326 research outputs found
Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions
Ground state of the two-dimensional hard-core-boson system in the presence of
the quenched random chemical potential is investigated by means of the
exact-diagonalization method for the system sizes up to L=5. The criticality
and the DC conductivity at the superfluid-localization transition have been
controversial so far. We estimate, with the finite-size scaling analysis, the
correlation-length and the dynamical critical exponents as nu=2.3(0.6) and z=2,
respectively. The AC conductivity is computed with the Gagliano-Balseiro
formula, with which the resolvent (dynamical response function) is expressed in
terms of the continued-fraction form consisted of Lanczos tri-diagonal
elements. Thereby, we estimate the universal DC conductivity as
sigma_c(omega=0)=0.135(0.01) ((2e)^2/h)
Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study
Folding of the triangular lattice in a discrete three-dimensional space is
investigated numerically. Such ``discrete folding'' has come under through
theoretical investigation, since Bowick and co-worker introduced it as a
simplified model for the crumpling of the phantom polymerized membranes. So
far, it has been analyzed with the hexagon approximation of the cluster
variation method (CVM). However, the possible systematic error of the
approximation was not fully estimated; in fact, it has been known that the
transfer-matrix calculation is limited in the tractable strip widths L \le 6.
Aiming to surmount this limitation, we utilized the density-matrix
renormalization group. Thereby, we succeeded in treating strip widths up to
L=29 which admit reliable extrapolations to the thermodynamic limit. Our data
indicate an onset of a discontinuous crumpling transition with the latent heat
substantially larger than the CVM estimate. It is even larger than the latent
heat of the planar (two dimensional) folding, as first noticed by the preceding
CVM study. That is, contrary to our naive expectation, the discontinuous
character of the transition is even promoted by the enlargement of the
embedding-space dimensions. We also calculated the folding entropy, which
appears to lie within the best analytical bound obtained previously via
combinatorics arguments
Deconfined criticality for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions
The criticality between the nematic and valence-bond-solid (VBS) phases was
investigated for the two-dimensional quantum S=1-spin model with the three-spin
and biquadratic interactions by means of the numerical diagonalization method.
It is expected that the criticality belongs to a novel universality class, the
so-called deconfined criticality, accompanied with unconventional critical
indices. In this paper, we incorporate the three-spin interaction, and adjust
the (redundant) interaction parameter so as to optimize the finite-size
behavior. Treating the finite-size cluster with N \le 20 spins, we estimate the
correlation-length critical exponent as \nu=0.88 (3)
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