when the interaction is strong enough to make the non-doped case a Mott insulator.…”

Scaling Theory vs Exact Numerical Results for Spinless Resonant Level Model

“…We begin with the hybridizationexpansion algorithm (CT-HYB) 22,23 and consider how to include U f c . Although a direct expansion with respect to U f c (CT-INT) 24 is rather straightforward for this model, the algorithm based on the CT-HYB brings an advantage in extending the method to the multichannel case. Since the matrix element for the f state is easily taken into account in the CT-HYB, increasing the channel number does not produce additonal cost concerning the evaluation of the f part.…”

“…The parameters α f and α c are introduced to avoid negative weight configurations, 24 which will be discussed later. Correspondingly, H c and H f are rewritten as We begin with the partition function Z in a form for expansion with respect to H hyb and H f c…”

“…At the same time, u(τ ) should be small because large values results in a high expansion order. These conditions lead to u 0 = δ, u 1 = U f c + δ for U f c > 0, and u 0 = −U f c + δ, u 1 = δ for U f c < 0 with δ being a small positive value, 24 e.g., δ = 0.01. Thus, α f = −δ/U f c for U f c > 0 and α f = 1 − δ/U f c for U f c < 0 in Eq.…”