Gauge cooling in complex Langevin for lattice QCD with heavy quarks

140

A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, κ, whose action is correct to κ n u m with n + m = 4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state in the limit of heavy baryons. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as a gap between the onset of isospin and baryon condensation.

Section: Comparison With Monte Carlomentioning

confidence: 99%

Heavy dense QCD and nuclear matter from an effective lattice theory

Langelage

Neuman

Philipsen

2014

140

“…Moreover, the theoretical foundation has been clarified [12,13]. The control over nonabelian gauge theories has been drastically improved with the implementation of gauge cooling [15], possibly adaptively [2], and first results for QCD at nonzero baryon chemical potential have appeared [16]. Another recent application is to SU(3) gauge theory in the presence of a nonzero theta-term [17].…”

Section: Jhep10(2014)159mentioning

confidence: 99%

“…The exact result is Z = I 1 (β)/β. For Langevin dynamics we can follow (at least) two approaches [18]: a complete 'gauge fixing', which will lead to a logarithm in the effective action due to the reduced Haar measure, and matrix updates combined with gauge cooling [15], which can readily be extended to full nonabelian gauge theories in four dimensions with dynamical fermions [16]. It is therefore interesting to compare both approaches with the Lefschetz thimbles.…”

Section: Su(2) Modelmentioning

confidence: 99%

“…It is by now well established that a straightforward application of this approach can lead to wrongly converging Langevin dynamics, due to an uncontrolled exploration of SL(2,C), the complexification of SU (2). Hence it needs to be combined with gauge cooling [15], so that the combined update reads 9) where Ω(t) is a U(t) dependent SL(2,C) gauge transformation, which minimises the distance from SU(2) [2,15]. In a simulation, the number of cooling steps applied after each Langevin update can be varied to achieve stability.…”

Section: Gauge Dynamics With Coolingmentioning

confidence: 99%

See 1 more Smart Citation

Some remarks on Lefschetz thimbles and complex Langevin dynamics

Aarts

Bongiovanni

Seiler

et al. 2014

Self Cite

Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble(s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics.

“…The disadvantage of the CLM is that there is a condition [7,8,10] to be satisfied to make it work, and hence there is a certain range of applicability. While the gauge cooling technique [27] (See refs. [10,28] for its justification) has enlarged this range of applicability to the extent that finite density QCD either with heavy quarks [29][30][31] or in the deconfined phase [32,33] can now be investigated, it is not yet clear whether one can investigate it even in the confined phase with light quarks [34][35][36][37][38][39][40][41].…”

Section: Jhep06(2017)023mentioning

confidence: 99%

Combining the complex Langevin method and the generalized Lefschetz-thimble method

Nishimura

Shimasaki

2017

Abstract:The complex Langevin method and the generalized Lefschetz-thimble method are two closely related approaches to the sign problem, which are both based on complexification of the original dynamical variables. The former can be viewed as a generalization of the stochastic quantization using the Langevin equation, whereas the latter is a deformation of the integration contour using the so-called holomorphic gradient flow. In order to clarify their relationship, we propose a formulation which combines the two methods by applying the former method to the real variables that parametrize the deformed integration contour in the latter method. Three versions, which differ in the treatment of the residual sign problem in the latter method, are considered. By applying them to a single-variable model, we find, in particular, that one of the versions interpolates the complex Langevin method and the original Lefschetz-thimble method.