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We present an algorithm to compute correlation functions for systems with thequantum numbers of many identical mesons from lattice quantum chromodynamics(QCD). The algorithm is numerically stable and allows for the computation of$n$-pion correlation functions for $n \in \{ 1, \dots, N\}$ using a single $N\times N$ matrix decomposition, improving on previous algorithms. We apply thealgorithm to calculations of correlation functions with up to 6144 $\pi^+$susing two ensembles of gauge field configurations generated with quark massescorresponding to a pion mass $m_\pi = 170$ MeV and spacetime volumes of$(4.4^3\times 8.8)\ {\rm fm}^4$ and $(5.8^3\times 11.6)\ {\rm fm}^4$. We alsodiscuss statistical techniques for the analysis of such systems, in which thecorrelation functions vary over many orders of magnitude. In particular, weobserve that the many-pion correlation functions are well approximated bylog-normal distributions, allowing the extraction of the energies of thesesystems. Using these energies, the large-isospin-density, zero-baryon-densityregion of the QCD phase diagram is explored. A peak is observed in the energydensity at an isospin chemical potential $\mu_I\sim 1.5 m_\pi$, signalling thetransition into a Bose-Einstein condensed phase. The isentropic speed of soundin the medium is seen to exceed the ideal-gas (conformal) limit ($c_s^2\leq1/3$) over a wide range of chemical potential before falling towards theasymptotic expectation at $\mu_I\sim 15 m_\pi$. These, and other thermodynamicobservables, indicate that the isospin chemical potential must be large for thesystem to be well described by an ideal gas or perturbative QCD.

Lattice quantum chromodynamics at large isospin density: 6144 pions in a box