nLab sign problem in lattice QCD

Idea

In the context of nuclear physics, by the sign problem in lattice quantum chromodynamics is is meant the issue that

• for computational effectivity the partition function needs to be written as a (discretized) path integral of the exponentiated Euclidean action functional against a probability density (the “quark matrix”),

but

• in many situations, notably at finite chemical potential, the would-be probability measure turns out not to be positive definite, and in fact typically turns out to be complex,

• which means that various numerical evaluation methods fail.

The sign problem is one of the reasons that lattice QCD fails to be a fully satisfactory construction of non-perturbative QCD even for practical purposes. For instance, much of the phase diagram of QCD remains unknown (e.g. de Forcrand 13 CQF21), since the sign problem prevents lattice QCD computations at “almost all points” in phase space (Hsu-Reeb 08).

References

Exposition:

• Philippe de Forcrand, The sign problem in Lattice QCD, ETH 2013 (pdf)

Detailed review:

• Keitaro Nagata, Finite-density lattice QCD and sign problem: current status and open problems (arXiv:2108.12423)

Original articles:

• E. Y. Loh, Jr., J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar, Sign problem in the numerical simulation of many-electron systems Phys. Rev. B 41 9301 (1990) (doi:10.1103/PhysRevB.41.9301)

• Stephen D.H. Hsu, David Reeb, On the sign problem in dense QCD, Int. J. Mod. Phys. A 25, pp. 53-67 (2010) (arXiv:0808.2987)

• V. A. Goy, V. Bornyakov, D. Boyda, A. Molochkov, A. Nakamura, A. Nikolaev, V. Zakharov, Sign problem in finite density lattice QCD, Prog Theor Exp Phys (2017) 2017 (3): 031D01 (arXiv:1611.08093)

See also:

• Wikipedia, Numerical sign problem

• Xu Zhang, Gaopei Pan, Xiao Yan Xu, Zi Yang Meng, Sign Problem Finds Its Bounds (arXiv:2112.06139)

Proposal using quantum computation:

• Zohreh Davoudi, Niklas Mueller, Connor Powers, Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States [arXiv:2208.13112]