arXiv subjects

Yoshihiro Nishiyama

Publications and source records attributed to Yoshihiro Nishiyama.

At least 37 records · Page 2Linked to original sources

arXiv2014

Universal critical behavior of the two-magnon-bound-state mass gap for the (2+1)-dimensional Ising model

The two-magnon-bound-state mass gap m_2 for the two-dimensional quantum Ising model was investigated by means of the numerical diagonalization method; the low-lying spectrum is directly accessible via the numerical diagonalization method. It has been claimed that the ratio m_2/m_1 (m_1: one-magnon mass gap) is a universal constant in the vicinity of the critical point. Aiming to suppress corrections to scaling (lattice artifact), we consider the spin-S=1 Ising model with finely-adjusted extended interactions. The simulation result for the finite-size cluster with N \le 20 spins indicates the mass-gap ratio m_2/m_1=1.84(1).

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arXiv2013

Criticalities of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum Ising model

The inner product between the ground-state eigenvectors with proximate interaction parameters, namely, the fidelity, plays a significant role in the quantum dynamics. In this paper, the critical behaviors of the transverse- and longitudinal-field fidelity susceptibilities for the d=2 quantum (transverse-field) Ising model are investigated by means of the numerical diagonalization method; the former susceptibility has been investigated rather extensively. The critical exponents for these fidelity susceptibilities are estimated as α^{(t)}_F=0.752(24) and α^{(h)}_F=1.81(13), respectively. These indices are independent, and suffice for obtaining conventional critical indices such as ν=0.624(12) and γ=1.19(13).

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arXiv2013

Critical behavior of the fidelity susceptibility for the d=2 transverse-field Ising model

The overlap (inner product) between the ground-state eigenvectors with proximate interaction parameters, the so-called fidelity, plays a significant role in the quantum-information theory. In this paper, the critical behavior of the fidelity susceptibility is investigated for the two-dimensional tranverse-field (quantum) Ising model by means of the numerical diagonalization method. In order to treat a variety of system sizes N=12,14,...,32, we adopt the screw-boundary condition. Finite-size artifacts (scaling corrections) of the fidelity susceptibility appear to be suppressed, as compared to those of the Binder parameter. As a result, we estimate the fidelity-susceptibility critical exponent as α_F =0.715(20).

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arXiv2012

Deconfined-critical behavior of the VBS- and nematic-order parameters for the spatially anisotropic S=1-spin model

The phase transition between the valence-bond-solid (VBS) and nematic phases, the so-called deconfined criticality, was investigated for the quantum S=1-spin model on the spatially anisotropic triangular lattice with the biquadratic interaction by means of the numerical diagonalization method. We calculated both VBS- and nematic-order parameters, aiming to clarify the nature of this transition from complementary viewpoints. Simulating the clusters with N \le 20 spins, we estimate the correlation-length critical exponent as ν=0.95(14). We also calculated Fisher's exponent (anomalous dimension) for each order parameter.

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arXiv2012

Neel-VBS phase boundary of the extended J_1-J_2 model with biquadratic interaction

The J_1-J_2 model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical-diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking the advantage of the extended parameter space, we survey the phase boundary separating the N'eel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with N \le 36 spins, we observe a signature of continuous phase transition. Our tentative estimate for the correlation-length critical exponent is ν=1.1(3). In order to elucidate a non-local character of criticality, we evaluated the Roomany-Wyld βfunction around the critical point.

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arXiv2011

d=2 transverse-field Ising model under the screw-boundary condition: An optimization of the screw pitch

A length-N spin chain with the \sqrt{N}(=v)-th neighbor interaction is identical to a two-dimensional (d=2) model under the screw-boundary (SB) condition. The SB condition provides a flexible scheme to construct a d\ge2 cluster from an arbitrary number of spins; the numerical diagonalization combined with the SB condition admits a potential applicability to a class of systems intractable with the quantum Monte Carlo method due to the negative-sign problem. However, the simulation results suffer from characteristic finite-size corrections inherent in SB. In order to suppress these corrections, we adjust the screw pitch v(N) so as to minimize the excitation gap for each N. This idea is adapted to the transverse-field Ising model on the triangular lattice with N\le32 spins. As a demonstration, the correlation-length critical exponent $ν$ is analyzed in some detail.

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arXiv2011

Deconfined criticality for the S=1 spin model on the spatially anisotropic triangular lattice

The quantum S=1 spin model on the spatially anisotropic triangular lattice is investigated numerically. The nematic and valence-bond-solid (VBS) phases are realized by adjusting the spatial anisotropy and the biquadratic interaction. The phase transition between the nematic and VBS phases is expected to be a continuous one with unconventional critical indices (deconfined criticality). The geometrical character (spatial anisotropy) is taken into account by imposing the screw-boundary condition (Novotny's method). Diagonalizing the finite-size cluster with N \le 20 spins, we observe a clear indication of continuous phase transition. The correlation-length critical exponent is estimated as ν=0.92(10).

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arXiv2010

Crumpling transition of the discrete planar folding in the negative-bending-rigidity regime

The folding of the triangular lattice embedded in two dimensions (discrete planar folding) is investigated numerically. As the bending rigidity K varies, the planar folding exhibits a series of crumpling transitions at K \approx -0.3 and K \approx 0.1. By means of the transfer-matrix method for the system sizes L \le 14, we analyze the singularity of the transition at K \approx -0.3. As a result, we estimate the transition point and the latent heat as K=-0.270(2) and Q=0.043(10), respectively. This result suggests that the singularity belongs to a weak-first-order transition.

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arXiv2010

Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively.

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arXiv2010

Criticality of the (2+1)-dimensional S=1 transverse-field Ising model with extended interactions: Suppression of corrections to scaling

The criticality of the (2+1)-dimensional S=1 transverse-field Ising model is investigated with the numerical diagonalization method. The scaling behavior is improved by tuning the coupling-constant parameters; the S=1 spin model allows us to incorporate a variety of interactions such as the single-ion anisotropy and the biquadratic interactions. Simulating the clusters with N=6,8,...,20 spins, we estimate the critical indices as 1/ν=1.586(6) and η=0.034(4).

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arXiv2009

Deconfinement criticality for the spatially anisotropic triangular antiferromagnet with the ring exchange

The spatially anisotropic triangular antiferromagnet is investigated with the numerical diagonalization method. As the anisotropy varies, the model changes into a variety of systems such as the one-dimensional, triangular, and square-lattice antiferromagnets. Taking into account such a geometrical character, we impose the screw-boundary condition, which interpolates smoothly the one- and two-dimensional lattice structures. Diagonalizing the finite clusters with N=16,20,...,32 spins, we observe an intermediate phase between the VBS and Neel phases. Suppressing the intermediate phase by applying the ring exchange, we realize a direct VBS-Neel transition. The simulation data indicate that the transition is a continuous one with the correlation-length critical exponent ν=0.80(15). These features are in agreement with the deconfinement-criticality scenario advocated by Senthil and coworkers in the context of the high-temperature superconductivity.

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arXiv2008

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 \ge 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: 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 ν=0.675(20) and γ/ν=1.97(10).

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arXiv2008

Bound-state energy of the d=3 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 the numerical diagonalization for finite clusters with N \le 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).

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arXiv2007

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 the 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 (\perp) and imaginary-time (\parallel) 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\le 28 spins, we obtained the correlation-length critical indices (ν_\perp,ν_\parallel)=(0.45(10),1.04(27)), and the crossover exponent ϕ=0.7(2). Our results are comparable to (ν_{\perp},ν_{\parallel})=(0.482,1.230), and ϕ=0.688 obtained by Diehl and Shpot for the (d,m)=(3,2) Lifshitz point with the ε-expansion method up to O(ε^2).

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arXiv2006

Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the 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 the cylindrical geometry, and explore its influence on the correlation length ξ=L^Ωf(εL^{y^*_t}, H L^{y^*_h}) with system size L, reduced temperature ε, and magnetic field H; the indices, y^*_{t,h}, and Ω, characterize FSS. For that purpose, we employed the transfer-matrix method with Novotny's 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 Ω=1.40(15), y^*_t=2.8(2), and y^*_h=4.3(1). Additionally, under postulating Ω=4/3, we arrive at y^*_t=2.67(10) and y^*_h=4.0(2). These indices differ from the naively expected ones, Ω=1, y^*_t=2 and y^*_h=3. Rather, our data support the generic formulas, Ω=(d-1)/3, y^*_t=2(d-1)/3, and y^*_h=d-1, advocated for the cylindrical geometry in d \ge 4.

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arXiv2006

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 non-trivial 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.

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arXiv2005

Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism

A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N =4,5,...,10, we obtain an estimate for the correlation-length critical exponent nu = 0.81(5).

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arXiv2005

Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime

Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such ``discrete folding'' was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium. According to their cluster-variation method (CVM) analysis, there appear various types of phases as the bending rigidity K changes in the range -infty < K < infty. In this paper, we investigate the K<0 regime, for which the CVM analysis with the single-hexagon-cluster approximation predicts two types of (crumpling) transitions of both continuous and discontinuous characters. We diagonalized the transfer matrix for the strip widths up to L=26 with the aid of the density-matrix renormalization group. Thereby, we found that discontinuous transitions occur successively at K=-0.76(1) and -0.32(1). Actually, these transitions are accompanied with distinct hysteresis effects. On the contrary, the latent-heat releases are suppressed considerably as Q=0.03(2) and 0.04(2) for respective transitions. These results indicate that the singularity of crumpling transition can turn into a weak-first-order type by appreciating the fluctuations beyond a meanfield level.

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