相关论文: Monte Carlo Hamiltonian from Stochastic Basis

Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…

Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian…

We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they…

In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…

We present a quantum Monte Carlo method which allows calculations on many-fermion systems at finite temperatures without any sign decay. This enables simulations of the grand-canonical ensemble at large system sizes and low temperatures.…

We derive an effective Hamiltonian for phase fluctuations in an s-wave superconductor starting from the attractive Hubbard model on a square lattice. In contrast to the common assumption, we find that the effective Hamiltonian is not the…

Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompatible with motion generated by non-canonical dynamics. These…

We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. To this end we devise a heuristic way of constructing local integrals of motion of very high quality, which…

A quantum Monte-Carlo is proposed to describe fusion/fission processes when fluctuation and dissipation, with memory effects, are important. The new theory is illustrated for systems with inverted harmonic potentials coupled to a heat-bath.

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…

The Monte Carlo (MC) estimates of thermal averages are usually functions of system control parameters $\lambda $, such as temperature, volume, interaction couplings, etc. Given the MC average at a set of prescribed control parameters…

In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our…

A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction…

Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic…

A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in…

Numerical Generalized Randomized Hamiltonian Monte Carlo is introduced, as a robust, easy to use and computationally fast alternative to conventional Markov chain Monte Carlo methods for continuous target distributions. A wide class of…

We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the…

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…

We propose a new Monte Carlo algorithm for the numerical study of general lattice models in Hamiltonian form. The algorithm is based on an initial Ansatz for the ground state wave function depending on a set of free parameters which are…