Angle-resolved photoemission measurement with synchrotron radiation has been performed on single-crystal ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$. Two dispersive bands intersecting the Fermi level midway between the Γ point and the Brillouin-zone boundary were observed. The other bands with higher binding energy are almost dispersionless in contrast with the band-structure calculation. The present experimental result indicates the existence of a Fermi surface and Fermi-liquid states in the high-$T_c$ superconductor as well as band renormalization due to the strong electron correlation.

We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff’s idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) $\mathrm{XY}$ and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, $\xi \propto \exp (c/\sqrt{{T/T}_{\mathrm{KT}}-1}),$ we determine the KT transition temperature and the decay exponent $\eta$ as $T_{\mathrm{KT}}=0.8933\mathrm{}\left(6\right)\mathrm{}$ and $\eta =0.243\mathrm{}\left(4\right)\mathrm{}$ for the 2D $\mathrm{XY}$ model. We investigate two transitions of the KT type for the 2D q-state clock models with $q=6,8,12\mathrm{}$ and confirm the prediction of $\eta {=4/q}^2$ at $T_1,$ the low-temperature critical point between the ordered and $\mathrm{XY}$-like phases, systematically.

We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear system size L=65536, we investigate the Kosterlitz-Thouless (KT) transition. Using the generalized version of the probability-changing cluster algorithm based on the helicity modulus, we locate the KT transition temperature in a self-adapted way. The obtained inverse KT temperature \beta_{KT} is 1.11996(6). We estimate the exponent to specify the multiplicative logarithmic correction, -2r, and precisely reproduce the theoretical prediction -2r=1/8