Related papers: The fermion sign problem in Gauss law sectors of q…
A grand canonical system of non-interacting fermions on a square lattice is considered at zero temperature. Three different phases exist: an empty lattice, a completely filled lattice and a liquid phase which interpolates between the other…
We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and…
We propose a framework based on the concept of the semigroup to understand the fermion sign problem. By using properties of contraction semigroups, we obtain sufficient conditions for quantum lattice fermion models to be sign-problem-free.…
Monte Carlo simulations are a powerful tool for elucidating the properties of complex systems across many disciplines. Not requiring any a priori knowledge, they are particularly well suited for exploring new phenomena. However, when…
Due to the fermion sign problem, standard lattice Monte-Carlo method for QCD fail at small temperatures and high baryon densities. $G_2$-QCD, QCD with the gauge group $SU(3)$ replaced by the exceptional Lie group $G_2$, can be simulated…
Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to $U(1)$ quantum link gauge fields has…
Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we…
We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated…
Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further understanding of essential features in such systems. Quantum Monte Carlo…
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to…
Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Meron-cluster algorithms lead to an efficient solution of sign problems for both fermionic and bosonic models. Here we apply the meron concept to…
Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo…
In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). Especially, MQMC…
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…
The microscopic mechanism of itinerant ferromagnetism is a long-standing problem due to the lack of non-perturbative methods to handle strong magnetic fluctuations of itinerant electrons. We have non-pertubatively studied thermodynamic…
The ab initio thermodynamic simulation of correlated Fermi systems is of central importance for many applications, such as warm dense matter, electrons in quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo (PIMC)…
Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the calculation of out-of-equilibrium physics,…
We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory, that was recently shown in Monte Carlo simulations to exhibit $\mathbb{Z}_2$ topological order and massless Dirac fermion excitations. On…
The recently developed Meron-Cluster algorithm completely solves the exponentially difficult sign problem for a number of models previously inaccessible to numerical simulation. We use this algorithm in a high-precision study of a model of…
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this…