Dénes Sexty

Simulating full QCD at nonzero density using the complex Langevin equation

Abstract The complex Langevin method is extended to full QCD at non-zero chemical potential. The use of gauge cooling stabilizes the simulations at small enough lattice spacings. At large fermion mass the results are compared to the HQCD approach, in which the spatial hoppings of fermionic variables are neglected, and good agreement is found. The method allows simulations also at high densities, all the way up to saturation.

Gauge cooling in complex Langevin for lattice QCD with heavy quarks

Abstract We employ a new method, “gauge cooling”, to stabilize complex Langevin simulations of QCD with heavy quarks. The results are checked against results obtained with reweighting; we find agreement within the estimated errors, except for strong gauge coupling in the confinement region. The method allows us to go to previously unaccessible high densities.

Controlling complex Langevin dynamics at finite density

At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care. In this review, we first summarise our current understanding of the approach, combining analytical and numerical insight. In the second part we study SL(C, ℂ) gauge cooling, which was introduced recently as a tool to control complex Langevin dynamics in nonabelian gauge theories. We present new results in Polyakov chain models and in QCD with heavy quarks and compare various adaptive cooling implementations.

Bose-Einstein condensation in relativistic field theories far from equilibrium.

The formation of Bose condensates far from equilibrium can play an important role in our understanding of collision experiments of heavy nuclei or for the evolution of the early universe. In the relativistic quantum world particle number changing processes can counteract Bose condensation, and there is a considerable debate about the relevance of this phenomenon in this context. We show that the involved question of Bose condensation from initial over-population can be answered for the example of scalar field theories. Condensate formation occurs as a consequence of an inverse particle cascade with a universal power-law spectrum. This particle transport towards low momenta is part of a dual cascade, in which energy is also transfered by weak wave turbulence towards higher momenta. To highlight the importance of number changing processes for the subsequent decay of the condensate, we also compare to non-relativistic theories with exact number conservation. We discuss the relevance of these results for nonabelian gauge theories.

Some remarks on Lefschetz thimbles and complex Langevin dynamics

A bstractLefschetz 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.

Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas

Nonthermal fixed points of the dynamics of a dilute degenerate Bose gas far from thermal equilibrium are analyzed in two and three spatial dimensions. Universal power-law distributions, previously found within a nonperturbative quantum-field theoretical approach and recently shown to be related to vortical dynamics and superfluid turbulence [Phys. Rev. B 84, 020506(R) (2011)], are studied in detail. The results imply an interpretation of the scaling behavior in terms of independent vortex excitations of the superfluid and show that the statistics of topological excitations can be described in the framework of wave turbulence. The particular scaling exponents observed in the single-particle momentum distributions are found to be consistent with irreversibility as well as conservation laws obeyed by the wave interactions. Moreover, long-wavelength acoustic excitations of the vortex-bearing condensate, driven by vortex annihilations, are found to follow a nonthermal power law. Considering vortex correlations in a statistical model, the long-time departure from the nonthermal fixed point is related to vortex-antivortex pairing. The studied nonthermal fixed points are accessible in cold-gas experiments. The results shed light on fundamental aspects of superfluid turbulence and have strong potential implications for related phenomena, e.g., in early-universe inflation or quark-gluon plasma dynamics.

Over-populated gauge fields on the lattice

We study nonequilibrium dynamics of SU(2) pure gauge theory starting from initial over-population, where intense classical gauge fields are characterized by a single momentum scale Q_s. Classical-statistical lattice simulations indicate a quick evolution towards an approximate scaling behavior with exponent 3/2 at intermediate times. Remarkably, the value for the scaling exponent may be understood as arising from the leading O(g^2) contribution in the presence of a time-dependent background field. The phenomenon is associated to weak wave turbulence describing an energy cascade towards higher momenta. This particular aspect is very similar to what is observed for scalar theories, where an effective cubic interaction arises because of the presence of a time-dependent Bose condensate.

Stability of complex Langevin dynamics in effective models

A bstractThe sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.

New algorithms for finite density QCD

Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of theories with non-real measures. Similarities and differences of the two approaches are pointed out. Results using the complex Langevin method, which allows simulations to evade the sign problem in full QCD, are presented. Promising results of the thimble approach for non-gauge theories are also discussed.

The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics

A bstractComplex Langevin simulations allow numerical studies of theories that exhibit a sign problem, such as QCD, and are thereby potentially suitable to determine the QCD phase diagram from first principles. Here we study QCD in the limit of heavy quarks for a wide range of temperatures and chemical potentials. Our results include an analysis of the adaptive gauge cooling technique, which prevents large excursions into the non-compact directions of the SL(3, ℂ