Yoshihiro Nishiyama

Isotropic spin-1 chains with bond alternation: analytic and numerical studies

Isotropic spin-1 chains with bond alternation are studied. Analytic (both variational and perturbative) results are presented. A phase transition is found to separate the S=1 Haldane phase and the dimer phase. The critical point is numerically determined using the Binder parameter. The universality class is predicted to be given by the level-1 SU(2) Wess-Zumin-Witten model, and this prediction is supported by the present exact diagonalization study. The dimer phase is found to be connected to the S=2 Haldane phase in a special limit. The change of the excitation spectra and the string order parameter with bond alternation is discussed.

Real-space renormalization-group analysis of the S=2 antiferromagnetic Heisenberg chain

The S=2 antiferromagnetic Heisenberg open chain is analyzed with the real-space numerical renormalization-group method improved by White. The low-ly ing spectrum and the one-point function are evaluated to show the degeneracy and the boundary effect on the ground state. Generalized string correlation funct ions were calculated for θ=π and θ=π 2. The θ=π 2 string correlation is found to indicate the long-range hidden order of the ground state. These results are quite consistent with the S=2 VBS argument.

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 Novotnys 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 Novotnys 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).

Bound-state energy of the three-dimensional Ising model in the broken-symmetry phase: suppressed finite-size corrections.

The low-lying spectrum of the three-dimensional Ising model is investigated numerically; we made use of an equivalence between the excitation gap and the reciprocal correlation length. In the broken-symmetry phase, the magnetic excitations are attractive, forming a bound state with an excitation gap m_{2} (<2m_{1}) ( m_{1} : elementary excitation gap). It is expected that the ratio m_{2}/m_{1} is a universal constant in the vicinity of the critical point. In order to estimate m_{2}/m_{1} , we perform a numerical diagonalization for finite clusters with N < or = 15 spins. In order to reduce the finite-size errors, we incorporated the extended (next-nearest-neighbor and four-spin) interactions. As a result, we estimate the mass-gap ratio as m_{2}/m_{1}=1.84(3) .

Third neighbor correlators of spin 1/2 Heisenberg antiferromagnet

We exactly evaluate the third-neighbor correlator S(z)(j)S(z)(j+3) and all the possible nonzero correlators S(alpha)(j)S(beta)(j+1)S(gamma;)(j+2)S(delta)(j+3) of the one-dimensional spin-1/2 Heisenberg XXX antiferromagnet in the ground state without magnetic field. All the correlators are expressed in terms of certain combinations of logarithm ln 2, the Riemann zeta function zeta(3), zeta(5) with rational coefficients. The results accurately coincide with the numerical ones obtained by the density-matrix renormalization group method and the numerical diagonalization.

Multicriticality of the (2+1) -dimensional gonihedric model: A realization of the (d,m) = (3,2) Lifshitz point

Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the (2+1) -dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space (perpendicular) and imaginary-time (||) sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with N< or =28 spins, we obtained the correlation-length critical indices (nu{perpendicular},nu{||})=[0.45(10),1.04(27)] , and the crossover exponent phi=0.7(2) . Our results are comparable to (nu{perpendicular},nu{||})=(0.482,1.230) , and phi=0.688 obtained by Diehl and Shpot for the (d,m)=(3,2) Lifshitz point with the epsilon-expansion method up to O(epsilon{2}) .

Numerical-Diagonalization Analyses of an Effective Hamiltonian for the Haldane System.

Numerical-diagonalization analyses of an effective Hamiltonian for the Haldane system are given; the phase diadram of this Hamiltonian was previously studied only by means of the Hatree-Fock approximation. Phase transitions of the transverse-Ising-model type are found, and the phase diagram in the λ- D plane is depicted. The dependence of the phase boundary on the next-nearest-neighbor competing interaction is also studied in this effective-Hamiltonian formalism. A physical point of view is obtained by inspecting the low-lying excitation spectra of the effective Hamiltonian, and the correspondence to the original Haldane system is discussed.

Finite-size scaling of the d=5 Ising model embedded in a cylindrical geometry: the influence of hyperscaling violation.

Finite-size scaling (FSS) of the five-dimensional (d=5) Ising model is investigated numerically. Because of the hyperscaling violation in d>4 , FSS of the d=5 Ising model no longer obeys the conventional scaling relation. Rather, it is expected that the FSS behavior depends on the geometry of the embedding space (boundary condition). In this paper, we consider a cylindrical geometry and explore its influence on the correlation length xi=L;{Omega}f(L;{y_{t};{*}},HL;{y_{h};{*}}) with system size L , reduced temperature , and magnetic field H ; the indices y_{t,h};{*} and Omega characterize FSS. For that purpose, we employed the transfer-matrix method with Novotnys technique, which enables us to treat an arbitrary (integral) number of spins, N=8,10,...,28 ; note that, conventionally, N is restricted in N(=L;{d-1})=16,81,256,... . As a result, we estimate the scaling indices as Omega=1.40(15) , y_{t};{*}=2.8(2) , and y_{h};{*}=4.3(1) . Additionally, postulating Omega=43 , we arrive at y_{t};{*}=2.67(10) and y_{h};{*}=4.0(2) . These indices differ from the naively expected ones Omega=1 , y_{t};{*}=2 and y_{h};{*}=3 . Rather, our data support the generic formulas Omega=(d-1)3 , y_{t};{*}=2(d-1)3 , and y_{h};{*}=d-1 , advocated for a cylindrical geometry in d4 .

Eliminated corrections to scaling around a renormalization-group fixed point: transfer-matrix simulation of an extended d=3 Ising model.

Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of scale invariance, we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as nu=0.6245(28) and y(h)=2.4709(73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.

New order parameter and numerical techniques for the ground-state Mott transition in infinite dimensions

The ground-state Mott transition of the Hubbard model on the Bethe lattice with an infinite coordination number is investigated. The system is mapped to a numerically tractable finite model according to the proposal by Si et al. The intersection points of curves of our new order parameter with a varying mapping precision are found to yield a systematic estimate of the Mott transition point. The meaning of the order parameter is investigated. The White method is applied in order to examine very large mapped systems approximately. Transition properties are discussed in detail.