Equation of state for cold and dense heavy QCD

Glesaaen, Jonas; Neuman, Mathias; Philipsen, Owe

doi:10.1007/jhep03(2016)100

Cited by 26 publications

(54 citation statements)

References 33 publications

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“…3 The dependency of M, M † on ηµ and µq can be factored out as it will be shown in the dual partition function Eq. (27).…”

Section: Index Contraction and Tensor Networkmentioning

confidence: 99%

“…Before discussing these two possibilities, we want to highlight some features of the partition function Eq. (27).…”

Section: A General Propertiesmentioning

confidence: 99%

“…We now want to comment on the complexity of the dual partition function Eq. (27). Given the background {n p ,n p , k , f , m x }, the weight of the configuration is obtained by contracting the tensor network T ρ x .…”

Section: B Complexity and Sampling Strategiesmentioning

confidence: 99%

“…More recently, other approaches that are not limited to small µ B have been proposed, such as the Complex Langevin approach [20,21], the Lefschetz thimble approach [22][23][24], or the density of states method [25]. To name also some approaches that are in the spirit of a dual representation: the 3-dimensional effective theory [26,27] (a joint strong coupling and hopping parameter expansion that can be mapped to SU(3) spin model), decoupling the gauge links using Hubbard-Stratonovich transformations [28], "Induced QCD" based on an alternative discretization of Yang Mills Theory [29,30]. All these approaches have their shortcomings, and a method that allows to simulate lattice QCD at finite density has not yet been established.…”

Section: Introductionmentioning

confidence: 99%

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New dual representation for staggered lattice QCD

Gagliardi

Unger

2020

Phys. Rev. D

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We propose a new strategy to evaluate the partition function of lattice QCD with Wilson gauge action coupled to staggered fermions, based on a strong coupling expansion in the inverse bare gauge coupling β = 2N/g 2 . Our method makes use of the recently developed formalism to evaluate the SU(N ) 1−link integrals and consists in an exact rewriting of the partition function in terms of a set of additional dual degrees of freedom which we call "Decoupling Operator Indices" (DOI). The method is not limited to any particular number of dimensions or gauge group U(N ), SU(N ). In terms of the DOI the system takes the form of a Tensor Network which can be simulated using Wormlike algorithms. Higher order β-corrections to strong coupling lattice QCD can be, in principle, systematically evaluated, helping to answer the question whether the finite density sign problem remains mild when plaquette contributions are included. Issues related to the complexity of the description and strategies for the stochastic evaluation of the partition function are discussed.

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“…3 The dependency of M, M † on ηµ and µq can be factored out as it will be shown in the dual partition function Eq. (27).…”

Section: Index Contraction and Tensor Networkmentioning

confidence: 99%

“…Before discussing these two possibilities, we want to highlight some features of the partition function Eq. (27).…”

Section: A General Propertiesmentioning

confidence: 99%

Section: B Complexity and Sampling Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New dual representation for staggered lattice QCD

Gagliardi

Unger

2020

Phys. Rev. D

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“…However, the geometry of the terms in the effective action is exactly that of the set of connected graphs that can be embedded on a square lattice. Employing a combinatorial embedding technique [23], the calculation can be performed systematically and fully analytically. Doing this for a sequence of lattice spacings and extrapolating to the continuum we compare with the numerical evaluation in Figure 7 and find quantitative agreement.…”

Section: Th Quark Confinement and The Hadron Spectrummentioning

confidence: 99%

Towards a theoretical description of dense QCD

Philipsen¹

2017

EPJ Web Conf.

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Abstract. The properties of matter at finite baryon densities play an important role for the astrophysics of compact stars as well as for heavy ion collisions or the description of nuclear matter. Because of the sign problem of the quark determinant, lattice QCD cannot be simulated by standard Monte Carlo at finite baryon densities. I review alternative attempts to treat dense QCD with an effective lattice theory derived by analytic strong coupling and hopping expansions, which close to the continuum is valid for heavy quarks only, but shows all qualitative features of nuclear physics emerging from QCD. In particular, the nuclear liquid gas transition and an equation of state for baryons can be calculated directly from QCD. A second effective theory based on strong coupling methods permits studies of the phase diagram in the chiral limit on coarse lattices.

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Reaction Rates and Transport in Neutron Stars

Schmitt

Shternin

2018

Astrophysics and Space Science Library

100

122

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Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions. arXiv:1711.06520v3 [astro-ph.HE] 29 Oct 2018 65 References 66 I. INTRODUCTION A. ContextTransport describes how conserved quantities such as energy, momentum, particle number, or electric charge are transferred from one region to another. Such a transfer occurs if the system is out of equilibrium, for instance through a temperature gradient or a non-uniform chemical composition. Different theoretical methods are used to understand transport, depending on how far the system is away from its equilibrium state. If the system is close to equilibrium locally and perturbations are on large scales in space and time, hydrodynamics is a powerful technique. Further away from equilibrium other techniques are required, for example kinetic theory, which can also be used to provide the transport coefficients needed in the hydrodynamic equations. In any case, transport is determined by interactions on a microscopic level, and it is the resulting transport properties that we are concerned with in this review.Signals from neutron stars are sensitive to equilibrium properties such as the equation of state but also, to a large extent, to transport properties -here, by neutron stars we mean all objects with a radius of about 10 km and a mass of about 1-2 solar masses, including the possibilities of hybrid stars, which have a quark matter core, and pure quark stars. Therefore, understanding transport is crucial to interpret astrophysical observations, and, turning the argument around, we can use astrophysical observations to improve our understanding of transport in dense matter and thus ultimately our understanding of the microscopic interactions.Transport properties are most commonly computed from particle collisions. (Although, in strongly coupled systems, the picture of well-defined particles scattering off each other has to be taken with care.) These can be scattering processes in which energy and momentum is exchanged without changing the chemical composition of the system, or these can be flavor-changing processes from the electroweak interaction. Understanding transport thus amounts to understanding the rates of these processes, as a function of temperature and density. Electroweak processes are well understood, but large uncertainties arise if the strong interaction is involved in a reaction that contributes to transport. Therefore, approximations such as weak-coupling techniques or one-pion exchange for nucleon-nucleon collisions are being used, and efforts in current research aim at improving these approximations.In a neutron star, most of the particles involved in these processes are fermions: electrons, muons, neutrinos, neutrons, protons, hyperons, and quarks. Since the Fermi momenta of these fermions are typically much larger tha...

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Equation of state for cold and dense heavy QCD

Cited by 26 publications

References 33 publications

New dual representation for staggered lattice QCD

New dual representation for staggered lattice QCD

Towards a theoretical description of dense QCD

Reaction Rates and Transport in Neutron Stars

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