Two-Flavor Lattice QCD with a Finite Density of Heavy Quarks: Heavy-Dense Limit and "Particle-Hole" Symmetry

We investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come from by studying the heavy-dense fermion determinant and the corresponding strong-coupling partition function (which can be integrated analytically). We then add in a first step an effective Polyakov loop gauge action (which reproduces the leading terms in the character expansion of the Wilson gauge action) to the heavy-dense partition function and try to analyze how some of the properties of the half-filling point change when leaving the strong coupling limit. In a second step, we take also the leading nearest-neighbor fermion hopping terms into account (including gauge interactions in the fundamental representation) and mention how the method could be improved further to incorporate the full set of nearest-neighbor fermion hoppings. Using our mean-field method, we also obtain an approximate ($\mu$,T) phase diagram for heavy-dense LQCD at finite inverse gauge coupling $\beta$. Finally, we propose a simple criterion to identify the chemical potential beyond which lattice artifacts become dominant.Comment: 39 pages, 22 figure

Euclidean Dynamical Triangulation revisited: is the phase transition really first order?

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [3,4]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [3,4] an artificial harmonic potential was added to the action; in [4] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [6]. With these improved methods, on systems of size up to 64k 4-simplices, we confirm that the phase transition is first order.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order? (extended version)

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [5,9]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [5,9] an artificial harmonic potential was added to the action; in [9] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [12]. With these improved methods, on systems of size up to 64k 4-simplices, we confirm that the phase transition is first order. In addition, we discuss a local criterion to decide whether parts of a triangulation are in the elongated or crumpled state and describe a new correspondence between EDT and the balls in boxes model. The latter gives rise to a modified partition function with an additional, third coupling. Finally, we propose and motivate a class of modified path-integral measures that might remove the metastability of the Markov chain and turn the phase transition into second order.Comment: 26 pages, 21 figures, extended version of arXiv:1311.471

Sampling of General Correlators in Worm Algorithm-based Simulations

Using the complex $\phi^4$-model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator $$, but also more general correlators such as$$ or $$, as well as condensates like$$, can be measured at every step of the Monte Carlo evolution of the worm instead of on closed-worm configurations only. The method generalizes straightforwardly to other systems simulated by worms, such as spin or sigma models.Comment: 43 pages, 15 figure

Oscillating propagators in heavy-dense QCD

Using Monte Carlo simulations and extended mean field theory calculations we show that the $3$-dimensional $Z_3$ spin model with complex external fields has non-monotonic spatial correlators in some regions of its parameter space. This model serves as a proxy for heavy-dense QCD in $(3+1)$ dimensions. Non-monotonic spatial correlators are intrinsically related to a complex mass spectrum and a liquid-like (or crystalline) behavior. A liquid phase could have implications for heavy-ion experiments, where it could leave detectable signals in the spatial correlations of baryons.Comment: 16 pages, 9 figures, updated to match published versio

Bulk-preventing actions for SU(N) gauge theories

We introduce a one-parameter family of SU(N) gauge actions which, when used in combination with an HMC update algorithm, prevent the gauge system from entering an artificial bulk-"phase". We briefly discuss the mechanism behind the bulk-prevention and present test results for different SU(N) gauge groups.Peer reviewe

Bulk-preventing actions for SU(N) gauge theories

We introduce a one-parameter family of SU(N) gauge actions which, when used in combination with an HMC update algorithm, prevent the gauge system from entering an artificial bulk-"phase". We briefly discuss the mechanism behind the bulk-prevention and present test results for different SU(N) gauge groups.Peer reviewe

Nonperturbative Decoupling of Massive Fermions.

SU(2) gauge theory with N_{f}=24 massless fermions is noninteracting at long distances, i.e., it has an infrared fixed point at vanishing coupling. With massive fermions, the fermions are expected to decouple at energy scales below the fermion mass, and the infrared behavior is that of confining SU(2) pure gauge theory. We demonstrate this behavior nonperturbatively with lattice Monte Carlo simulations by measuring the gradient flow running coupling

Nonperturbative Decoupling of Massive Fermions

Funding Information: The support of the Academy of Finland Grants No. 308791, No. 310130, and No. 320123 is acknowledged. Partially funded by the Swiss National Science Foundation (SNSF) through Grant No. 200021_175761. The authors wish to acknowledge CSC—IT Center for Science, Finland, for generous computational resources. Publisher Copyright: © 2022 authors. Published by the American Physical Society.SU(2) gauge theory with Nf=24 massless fermions is noninteracting at long distances, i.e., it has an infrared fixed point at vanishing coupling. With massive fermions, the fermions are expected to decouple at energy scales below the fermion mass, and the infrared behavior is that of confining SU(2) pure gauge theory. We demonstrate this behavior nonperturbatively with lattice Monte Carlo simulations by measuring the gradient flow running coupling.Peer reviewe