Improving the sign problem in QCD at finite density

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.

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Improving the sign problem in QCD at finite density

Nuclear Physics B - Proceedings Supplements ◽

10.1016/s0920-5632(00)91677-3 ◽

2000 ◽

Vol 83-84 ◽

pp. 372-374 ◽

Cited By ~ 1

Author(s):

Ph. de Forcrand ◽

V. Laliena

Keyword(s):

Finite Density ◽

Sign Problem

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Sign problem in finite density lattice QCD

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptx018 ◽

2017 ◽

Vol 2017 (3) ◽

Cited By ~ 5

Author(s):

V. A. Goy ◽

V. Bornyakov ◽

D. Boyda ◽

A. Molochkov ◽

A. Nakamura ◽

...

Keyword(s):

Lattice Qcd ◽

Finite Density ◽

Sign Problem

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Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

EPJ Web of Conferences ◽

10.1051/epjconf/201817507017 ◽

2018 ◽

Vol 175 ◽

pp. 07017 ◽

Cited By ~ 3

Author(s):

Keitro Nagata ◽

Jun Nishimura ◽

Shinji Shimasaki

Keyword(s):

Low Temperature ◽

Deformation Parameter ◽

Original System ◽

Baryon Number ◽

Finite Density ◽

Clear Sign ◽

Sign Problem ◽

Singular Drift ◽

Langevin Simulation ◽

Severe Sign

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and intro-duce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a 43 × 8 lattice and show that our method works well even in the region where the reweighing method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.

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Accurate simulation of the finite density lattice Thirring model

EPJ Web of Conferences ◽

10.1051/epjconf/201817507011 ◽

2018 ◽

Vol 175 ◽

pp. 07011

Author(s):

Jarno Rantaharju

Keyword(s):

Boundary Conditions ◽

World Line ◽

Thirring Model ◽

Open Boundary ◽

Test Case ◽

Open Boundary Conditions ◽

Massless Limit ◽

Finite Density ◽

Sign Problem ◽

Sign Problems

We present a study of the finite density lattice Thirring model in 1+1 dimensions using the world-line/fermion-bag algorithm. The model has features similar to QCD and provides a test case for exploring the accuracy of various methods of solving sign problems. In the massless limit and with open boundary conditions we show that the sign problem is an artifact of the auxiliary field approach and is completely eliminated in the fermion bag approach. With periodic boundary conditions the sign problem is mild in the fermion bag method. We present accurate results for various quantities in the model that can be used as a benchmark for comparison with other methods of solving sign problems.

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Tensor renormalization group approach to four-dimensional complex ϕ4 theory at finite density

Journal of High Energy Physics ◽

10.1007/jhep09(2020)177 ◽

2020 ◽

Vol 2020 (9) ◽

Author(s):

Shinichiro Akiyama ◽

Daisuke Kadoh ◽

Yoshinobu Kuramashi ◽

Takumi Yamashita ◽

Yusuke Yoshimura

Keyword(s):

Field Theory ◽

Renormalization Group ◽

Large Volume ◽

Numerical Algorithms ◽

Two Dimensions ◽

Test Bed ◽

Finite Density ◽

Sign Problem ◽

Tensor Network ◽

Volume Limit

Abstract Tensor network is an attractive approach to the field theory with negative sign problem. The complex ϕ4 theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm with a parallel computation. We find a clear signal of the Silver Blaze phenomenon on a large volume of V = 10244, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.

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On a modification method of Lefschetz thimbles

EPJ Web of Conferences ◽

10.1051/epjconf/201817511016 ◽

2018 ◽

Vol 175 ◽

pp. 11016

Author(s):

Shoichiro Tsutsui ◽

Takahiro M. Doi

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Partition Function ◽

Imaginary Part ◽

Finite Density ◽

Sign Problem ◽

Modification Method

The QCD at finite density is not well understood yet, where standard Monte Carlo simulation suffers from the sign problem. In order to overcome the sign problem, the method of Lefschetz thimble has been explored. Basically, the original sign problem can be less severe in a complexified theory due to the constancy of the imaginary part of an action on each thimble. However, global phase factors assigned on each thimble still remain. Their interference is not negligible in a situation where a large number of thimbles contribute to the partition function, and this could also lead to a sign problem. In this study, we propose a method to resolve this problem by modifying the structure of Lefschetz thimbles such that only a single thimble is relevant to the partition function. It can be shown that observables measured in the original and modified theories are connected by a simple identity. We exemplify that our method works well in a toy model.

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