Lattice QCD at nonzero isospin chemical potential

Quantum chromodynamics (QCD) at nonzero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the factorially large numbers of Wick contractions required in multihadron systems. We then use these methods to study systems with the quantum numbers of up to 72 pi(+)'s on three ensembles of gauge configurations with spatial extents L similar to 2.0, 2.5 and 3.0 fm, and light quark masses corresponding to a pion mass of 390 MeV. The ground state energies of these systems are extracted and the volume dependence of these energies is utilized to determine the two- and three-body interactions among pi(+)'s. The systems studied correspond to isospin densities of up to rho(I) similar to 9 fm(-3) and probe isospin chemical potentials, mu(I), in the range m(pi) less than or similar to mu(1) less than or similar to 4.5m(pi), allowing us to investigate aspects of the QCD phase diagram at low temperature and for varying isospin chemical potential. By studying the energy density of the system, we provide numerical evidence for the conjectured transition of the system to a Bose-Einstein condensed phase at mu(1) greater than or similar to m(pi).