Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry

Rindlisbacher, Tobias; Forcrand, Philippe de

doi:10.1007/jhep02(2016)051

Cited by 19 publications

(26 citation statements)

References 21 publications

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“…positively correlated. Such a correlation was anticipated in [42], and observed in simulations of heavy-dense lattice QCD [14,15,19,20]. It is interesting to note that the crossover point where the phase of the determinant vanishes lies near to the quark-number density of 1.5 where the fermi states are half-filled.…”

Section: Complex Langevin For Finite Density Lattice Qcdsupporting

confidence: 52%

Applying complex Langevin simulations to lattice QCD at finite density

Kogut

Sinclair

2019

Phys. Rev. D

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We study the use of the complex-Langevin equation (CLE) to simulate lattice QCD at a finite chemical potential (µ) for quark-number, which has a complex fermion determinant that prevents the use of standard simulation methods based on importance sampling. Recent enhancements to the CLE specific to lattice QCD inhibit runaway solutions which had foiled earlier attempts to use it for such simulations. However, it is not guaranteed to produce correct results. Our goal is to determine under what conditions the CLE yields correct values for the observables of interest. Zero temperature simulations indicate that for moderate couplings, good agreement with expected results is obtained for small µ and for µ large enough to reach saturation, and that this agreement improves as we go to weaker coupling.For intermediate µ values these simulations do not produce the correct physics. We compare our results with those of the phase-quenched approximation. Since there are indications that correct results might be obtained if the CLE trajectories remain close to the SU (3) manifold, we study how the distance from this manifold depends on the quark mass and on the coupling. We find that this distance decreases with decreasing quark mass and as the coupling decreases, i.e. as the simulations approach

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Section: Complex Langevin For Finite Density Lattice Qcdsupporting

confidence: 52%

Applying complex Langevin simulations to lattice QCD at finite density

Kogut

Sinclair

2019

Phys. Rev. D

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“…Furthermore, since the antiparticle contribution in L F is negligible in the limit M → ∞, we obtain O that does not depend on the sign of ϕ c,x and has no explicit µ dependence. This relation is nothing but the particle-hole (P-H) symmetry [38]. From this symmetry, one can easily derive the relation…”

Section: B Particle-hole Symmetrymentioning

confidence: 99%

“…In Sec. III, we formulate Z 3 -EPLM, and also discuss how important the particle-hole (P-H) symmetry [38] is in EPLM. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Sign problem in a Z3 -symmetric effective Polyakov-line model

et al. 2017

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As an effective model corresponding to Z3-symmetric QCD (Z3-QCD), we construct a Z3-symmetric effective Polyakov-line model (Z3-EPLM) by using the logarithmic fermion effective action. Since Z3-QCD tends to QCD in the zero-temperature limit, Z3-EPLM also agrees with the ordinary effective Polyakov-line model (EPLM) there; note that (ordinary) EPLM does not possess Z3 symmetry. Our main purpose is to discuss a sign problem appearing in Z3-EPLM. The action of Z3-EPLM is real, when the Polyakov line is not only real but also its Z3 images. This suggests that the sign problem becomes milder in Z3-EPLM than in EPLM. In order to confirm this suggestion, we do lattice simulations for both EPLM and Z3-EPLM by using the reweighting method with the phase quenched approximation. In the low-temperature region, the sign problem is milder in Z3-EPLM than in EPLM. We also propose a new reweighting method. This makes the sign problem very weak in Z3-EPLM.

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“…On finer lattices the saturation density in physical units grows and in the continuum limit moves to infinity. This lattice artefact starts to make itself felt already quite early, as is also apparent in the numerical behaviour of the Polyakov loop [8] and related to the half-filling symmetry of the static action [15].…”

Section: Continuum Approachmentioning

confidence: 95%

“…The static determinant has a particle-hole symmetry about half-filling akin to the Hubbard model [15]. The expansion is then in spatial hops of the remaining kinetic determinant,…”

Section: Jhep03(2016)100mentioning

confidence: 99%

Equation of state for cold and dense heavy QCD

Glesaaen

Neuman

Philipsen

2016

J. High Energ. Phys.

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A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order ∼ u 5 κ 8 in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.

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Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry

Cited by 19 publications

References 21 publications

Applying complex Langevin simulations to lattice QCD at finite density

Applying complex Langevin simulations to lattice QCD at finite density

Sign problem in a Z3 -symmetric effective Polyakov-line model

Equation of state for cold and dense heavy QCD

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