A Random-Batch Monte Carlo Method for Many-Body Systems with Singular Kernels

A Random Number Based Method for Monte Carlo Integration

A new method is proposed for Monte Carlo integration. This method is more efficient with wider coverage, including improper integrals, while the classical Monte Carlo integration can only handle bounded domain integrals. To implement this method in computer programming, you only need a random number generator. Unlike the deterministic numerical integration methods, the expected error of this me...

A Fourier–Wavelet Monte Carlo Method for Fractal Random Fields

A new hierarchical method for the Monte Carlo simulation of random fields called the Fourier–wavelet method is developed and where 0 , H , 1 is the Hurst exponent and k?l denotes applied to isotropic Gaussian random fields with power law spectral the expected value. density functions. This technique is based upon the orthogonal Here we develop a new Monte Carlo method based upon decomposition o...

The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations

Article history: Received 9 April 2014 Received in revised form 26 May 2014 Accepted 28 May 2014 Available online 2 June 2014

Simulation of quantum many-body systems with strings of operators and Monte Carlo tensor contractions.

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to hi...

Many-body effects on graphene conductivity: Quantum Monte Carlo calculations