Related papers: Sign problem and Monte Carlo calculations beyond L…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how…
We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…
In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
The notorious fermion sign problem, arising from fermion statistics, presents a fundamental obstacle to the numerical simulation of quantum many-body systems. Here, we introduce a framework that circumvents the sign problem in the studies…
Frustrated spin systems generically suffer from the negative sign problem inherent to Monte Carlo methods. Since the severity of this problem is formulation dependent, optimization strategies can be put forward. We introduce a phase pinning…
We report recent progress in the study of a particular class of spin 1/2 XXZ model on two-dimensional lattices with frustrated diagonal and unfrustrated off-diagonal interactions. Quantum Monte Carlo simulations can be constructed without a…
The tempered Lefschetz thimble method is a parallel-tempering algorithm towards solving the numerical sign problem. It uses the flow time of the gradient flow as a tempering parameter and is expected to tame both the sign and multimodal…
We explore different ways of incorporating accurate trial wave functions into free projection auxiliary field quantum Monte Carlo (fp-AFQMC). Trial states employed include coupled cluster singles and doubles, multi-Slater, and symmetry…
A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is…
The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical…
The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem, where the system is tempered by the antiholomorphic gradient flow to tame both the sign and ergodicity problems…
The recently developed auxiliary field diffusion Monte Carlo method is applied to compute the equation of state and the compressibility of neutron matter. By combining diffusion Monte Carlo for the spatial degrees of freedom and auxiliary…
The necessity of computing integrals with complex weights over manifolds with a large number of dimensions, e.g., in some field theoretical settings, poses a problem for the use of Monte Carlo techniques. Here it is shown that very general…
At nonzero quark chemical potential dynamical lattice simulations of QCD are hindered by the sign problem caused by the complex fermion determinant. The severity of the sign problem can be assessed by the average phase of the fermion…
We consider the one-dimensional quantum-statistical problem of interacting spin-less particles in an infinite deep potential valley and on a ring. Several limits for the applicability of the Quantum Monte Carlo (QMC) methods were revealed…
In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…
The paper proposes a new Monte-Carlo simulator combining the advantages of Sequential Monte Carlo simulators and Hamiltonian Monte Carlo simulators. The result is a method that is robust to multimodality and complex shapes to use for…
Ab-initio studies of strongly interacting bosonic and fermionic systems is greatly facilitated by efficient Monte Carlo algorithms. This article emphasizes this requirement, and outlines the ideas behind the construction of the cluster…