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The study of QFTs at finite density is hindered by the presence of the so-called sign problem. The action definition of such systems is, in fact, complex-valued making standard importance sampling Monte Carlo methods ineffective. In this…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the…
Some recent developments to handle the numerical sign problem in QCD and related theories at nonzero density are reviewed. In this contribution I focus on changing the integration order to soften the severity of the sign problem, the…
We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we…
The theoretical treatment of Fermi systems consisting of particles with unequal masses is challenging. Even in one spatial dimension analytic solutions are limited to special configurations and numerical progress with Monte Carlo…
The action of the 2d O(3) non-linear sigma model on the lattice in a bath of particles, when expressed in terms of standard O(3) degrees of freedom, is complex. A reformulation of the model in terms of new variables that makes the action…
Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method…
To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original…
Long-range interactions in finite density QCD necessitate a non-perturbative approach in order to reliably map out the key features and spectrum of the QCD phase diagram. However, the complex nature of the fermion determinant in this sector…
We solve a variety of sign problems for models in lattice field theory using the Hamiltonian formulation, including Yukawa models and simple lattice gauge theories. The solutions emerge naturally in continuous time and use the dual…
The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In the canonical approach, the grand partition function is written as a fugacity expansion: $Z_G(\mu,T) = \sum_n Z_C(n,T)…
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…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
In recent years the complex action problem of lattice field theory at finite density was overcome for several system by mapping them to dual variables (flux lines and surfaces). We illustrate this mapping for the case of the U(1) gauge…
Lattice simulations of non-zero density QCD introduce the so-called sign problem (complex or negative probabilities), which invalidates importance sampling methods. To circumvent this, we use the Complex Langevin Equation (CLE), to measure…
We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series specifying an unknown function in terms of itself. The range of convergence of this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than that…
We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…
Lattice scalar field theories encounter a sign problem when the coupling constant is complex. This is a close cousin of the real-time sign problems that afflict the lattice Schwinger-Keldysh formalism, and a more distant relative of the…
Monte Carlo simulations away from half-filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented…
Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…