Finite-density transition line for QCD with 695 MeV dynamical fermions

Greensite, Jeff; Höllwieser, Roman

doi:10.1103/physrevd.97.114504

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…The main source of interest is the possibility of obtaining information about QCD at finite baryon density via analytic continuation, thus partially avoiding the sign problem. Moreover, numerical results at imaginary µ are also a relevant test bed for effective models trying to reproduce the properties of QCD at finite density [27][28][29]. Furthermore, imaginary chemical potentials are an interesting extension of the QCD phase diagram per se, as, for particular choices of the chemical potentials, one recovers exact symmetries even in the presence of finite quark masses, leading to the presence of interesting phase transitions and critical points which, in principle, could be relevant also for the physical region of the phase diagram.…”

Section: Introductionmentioning

confidence: 99%

Roberge-Weiss endpoint and chiral symmetry restoration in Nf=2+1 QCD

et al. 2019

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We investigate the fate of the Roberge-Weiss endpoint transition and its connection with the restoration of chiral symmetry as the chiral limit of N f = 2 + 1 QCD is approached. We adopt a stout staggered discretization on lattices with Nt = 4 sites in the temporal direction; the chiral limit is approached maintaining a constant physical value of the strange-to-light mass ratio and exploring three different light quark masses, corresponding to pseudo-Goldstone pion masses mπ ≃ 100, 70 and 50 MeV around the transition. A finite size scaling analysis provides evidence that the transition remains second order, in the 3D Ising universality class, in all the explored mass range. The residual chiral symmetry of the staggered action also allows us to investigate the relation between the Roberge-Weiss endpoint transition and the chiral restoration transition as the chiral limit is approached: our results, including the critical scaling of the chiral condensate, are consistent with a coincidence of the two transitions in the chiral limit; however we are not able to discern the symmetry controlling the critical behavior, because the critical indexes relevant to the scaling of the chiral condensate are very close to each other for the two possible universality classes (3D Ising or O(2)).

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Section: Introductionmentioning

confidence: 99%

Roberge-Weiss endpoint and chiral symmetry restoration in Nf=2+1 QCD

et al. 2019

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“…This was studied in the strong coupling expansion [28], but also in full lattice QCD simulations. It was found that this effective theory is more tractable than the underlying lattice gauge theory (LGT) when confronting the sign problem at finite density, for recent advances see [29]. The developed algorithms in this article can be adapted to this problem, where the individual Polyakov lines and not their average over the whole lattice are constrained.…”

Section: Discussionmentioning

confidence: 99%

Constrained hybrid Monte Carlo algorithms for gauge–Higgs models

Günther

Höllwieser

Knechtli

2020

Computer Physics Communications

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We present the construction of Hybrid Monte Carlo (HMC) algorithms for constrained Hamiltonian systems of gauge-Higgs models in order to measure the constraint effective Higgs potential. In particular we focus on SU(2) Gauge-Higgs Unification models in five dimensions, where the Higgs field is identified with (some of) the five-dimensional components of the gauge field. Previous simulations have identified regions in the Higgs phase of these models which have properties of 4D adjoint or Abelian gauge-Higgs models. We develop new methods to measure constraint effective potentials, using an extension of the so-called Rattle algorithm to general Hamiltonians for constrained systems, which we adapt to the 4D Abelian gauge-Higgs model and the 5D SU(2) gauge theory on the torus and on the orbifold. The derivative of the potential is determined via the expectation value of the Lagrange multiplier for the constraint. To our knowledge, this is the first time this problem has been addressed for theories with gauge fields. The algorithm can also be used in four dimensions to study finite temperature and density transitions via effective Polyakov loop actions.

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“…Early studies employed renormalizationgroup inspired bond moving procedures [82] and microcanonical methods [83]. More recent efforts have been the inverse Monte Carlo method [84,85], the relative weights method [86][87][88][89][90][91] and the expectation value matching procedure in [92].…”

Section: Derivation Of the Effective Actionsmentioning

confidence: 99%

Aspects of heavy, dense lattice QCD : series expansion methods, baryon versus isospin density and large Nc

Scheunert¹

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For finite baryon chemical potential, conventional lattice descriptions of quantum chromodynamics (QCD) have a sign problem which prevents straightforward simulations based on importance sampling. In this thesis we investigate heavy dense QCD by representing lattice QCD with Wilson fermions at finite temperature and density in terms of Polyakov loops. We discuss the derivation of $3$-dimensional effective Polyakov loop theories from lattice QCD based on a combined strong coupling and hopping parameter expansion, which is valid for heavy quarks. The finite density sign problem is milder in these theories and they are also amenable to analytic evaluations. The analytic evaluation of Polyakov loop theories via series expansion techniques is illustrated by using them to evaluate the $\SU{3}$ spin model. We compute the free energy density to $14$th order in the nearest neighbor coupling and find that predictions for the equation of state agree with simulations to $\mathcal{O}(1\%)$ in the phase were the (approximate) $Z(3)$ center symmetry is intact. The critical end point is also determined but with less accuracy and our results agree with numerical results to $\mathcal{O}(10\%)$. While the accuracy for the endpoint is limited for the current length of the series, analytic tools provide valuable insight and are more flexible. Furthermore they can be generalized to Polyakov-loop-theories with $n$-point interactions. We also take a detailed look at the hopping expansion for the derivation of the effective theory. The exponentiation of the action is discussed by using a polymer expansion and we also explain how to obtain logarithmic resummations for all contributions, which will be achieved by employing the finite cluster method know from condensed matter physics. The finite cluster method can also be used to evaluate the effective theory and comparisons of the evaluation of the effective action and a direction evaluation of the partition function are made. We observe that terms in the evaluation of the effective theory correspond to partial contractions in the application of Wick's theorem for the evaluation of Grassmann-valued integrals. Potential problems arising from this fact are explored. Next to next to leading order results from the hopping expansion are used to analyze and compare the onset transition both for baryon and isospin chemical potential. Lattice QCD with an isospin chemical potential does not have a sign problem and can serve as a valuable cross-check. Since we are restricted by the relatively short length of our series, we content ourselves with observing some qualitative phenomenological properties arising in the effective theory which are relevant for the onset transition. Finally, we generalize our results to arbitrary number of colors $N_c$. We investigate the transition from a hadron gas to baryon condensation and find that for any finite lattice spacing the transition becomes stronger when $N_c$ is increased and to be first order in the limit of infinite $N_c$. Beyond the onset, the pressure is shown to scale as $p \sim N_c$ through all available orders in the hopping expansion, which is characteristic for a phase termed quarkyonic matter in the literature. Some care has to be taken when approaching the continuum, as we find that the continuum limit has to be taken before the large $N_c$ limit. Although we currently are unable to take the limits in this order, our results are stable in the controlled range of lattice spacings when the limits are approached in this order.

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Finite-density transition line for QCD with 695 MeV dynamical fermions

Cited by 5 publications

References 32 publications

Roberge-Weiss endpoint and chiral symmetry restoration in Nf=2+1 QCD

Roberge-Weiss endpoint and chiral symmetry restoration in Nf=2+1 QCD

Constrained hybrid Monte Carlo algorithms for gauge–Higgs models

Aspects of heavy, dense lattice QCD : series expansion methods, baryon versus isospin density and large Nc

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