A brief summary of the formulation of QCD at finite chemical potental, µ, is presented. The failure of the quenched approximation to the problem is reviewed.Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential ≈ . However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, (e µ/T ), does show signals of critical behaviour in the expected region of chemical potential.Results are presented for a simulation at finite density of the Gross-Neveu model on a 16 3 lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when µ passed through the value mπ 2.

We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point µ c in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations.We observe, however, two unphysical critical points: the onset for the number density µ o , and µ s the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point µ c , and offers a new intepretation of µ o , which confirms * UKQCD Collaboration 1 its unphysical nature. The perspectives for future lattice QCD calculations of the properties of dense baryonic matter are briefly discussed.2

The singular value decomposition technique is used to reconstruct the electronic spectral weight function for a half-filled Hubbard model with on-site repulsion U = 4t from Quantum Monte Carlo data. A two-band structure for the single-particle excitation spectrum is found to persist as the lattice size exceeds the spin-spin correlation length. The observed bands are flat in the vicinity of the (0, π), (π, 0) points in the Brillouin zone, in accordance with experimental data for high-temperature superconducting compounds.PACS numbers: 74.20.Mn, 74.25.Dw The study of the normal properties of the hightemperature superconducting compounds and the attempts to construct a microscopic theory of superconductivity in these materials has been in large part dedicated to the investigation of the Fermi surface structure and its dependence on the strong electronic correlations and antiferromagnetic order. An essential part of these numerical results was the extraction of the spectral weight function (SWF) for singleparticle excitations from the Quantum Monte Carlo data calculated for imaginary time.The SWF is obtained as a solution of the following inverse problem [7]:where G( k, τ ) is the Matsubara Green's function for lattice momentum k and imaginary-time separation τ , obtained in the finite-temperature Monte Carlo simulations at temperature 1/β, and A( k, ω) is the corresponding SWF. This inverse problem admits an infinite class of solutions for A( k, ω) which will satisfy Eq.(1) within small perturbations of the l.h.s., originating from the statistical noise on the simulation data. In recent works the oneelectron SWF for the single-band 2D Hubbard model was obtained from Monte Carlo data using a maximum entropy approach [8], [9], [13]. The finite-size effects evident in the data itself, as well as in the reconstruction of the SWF, led the authors of Ref.[8] to conclude that the pseudogap in the single-particle spectrum observed in small clusters (up to 82 ) is a lattice-size artifact which disappears as the size of the simulated system increases. They suggested therefore that for on-site repulsion weaker than the Hubbard bandwidth (8t) the antiferromagnetic correlation length would be comparable to the size of a sufficiently small lattice and would effectively create longrange antiferromagnetic order. Based on this conclusion the U = 4t coupling (where U is the on-site Coulomb repulsion and t is the nearest-neighbour hopping parameter) was regarded as belonging to the weak-coupling regime, where the band structure is essentially similar to that of noninteracting electrons for all temperatures above zero, in accordance with the Mermin-Wagner theorem. Following this argument, a gap originating from spin-density waves (SDW) will be both temperature and finite-size sensitive. The low-temperature simulations, as presented in [10] for β = 12 show indeed a stable gap even for relatively large lattice size. Such temperature dependence of the gap would be expected to correspond to a strong temperature dependence of the spin-...

A conserving T-matrix approximation is applied to the two-dimensional attractive Hubbard model in the low-density regime. A set of self-consistent equations is solved in the real-frequency domain to avoid the analytic continuation procedure. By tuning the chemical potential the particle density was varied in the limits 0.01 < n < 0.18. For the value of the attractive potential U=8t the binding energy of pairs monotonically decreases with increasing n, from its zero-density limit 2.3t and vanishes at a critical density n=0.19. A pairing-induced pseudogap in the single-particle density of states is found at low densities and temperatures.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

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