121329015
A critical-amplitude relation for one-dimensional quantum transitions and determination of the exponent eta
A new critical-amplitude relation which holds for one-dimensional quantum ground-state transitions is presented. The relation yields an estimate of the sound velocity which appears in the conformal field theory as an a priori unknown parameter. With the use of this relation, the exponent eta can be explicitly determined from only the scaling fit of the off-critical energy gap. The relation is confirmed in the transverse Ising model, the S= 1/2 anisotropic XY model, and the three-state Potts model.
7173148
Numerical diagonalization analysis of the criticality of the (2+1)-dimensional XY model: off-diagonal Novotny's method.
The criticality of the (2+1)-dimensional XY model is investigated with the numerical diagonalization method. So far, it has been considered that the diagonalization method would not be very suitable for analyzing the criticality in large dimensions (d> or =3) ; in fact, the tractable system size with the diagonalization method is severely restricted. In this paper, we employ Novotny's method, which enables us to treat a variety of system sizes N=6,8,...,20 (N is the number of spins constituting a cluster). For that purpose, we develop an off-diagonal version of Novotny's method to adopt the off-diagonal (quantum-mechanical XY) interaction. Moreover, in order to improve the finite-size-scaling behavior, we tune the coupling-constant parameters to a scale-invariant point. As a result, we estimate the critical indices as nu=0.675(20) and gamma/nu=1.97(10).
17580195
Asymptotic behavior of the emptiness formation probability in the critical phase of XXZ spin chain
Abstract We study the emptiness formation probability (EFP) for the spin 1/2 XXZ spin chain. EFP P ( n ) detects a formation of ferromagnetic string of the length n in the ground state. It is expected that EFP decays in a Gaussian way for large strings P ( n )∼ n − γ C − n 2 . Here, we propose the explicit expressions for the rate of Gaussian decay C as well as for the exponent  γ . In order to confirm the validity of our formulas, we employed an ab initio simulation technique of the density-matrix renormalization group to simulate XXZ spin chain of sufficient length. Furthermore, we performed Monte Carlo integration of the Jimbo–Miwa multiple integral for P ( n ). Those numerical results for P ( n ) support our formulas fairly definitely.
119528854
Emptiness Formation Probability for the One-Dimensional Isotropic XY Model
We study a correlation function for the one-dimensional isotropic XY model (XX0 model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.