相关论文: The Loop Algorithm

Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip…

The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem…

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local…

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic…

We present an algorithmic framework for a variant of the quantum Monte Carlo operator-loop algorithm, where non-local cluster updates are constructed in a way that makes each individual loop smaller. The algorithm is designed to increase…

A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is…

Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is…

An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin…

Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…

We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…

A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of…

Within a general cluster framework, we discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail. For…

The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on…

We present a new algorithm for quantum Monte Carlo simulation based on global updating with loops. While various theoretical predictions are confirmed in one dimension, we find, for S=1 systems on a square lattice with an antiferromagnetic…

An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…

Monte Carlo simulation using the standard single-spin flip algorithm often fails to sample over the entire configuration space at low temperatures for frustrated spin systems. A typical example is a class of spin-ice type Ising models. In…

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating…

The directed-loop scheme is a framework for generalized loop-type updates in quantum Monte Carlo, applicable both to world-line and stochastic series expansion methods. Here, the directed-loop equations, the solution of which gives the…

We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…

On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…