scholarly journals New Canonical and Grand Canonical Density of States Techniques for Finite Density Lattice QCD

Particles ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 87-98
Author(s):  
Christof Gattringer ◽  
Michael Mandl ◽  
Pascal Törek
Keyword(s):  
Lattice Qcd ◽  
Density Of States ◽  
Chemical Potential ◽  
Vacuum Expectation ◽  
Expectation Values ◽  
New Techniques ◽  
Finite Density ◽  
Quantum Chromo Dynamics ◽  
Grand Canonical ◽  
Fermion Action

We discuss two new density of states approaches for finite density lattice QCD (Quantum Chromo Dynamics). The paper extends a recent presentation of the new techniques based on Wilson fermions, while here, we now discuss and test the case of finite density QCD with staggered fermions. The first of our two approaches is based on the canonical formulation where observables at a fixed net quark number N are obtained as Fourier moments of the vacuum expectation values at imaginary chemical potential θ . We treat the latter as densities that can be computed with the recently developed functional fit approach. The second method is based on a direct grand canonical evaluation after rewriting the QCD partition sum in terms of a suitable pseudo-fermion representation. In this form, the imaginary part of the pseudo-fermion action can be identified and the corresponding density may again be computed with the functional fit approach. We develop the details of the two approaches and discuss some exploratory first tests for the case of free fermions where reference results for assessing the new techniques may be obtained from Fourier transformation.

scholarly journals FINITE DENSITY ALGORITHM IN LATTICE QCD—A CANONICAL ENSEMBLE APPROACH

2002 ◽  
Vol 16 (14n15) ◽  
pp. 2017-2032 ◽  
Author(s):  
KEH-FEI LIU
Keyword(s):  
Monte Carlo ◽  
Lattice Qcd ◽  
Efficient Method ◽  
Chemical Potential ◽  
Canonical Ensemble ◽  
Unbiased Estimate ◽  
Baryon Number ◽  
Monte Carlo Algorithm ◽  
Finite Density ◽  
Ensemble Approach

I will review the finite density algorithm for lattice QCD based on finite chemical potential and summarize the associated difficulties. I will propose a canonical ensemble approach which projects out the finite baryon number sector from the fermion determinant. For this algorithm to work, it requires an efficient method for calculating the fermion determinant and a Monte Carlo algorithm which accommodates unbiased estimate of the probability. I shall report on the progress made along this direction with the Padé–Z2 estimator of the determinant and its implementation in the newly developed Noisy Monte Carlo algorithm.

Induced fermionic current by a magnetic flux in a cosmic string spacetime at finite temperature

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641021
Author(s):  
Eugênio R. Bezerra de Mello ◽  
Aram A. Saharian ◽  
Azadeh Mohammadi
Keyword(s):  
Magnetic Flux ◽  
Periodic Function ◽  
Cosmic String ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Vacuum Expectation ◽  
Expectation Values ◽  
Quantum Flux ◽  
Current Densities ◽  
Azimuthal Current

Here we analyze the finite temperature expectation values of the charge and current densities for a massive fermionic quantum field with nonzero chemical potential [Formula: see text], induced by a magnetic flux running along the axis of an idealized cosmic string. These densities are decomposed into the vacuum expectation values and contributions coming from the particles and antiparticles. Specifically the charge density is an even periodic function of the magnetic flux with the period equal to the quantum flux and an odd function of the chemical potential. The only nonzero component of the current density corresponds to the azimuthal current and it is an odd periodic function of the magnetic flux and an even function of the chemical potential. Both analyzed are developed for the cases where [Formula: see text] is smaller than the mass of the field quanta [Formula: see text].

scholarly journals New density of states approaches to finite density lattice QCD

2019 ◽  
Vol 100 (11) ◽  
Author(s):  
Christof Gattringer ◽  
Michael Mandl ◽  
Pascal Törek
Keyword(s):  
Lattice Qcd ◽  
Density Of States ◽  
Finite Density

scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

scholarly journals Aspects of quantum information in finite density field theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Lucas Daguerre ◽  
Raimel Medina ◽  
Mario Solís ◽  
Gonzalo Torroba
Keyword(s):  
Field Theory ◽  
Quantum Information ◽  
Mutual Information ◽  
Fermi Surface ◽  
Relative Entropy ◽  
Chemical Potential ◽  
Operator Product ◽  
Dirac Fermions ◽  
Long Distance ◽  
Finite Density

Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

scholarly journals Phase fluctuation of fermion determinant in lattice QCD at finite density

2004 ◽  
Vol 129-130 ◽  
pp. 539-541 ◽  
Author(s):  
Yuji Sasai ◽  
Atsushi Nakamura ◽  
Tetsuya Takaishi
Keyword(s):  
Lattice Qcd ◽  
Phase Fluctuation ◽  
Finite Density
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