Lattice QCD with chemical potential: Evading the fermion-sign problem

Pramana ◽  
2004 ◽  
Vol 63 (6) ◽  
pp. 1211-1224 ◽  
Author(s):  
Sourendu Gupta
Keyword(s):  
Lattice Qcd ◽  
Chemical Potential ◽  
Sign Problem

scholarly journals Lattice QCD at Finite Temperature and Density

2007 ◽  
Vol 22 (07n10) ◽  
pp. 457-471 ◽  
Author(s):  
M. P. LOMBARDO
Keyword(s):  
Lattice Qcd ◽  
Finite Temperature ◽  
Taylor Expansion ◽  
Critical Line ◽  
Chemical Potential ◽  
Normal Phase ◽  
Theoretical Physics ◽  
General Introduction ◽  
Sign Problem ◽  
The Subject

A general introduction into the subject aimed at a general theoretical physics audience. We introduce the sign problem posed by finite density lattice QCD, and we discuss the main methods proposed to circumvent it, with emphasis on the imaginary chemical potential approach. The interrelation between Taylor expansion and analytic continuation from imaginary chemical potential is discussed in detail. The main applications to the calculation of the critical line, and to the thermodynamics of the hot and normal phase are reviewed.

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

2021 ◽  
Author(s):  
◽  
Jonas Benedict Scheunert
Keyword(s):  
Lattice Qcd ◽  
Series Expansion ◽  
Chemical Potential ◽  
Finite Lattice ◽  
Polyakov Loop ◽  
Cluster Method ◽  
Effective Theory ◽  
Valuable Insight ◽  
Sign Problem ◽  
The Continuum

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.

scholarly journals Life Outside the Golden Window: Statistical Angles on the Signal-to-Noise Problem

2018 ◽  
Vol 175 ◽  
pp. 05003 ◽  
Author(s):  
Michael Wagman
Keyword(s):  
Lattice Qcd ◽  
Correlation Functions ◽  
Chemical Potential ◽  
Time Correlation ◽  
Time Interval ◽  
Signal To Noise ◽  
Complex Phase ◽  
Sign Problem ◽  
Heavy Tailed ◽  
Potential Sign

Lattice QCD simulations of multi-baryon correlation functions can predict the structure and reactions of nuclei without encountering the baryon chemical potential sign problem. However, they suffer from a signal-to-noise problem where Monte Carlo estimates of observables have quantum fluctuations that are exponentially larger than their average values. Recent lattice QCD results demonstrate that the complex phase of baryon correlations functions relates the baryon signal-to-noise problem to a sign problem and exhibits unexpected statistical behavior resembling a heavy-tailed random walk on the unit circle. Estimators based on differences of correlation function phases evaluated at different Euclidean times are discussed that avoid the usual signal-to-noise problem, instead facing a signal-to-noise problem as the time interval associated with the phase difference is increased, and allow hadronic observables to be determined from arbitrarily large-time correlation functions.

scholarly journals A study of the sign problem for lattice QCD with chemical potential

2009 ◽  
Vol 682 (2) ◽  
pp. 240-245 ◽  
Author(s):  
Julia Danzer ◽  
Christof Gattringer ◽  
Ludovit Liptak ◽  
Marina Marinkovic
Keyword(s):  
Lattice Qcd ◽  
Chemical Potential ◽  
Sign Problem

scholarly journals Improved convergence of Complex Langevin simulations

2018 ◽  
Vol 175 ◽  
pp. 07039 ◽  
Author(s):  
Felipe Attanasio ◽  
Benjamin Jäger
Keyword(s):  
Lattice Qcd ◽  
Phase Structure ◽  
Chemical Potential ◽  
New Method ◽  
Strongly Interacting ◽  
Sign Problem

The sign problem appears in lattice QCD as soon as a non-zero chemical potential is introduced. This prevents direct simulations to determine the phase structure of the strongly interacting matter. Complex Langevin methods have been successfully used for various models or approximations of QCD. However, in some scenarios it converges to incorrect results. We present developments of our new method that helps to improve the convergence by keeping the system closer to the SU(3) manifold and discuss preliminary tests and results.

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 Sign problem via imaginary chemical potential

2007 ◽  
Vol 75 (11) ◽  
Author(s):  
K. Splittorff ◽  
B. Svetitsky
Keyword(s):  
Chemical Potential ◽  
Sign Problem

scholarly journals The critical points of strongly coupled lattice QCD at nonzero chemical potential

1997 ◽  
Vol 56 (11) ◽  
pp. 7063-7072 ◽  
Author(s):  
Ian M. Barbour ◽  
Susan E. Morrison ◽  
Elyakum G. Klepfish ◽  
John B. Kogut ◽  
Maria-Paola Lombardo
Keyword(s):  
Lattice Qcd ◽  
Critical Points ◽  
Chemical Potential ◽  
Strongly Coupled
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