Searcharxiv⌕ Search

arXiv subjects

Y. Nishiyama

Publications and source records attributed to Y. Nishiyama.

5 recordsLinked to original sources
arXiv2018

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O$(3)$ symmetry) displays the inductor $σ(ω) =(iωL)^{-1}$ and capacitor $i ωC$ behaviors for the ordered and disordered phases, respectively. Both constants, $C$ and $L$, have the same scaling dimension as that of the reciprocal paramagnetic gap $Δ^{-1}$. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O$(2)$ case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap $Δ$ directly. Thereby, the set of critical amplitude ratios as to $C$, $L$ and $Δ$ are estimated with the finite-size-scaling analysis for the cluster with $N \le 34$ spins.

cond-mat.stat-mech↗
arXiv2017

Duality-mediated critical amplitude ratios for the $(2+1)$-dimensional $S=1$ $XY$ model

The phase transition for the $(2+1)$-dimensional spin-$S=1$ $XY$ model was investigated numerically. Because of the boson-vortex duality, the spin stiffness $ρ_s$ in the ordered phase and the vortex-condensate stiffness $ρ_v$ in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios $ρ_{s,v}/Δ$ ($Δ$: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with $N \le 22$ spins. The ratio $ρ_s/ρ_v$ admits a quantitative measure of deviation from selfduality.

cond-mat.stat-mech↗
arXiv2002

Asymptotic Behavior of the Emptiness Formation Probability in the Critical Phase of XXZ Spin Chain

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^{-gamma} C^{-n^2}. Here, we propose the explicit expressions for the rate of Gaussian decay C as well as for the exponent gamma. 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.

cond-mat.stat-mech↗
arXiv2002

Quantum Correlations and Number Theory

We study spin-1/2 Heisenberg XXX antiferromagnet. The spectrum of the Hamiltonian was found by Hans Bethe in 1931. We study the probability of formation of ferromagnetic string in the antiferromagnetic ground state, which we call emptiness formation probability P(n). This is the most fundamental correlation function. We prove that for the short strings it can be expressed in terms of the Riemann zeta function with odd arguments, logarithm ln 2 and rational coefficients. This adds yet another link between statistical mechanics and number theory. We have obtained an analytical formula for P(5) for the first time. We have also calculated P(n) numerically by the Density Matrix Renormalization Group. The results agree quite well with the analytical ones. Furthermore we study asymptotic behavior of P(n) at finite temperature by Quantum Monte-Carlo simulation. It also agrees with our previous analytical results.

cond-mat.stat-mech↗