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Finite density lattice QCD without extrapolation: Bulk thermodynamics with physical quark masses from the canonical ensemble

Alexander Adam1, Szabolcs Borsányi1,*, Zoltán Fodor2,3,1,4,5, Jana N. Guenther1, Paolo Parotto6, Attila Pásztor4,7, Ludovica Pirelli1, and Chik Him Wong1

  • *Contact author: borsanyi@uni-wuppertal.de
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Phys. Rev. D 114, 074509 – Published 15 October, 2026

DOI: https://doi.org/10.1103/tptk-7718

Abstract

Quantum chromodynamics (QCD) at finite density is most often formulated on the lattice as a grand canonical ensemble. Since lattice QCD has a complex action problem at finite baryo-chemical potential (μB), its results at finite density are indirect: e.g. in the form of a set of expansion coefficients. In contrast, the canonical formulation offers direct results for integer-valued net-baryon number. In this work we present for the first time results in the canonical formulation with physical quark masses. To this end we use a high statistics finite-volume lattice (163×8) dataset that we generated at μB=0 with our 4HEX staggered action. We extend the canonical ensemble to noninteger net-baryon number and connect the results back to the grand canonical ensemble. Unlike reweighing to real μB, this method can also be used with rooted staggered quarks. For densities where the sign problem can be overcome by brute force computing power, this scheme provides lattice QCD results (e.g., for pressure, baryon density) directly, without relying on any extrapolation in the baryo-chemical potential. In this work we chart the phase diagram by studying bulk thermodynamic observables, which we show to be feasible up to μB≈500  MeV.

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Phys. Rev. D 114, 074509– Published 15 October, 2026
  • Received 29 April 2026
  • Accepted 11 August 2026
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