QCD at nonzero chemical potential: Recent progress on the lattice

Aarts, Gert; Attanasio, Felipe; Jäger, Benjamin; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu

doi:10.1063/1.4938590

Cited by 58 publications

(98 citation statements)

References 50 publications

(64 reference statements)

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“…The validity of this statement, however, is not entirely clear and may be model dependent. On the one hand, the above observation in HDQCD helped in exploring the phase diagram of the model [28], but on the other hand, in the case of full QCD, recent results [7] show that, using N t = 4, 6, 8 lattices, the breakdown of complex Langevin prevents the exploration of the confined region. We note that e.g.…”

Section: Introductionmentioning

confidence: 99%

Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential

et al. 2017

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We study three possible ways to circumvent the sign problem in the O(3) nonlinear sigma model in 1+1 dimensions. We compare the results of the worm algorithm to complex Langevin and multiparameter reweighting. Using the worm algorithm, the thermodynamics of the model is investigated, and continuum results are shown for the pressure at different µ/T values in the range 0 − 4. By performing T = 0 simulations using the worm algorithm, the Silver Blaze phenomenon is reproduced. Regarding the complex Langevin, we test various implementations of discretizing the complex Langevin equation. We found that the exponentialized Euler discretization of the Langevin equation gives wrong results for the action and the density at low T /m. By performing a continuum extrapolation, we found that this discrepancy does not disappear and depends slightly on temperature. The discretization with spherical coordinates performs similarly at low µ/T but breaks down also at some higher temperatures at high µ/T . However, a third discretization that uses a constraining force to achieve the φ 2 = 1 condition gives correct results for the action but wrong results for the density at low µ/T .

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Section: Introductionmentioning

confidence: 99%

Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential

et al. 2017

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“…Note that, in the case where the imaginary part of σ vanishes, CL reduces to real Langevin (RL). Unlike HMC (and also RL), however, it is understood that CL generally may not be guaranteed to converge to the correct result, if at all, unless certain criteria are satisfied [9,10]; as such, additional scrutiny is required to ensure correct results. One of the most common challenges in CL calculations are uncontrolled excursions of the auxiliary field into the complex plane due to singularities that appear in the determinants of M ↑,↓ .…”

Section: Complex Langevin Formalismmentioning

confidence: 99%

“…[11,15] where this has also been observed in the case of imaginary mass imbalances. Apart from that, an understanding of the emergence of the discrepancy between CL and perturbation theory for repulsive interactions and βµ > 0 with increasing imbalances requires a more detailed analysis, also with respect to the applicability of CL in this regime [9,10]. Encouraged by our results in 1D, we proceed to a special 3D case known as the unitary Fermi gas (UFG).…”

Section: Polarized Systemmentioning

confidence: 99%

Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

Loheac¹,

Braun

Drut

2018

EPJ Web Conf.

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Abstract. We calculate the pressure and density of polarized non-relativistic systems of two-component fermions coupled via a contact interaction at finite temperature. For the unpolarized one-dimensional system with an attractive interaction, we perform a thirdorder lattice perturbation theory calculation and assess its convergence by comparing with hybrid Monte Carlo. In that regime, we also demonstrate agreement with real Langevin. For the repulsive unpolarized one-dimensional system, where there is a so-called complex phase problem, we present lattice perturbation theory as well as complex Langevin calculations. For our studies, we employ a Hubbard-Stratonovich transformation to decouple the interaction and automate the application of Wick's theorem for perturbative calculations, which generates the diagrammatic expansion at any order. We find excellent agreement between the results from our perturbative calculations and stochastic studies in the weakly interacting regime. In addition, we show predictions for the strong coupling regime as well as for the polarized one-dimensional system. Finally, we show a first estimate for the equation of state in three dimensions where we focus on the polarized unitary Fermi gas.

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“…In the infinite volume limit this becomes a discontinuous jump indicating a first-order transition. The same effective theory evaluated for SU (2) shows indeed a second order transition [10]. The critical coupling λ c 1 can be translated to a lattice gauge coupling β c by inverting Equation (3) for every given N τ .…”

Section: Testing the Effective Theory At Zero Densitymentioning

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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QCD at nonzero chemical potential: Recent progress on the lattice

Cited by 58 publications

References 50 publications

Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential

Comparison of algorithms for solving the sign problem in the O(3) model in 1+1 dimensions at finite chemical potential

Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin

Towards a theoretical description of dense QCD

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