A Linux PC cluster for lattice QCD with exact chiral symmetry

A computational system for lattice QCD with exact chiral symmetry is described. The platform is a home-made Linux PC cluster, built with off-the-shelf components. At present this system constitutes of 64 nodes, with each node consisting of one Pentium 4 processor (1.6/2.0/2.5 GHz), one Gbyte of PC800/PC1066 RDRAM, one 40/80/120 Gbyte hard disk, and a network card. The computationally intensive parts of our program are written in SSE2 codes. The speed of this system is estimated to be 70 Gflops, and its price/performance is better than $1.0/Mflops for 64-bit (double precision) computations in quenched QCD. We discuss how to optimize its hardware and software for computing quark propagators via the overlap Dirac operator.Comment: 24 pages, LaTeX, 2 eps figures, v2:a note and references added, the version published in Int. J. Mod. Phys.

From insulator to quantum Hall liquid at low magnetic fields

We have performed low-temperature transport measurements on a GaAs two-dimensional electron system at low magnetic fields. Multiple temperature-independent points and accompanying oscillations are observed in the longitudinal resistivity between the low-field insulator and the quantum Hall (QH) liquid. Our results support the existence of an intermediate regime, where the amplitudes of magneto-oscillations can be well described by conventional Shubnikov-de Haas theory, between the low-field insulator and QH liquid.Comment: Magneto-oscillations governed by Shubnikov-de Haas theory are observed between the low-field insulator and quantum Hall liqui

A computational system for lattice QCD with overlap Dirac quarks

We outline the essential features of a Linux PC cluster which is now being developed at National Taiwan University, and discuss how to optimize its hardware and software for lattice QCD with overlap Dirac quarks. At present, the cluster constitutes of 30 nodes, with each node consisting of one Pentium 4 processor (1.6/2.0 GHz), one Gbyte of PC800 RDRAM, one 40/80 Gbyte hard disk, and a network card. The speed of this system is estimated to be 30 Gflops, and its price/performance ratio is better than $1.0/Mflops for 64-bit (double precision) computations in quenched lattice QCD with overlap Dirac quarks.Comment: 3 pages, Lattice 2002(machine

A note on Zolotarev optimal rational approximation for the overlap Dirac operator

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w (H_w^2)^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to $(H_w^2)^{-1/2}$, one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.Comment: 23 pages, 5 eps figures, v2:minor clarifications, and references added, to appear in Phys. Rev.

Beauty mesons in lattice QCD with exact chiral symmetry

We present the first study of treating b, c, and s quarks as Dirac fermions in lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at beta = 7.2 on the 32^3 x 60 lattice, we compute point-to-point quark propagators for 33 quark masses in the range 0.01 < m_q a < 0.85, and measure the time-correlation function of (pseudo-)scalar, (pseudo-)vector, and tensor mesons, for symmetric and asymmetric quark masses respectively. The lowest-lying mass spectra of mesons with quark contents b_bbar, c_bbar, s_bbar, and c_cbar are determined, together with the pseudoscalar decay constants. Our results are sumarized in Tables 1-5. Furthermore, we also determine the b and c quark masses in the MS_bar scheme, m_b = 4.65(5) GeV, and m_c = 1.16(4) GeV.Comment: 12 page