arXiv subjects

Ion-Olimpiu Stamatescu

Publications and source records attributed to Ion-Olimpiu Stamatescu.

At least 19 recordsLinked to original sources

arXiv2023

Complex Langevin: Correctness criteria, boundary terms and spectrum

The Complex Langevin (CL) method to simulate `complex probabilities', ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex `probability' measure. The situation may be spoiled in two ways: failure to converge and convergence to the wrong limit. It was found long ago that `wrong convergence' is caused by boundary terms; non-convergence may arise from bad spectral properties of the various evolution operators related to the CL process. Here we propose a class of criteria which allow to rule out boundary terms and at the same time bad spectrum. Ruling out boundary terms in the equilibrium distribution arising from a CL simulation implies that the so-called convergence conditions are fulfilled. This in turn has been shown to guarantee that the expectation values of holomorphic observables are given by complex linear combinations of $\exp(-S)$ over various integration cycles. If the spectrum is pathological, however, the CL simulation in general does not reproduce the integral over the desired real cycle.

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arXiv2019

Cooling Stochastic Quantization with colored noise

Smoothing of field configurations is highly important for precision calculations of physical quantities on the lattice. We present a cooling method based on Stochastic Quantization with a built-in UV momentum cutoff. The latter is implemented via a UV-regularized, hence colored, noise term. Our method is tested in a two-dimensional scalar field theory. We show, that UV modes can be removed systematically without altering the physics content of the theory. The approach has an interpretation in terms of the non-perturbative (Wilsonian) renormalization group that facilitates the physics interpretation of the cutoff procedure. It also can be used to define the maximal colored cooling applicable without changing the theory.

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arXiv2019

Reweighting Lefschetz Thimbles

We present a novel reweighting technique to calculate the relative weights in the Lefschetz thimble decomposition of a path integral. Our method is put to work using a $U(1)$ one-link model providing for a suitable testing ground and sharing many features with realistic gauge theories with fermions at finite density. We discuss prospects and future challenges to our method.

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arXiv2019

Complex Langevin and boundary terms

As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, we analyze the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. We also show how some simple modification stabilizes the CL process in such a way that it can produce results agreeing with direct integration. Besides explicitly demonstrating the connection between boundary terms and correct convergence our analysis also suggests a correctness criterion which could be applied in realistic lattice simulations.

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arXiv2018

Complex Langevin: Boundary terms and application to QCD

We employ the Complex Langevin method for simulation of complex-valued actions. First, we show how to test for convergence of the method by explicitely computing boundary terms and demonstrate this in a model. Then we investigate the deconfinement phase transition of QCD with $N_f=2$ Wilson-fermions using the Complex Langevin Method and. We give preliminary results for the transition temperatures up to $μ/T_c(μ=0)\approx 5$ and compute the curvature coefficient $κ_2$.

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arXiv2018

Reweighting Lefschetz Thimbles

One of the main challenges in simulations on Lefschetz thimbles is the computation of the relative weights of contributing thimbles. In this paper we propose a solution to that problem by means of computing those weights using a reweighting procedure. Besides we present recipes for finding parametrizations of thimbles and anti-thimbles for a given theory. Moreover, we study some approaches to combine the Lefschetz thimble method with the Complex Langevin evolution. Our numerical investigations are carried out by using toy models among which we consider a one-site z^4 model as well as a U(1) one-link model.

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arXiv2017

Getting even with CLE

In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain specific conditions which are not always satisfied. We here discuss the procedures to meet these conditions and the estimation of systematic errors and present some actual achievements.

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arXiv2017

Complex Langevin dynamics and zeroes of the fermion determinant

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.

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arXiv2016

On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models

In the complex Langevin approach to lattice simulations at nonzero density, zeroes of the fermion determinant lead to a meromorphic drift and hence a need to revisit the theoretical derivation. We discuss how poles in the drift affect the formal justification of the approach and then explore the various potential issues in simple models, in a manner that is applicable to heavy dense and full QCD.

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arXiv2016

Discussion of the loop formula for the fermionic determinant

A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of increasing length.

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arXiv2016

A note on the Loop Formula for the fermionic determinant

A formula expressing the fermionic determinant as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of increasing length.

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arXiv2015

Towards the heavy dense QCD phase diagram using Complex Langevin simulations

Monte Carlo methods cannot probe far into the QCD phase diagram with a real chemical potential, due to the famous sign problem. Complex Langevin simulations, using adaptive step-size scaling and gauge cooling, are suited for sampling path integrals with complex weights. We report here on tests of the deconfinement transition in pure Yang-Mills SU(3) simulations and present an update on the QCD phase diagram in the limit of heavy and dense quarks.

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arXiv2015

Insights into the heavy dense QCD phase diagram using Complex Langevin simulations

Complex Langevin simulations provide an alternative to sample path integrals with complex weights and therefore are suited to determine the phase diagram of QCD from first principles. Adaptive step-size scaling and gauge cooling are used to improve the convergence of our simulations. We present results for the phase diagram of QCD in the limit of heavy quarks and discuss the order of the phase transitions, which are studied by varying the spatial simulation volume.

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arXiv2015

Simple QED- and QCD-like Models at Finite Density

In this paper we discuss one-dimensional models reproducing some features of quantum electrodynamics and quantum chromodynamics at nonzero density and temperature. Since a severe sign problem makes a numerical treatment of QED and QCD at high density difficult, such models help to explore various effects peculiar to the full theory. Studying them gives insights into the large density behavior of the Polyakov loop by taking both bosonic and fermionic degrees of freedom into account, although in one dimension only the implementation of a global gauge symmetry is possible. For these models we evaluate the respective partition functions and discuss several observables as well as the Silver Blaze phenomenon.

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arXiv2015

The phase diagram of heavy dense QCD with complex Langevin simulations

The sign problem of QCD prevents standard lattice simulations to determine the phase diagram of strong interactions with a finite chemical potential directly. Complex Langevin simulations provide an alternative method to sample path integrals with complex weights. We report on our ongoing project to determine the phase diagram of QCD in the limit of heavy quarks (HDQCD) using Complex Langevin simulations.

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arXiv2014

Systematic approximation for QCD at non-zero density

We use the heavy dense formulation of QCD (HD-QCD) as the basis for an analytic expansion as systematic approximation to QCD at non-zero density, keeping the full Yang-Mills action. We analyse the structure of the baryonic density and other quantities and present data from the complex Langevin equation (CLE) and reweighting (RW) calculations for 2 flavours of Wilson fermions.

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arXiv2014

QCD at nonzero chemical potential: recent progress on the lattice

We summarise recent progress in simulating QCD at nonzero baryon density using complex Langevin dynamics. After a brief outline of the main idea, we discuss gauge cooling as a means to control the evolution. Subsequently we present a status report for heavy dense QCD and its phase structure, full QCD with staggered quarks, and full QCD with Wilson quarks, both directly and using the hopping parameter expansion to all orders.

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arXiv2014

Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion

Progress in simulating QCD at nonzero baryon density requires, amongst others, substantial numerical effort. Here we propose two different expansions to all orders in the hopping parameter, preserving the full Yang-Mills action, which are much cheaper to simulate. We carry out simulations using complex Langevin dynamics, both in the hopping expansions and in the full theory, for two flavours of Wilson fermions, and agreement is seen at sufficiently high order in the expansion. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.

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