Related papers: Mitigating the Hubbard Sign Problem with Complex-V…
Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet,…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung…
We introduce a Quantum Monte Carlo (QMC) method which efficiently simulates in a sign-problem-free way a broad class of frustrated $S=1/2$ models with competing antiferromagnetic interactions. Our scheme uses the basis of total spin…
The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is an efficient algorithm for addressing the numerical sign problem at moderate computational cost. It mitigates the sign problem while avoiding the ergodicity issues…
In this talk we show how the sign problem, occurring in dynamical simulations of random matrices at nonzero chemical potential, can be avoided by judiciously combining matrices into subsets. One can prove that these subsets have real and…
Quantum Monte-Carlo (QMC) simulations involving fermions have the notorious sign problem. Some well-known exceptions of the auxiliary field QMC algorithm rely on the factorizibility of the fermion determinant. Recently, a fermionic QMC…
We present a novel strategy to strongly reduce the severity of the sign problem, using line integrals along paths of changing imaginary action. Highly oscillating regions along these paths cancel out, decreasing their contributions. As a…
The quantum Monte Carlo algorithm is arguably one of the most powerful computational many-body methods, enabling accurate calculation of many properties in interacting quantum systems. In the presence of the so-called sign problem, the…
We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite-$U$ Hubbard model at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure -- a power law…
The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated…
We discuss the Fermion sign problem and, by examining a very general Hubbard-Stratonovich (HS) transformation, argue that the sign problem cannot be solved with such methods. We propose a different kind of transformation which, while not…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
Insurance companies make extensive use of Monte Carlo simulations in their capital and solvency models. To overcome the computational problems associated with Monte Carlo simulations, most large life insurance companies use proxy models…
Monte Carlo studies of many quantum systems face exponentially severe signal-to-noise problems. We show that noise arising from complex phase fluctuations of observables can be reduced without introducing bias using path integral contour…
This work shows that the recently discovered operator contraction identity for solving the discreet Path Integral of the harmonic oscillator can be applied equally to fermions in any dimension. This then yields an exactly solvable model for…
The multilevel blocking algorithm recently proposed as a possible solution to the sign problem in path-integral Monte Carlo simulations has been extended to systems with long-ranged interactions along the Trotter direction. As an…
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…
Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and…