Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




William Detmold


Systems of non-zero isospin chemical potential ( muI), where the chemical potential for up and down quarks is equal in magnitude but of opposite sign, do not suffer from the sign problem, and normal LQCD techniques can be successfully adapted to study such systems. From chiral perturbation theory (chiPT), in addition to the deconfined phase transition at high temperature at zero chemical potential, another phase transition from ordinary hadronic states to a Bose Einstein Condensate (BEC) state has been conjectured [1] at non-zero isospin chemical potential. Such a BEC phase is of phenomenological relevance in the interior of neutron stars.;In LQCD, one way to investigate non-zero isospin chemical potential system is from a grand canonical approach by directly working with fermion actions of targeted isospin chemical potentials. Another approach to isospin chemical potential is by explicitly constructing systems of fixed isospin density, and inferring the isospin chemical potential from its ground state energy. In Ref. [2], the first studies of nonzero isospin chemical potential system from this approach were presented, finding that the dependence of the isospin chemical potential on the isospin density agrees with predictions from Ref. [1] at low density. In this thesis, we studied systems with the quantum numbers of up to 72 pions with newly constructed algorithms, and clearly identified the conjectured phase transition from a pion gas to a BEC state at muI = 1.3 mpi at T ≈ 20 MeV for the first time.;Having numerically constructed a novel state of matter, a natural question to ask is how it can be investigated. The suppression of J/psi and Upsilon resonances [3] at non-zero temperature in heavy ion collision is an important diagnostic of the formation of a quark-gluon plasma. Such suppression effects have been experimentally observed at Super Proton Synchrotron (SPS), RHIC and LHC [3]. Heavy quarks are naturally also expected to be useful probes of phase transitions at non-zero baryon chemical potential and non-zero isospin chemical potential. In this thesis, we investigated both bottomonium and charmonium in media of non-zero isospin chemical potential.;The investigation of QCD at non-zero isospin density presented in this thesis provide a numerical window into a novel state of strongly interacting matter. This matter is difficult to create in experiment but may play an important role in dense astrophysical environments.



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