Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory

We analyze the zero-modes of the Dirac operator in quenched SU(3) gauge configurations at non-zero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different boundary conditions often the modes are localized at different space-time points and have different sizes. Our observations are consistent with patterns expected for Kraan - van Baal solutions of the classical Yang-Mills equations. These solutions consist of constituent monopoles and the zero-modes are localized on different constituents for different boundary conditions. Our findings indicate that the excitations of the QCD vacuum are more structured than simple instanton-like lumps.Comment: Remarks added. To appear in Phys. Rev.

Testing the self-duality of topological lumps in SU(3) lattice gauge theory

We discuss a simple formula which connects the field-strength tensor to a spectral sum over certain quadratic forms of the eigenvectors of the lattice Dirac operator. We analyze these terms for the near zero-modes and find that they give rise to contributions which are essentially either self-dual or anti self-dual. Modes with larger eigenvalues in the bulk of the spectrum are more dominated by quantum fluctuations and are less (anti) self-dual. In the high temperature phase of QCD we find considerably reduced (anti) self-duality for the modes near the edge of the spectral gap.Comment: Remarks added, to appear in Phys. Rev. Let

Electronic Structure of Atoms in Magnetic Quadrupole Traps

We investigate the electronic structure and properties of atoms exposed to a magnetic quadrupole field. The spin-spatial as well as generalized time reversal symmetries are established and shown to lead to a two-fold degeneracy of the electronic states in the presence of the field. Low-lying as well as highly excited Rydberg states are computed and analyzed for a broad regime of field gradients. The delicate interplay between the Coulomb and various magnetic interactions leads to complex patterns of the spatial spin polarization of individual excited states. Electromagnetic transitions in the quadrupole field are studied in detail thereby providing the selection rules and in particular the transition wavelengths and corresponding dipole strengths. The peculiar property that the quadrupole magnetic field induces permanent electric dipole moments of the atoms is derived and discussed.Comment: 17 pages, 13 figures, accepted for publication in PR

Locality and topology with fat link overlap actions

We study the locality and topological properties of fat link clover overlap (FCO) actions. We find that a small amount of fattening (2-4 steps of APE or 1 step of HYP) already results in greatly improved properties compared to the Wilson overlap (WO). We present a detailed study of the localisation of the FCO and its connection to the density of low modes of $A^\dagger A$. In contrast to the Wilson overlap, on quenched gauge backgrounds we do not find any dependence of the localization of the FCO on the gauge coupling. This suggests that the FCO remains local in the continuum limit. The FCO also faithfully reproduces the zero mode wave functions of typical lattice instantons, not like the Wilson overlap. After a general discussion of different lattice definitions of the topological charge we also show that the FCO together with the Boulder charge are likely to satisfy the index theorem in the continuum limit. Finally, we present a high statistics computation of the quenched topological susceptibility with the FCO action.Comment: 19 pages, LaTe

Numerical Study of the S=1S=1 Antiferrromagnetic Spin Chain with Bond Alternation

We study the $S=1$ quantum spin chain with bond alternation {\cal H}=\sum _i (1-(-1)^i\delta)\vect{S}_i\cdot \vect{S}_{i+1} by the density matrix renormalization group method recently proposed by Steven R. White (\PRL{69}{3844}{1993}). We find a massless point at $\delta _c =0.25 \pm 0.01$. We also find the edge states in the region $\delta <\delta_c$ under the open boundary condition, which disappear in the region $\delta >\delta _{c}$. At the massless point, the spin wave velocity $v_s$ is $3.66 \pm 0.10$ and the central charge $c$ is $1.0\pm 0.15$. Our results indicate that a continuous phase transition occurs at the massless point $\delta =\delta_c$ accompanying breaking of the hidden $Z_2\times Z_2$ symmetry.Comment: 9 pages and 1 PostScript figure, Revtex 3.0 (Minor corrections in TEX-file format to remove possible compilatory troubles.

Instantons and Chiral Symmetry on the Lattice

I address the question of how much of QCD in the chiral limit is reproduced by instantons. After reconstructing the instanton content of smoothed Monte Carlo lattice configurations, I compare hadron spectroscopy on this instanton ensemble to the spectroscopy on the original ``physical'' smoothed configurations using a chirally optimised clover fermion action. By studying the zero mode zone in simple instances I find that the optimised action gives a satisfactory description of it. Through the Banks-Casher formula, instantons by themselves are shown to break chiral symmetry but hadron correlators on the instanton backgrounds are strongly influenced by free quark propagation. This results in unnaturally light hadrons and a small splitting between the vector and the pseudoscalar meson channels. Superimposing a perturbative ensemble of zero momentum gauge field fluctuations (torons) on the instantons is found to be enough to eliminate the free quarks and restore the physical hadron correlators. I argue that the torons that are present only in finite volumes, are probably needed to compensate the unnaturally large finite size effects due to the lack of confinement in the instanton ensemble.Comment: 32 pages, LaTeX with 14 eps figure

Thermodynamics of quantum Heisenberg spin chains

Thermodynamic properties of the quantum Heisenberg spin chains with S = 1/2, 1, and 3/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.Comment: 9 pages, 10 figure