arXiv subjects

Yoshihiro Nishiyama

Publications and source records attributed to Yoshihiro Nishiyama.

At least 19 recordsLinked to original sources

arXiv2026

Longitudinal-field fidelity susceptibility analysis of the $J_1$-$J_2$ transverse-field Ising model around $J_2/J_1 \approx 0.5$

The square-lattice $J_1$-$J_2$ transverse-field (TF) Ising model was investigated with the exact diagonalization (ED) method. In order to analyze the TF-driven phase transition, we applied the longitudinal-field fidelity susceptibility $χ^{(h)}_F$, which is readily evaluated via the ED scheme. Here, the longitudinal field couples with the absolute value of the magnetic moment $|M|$ rather than the raw $M$ so that the remedied fidelity susceptibility exhibits a peak around the critical point; note that the spontaneous magnetization does not appear for the finite-size systems. As a preliminary survey, the modified fidelity susceptibility $χ^{(h)}_F$ is applied to the analysis of criticality for $J_2=0$, where a number of preceding results are available. Thereby, properly scaling the distance from the multi-criticality, $η=0.5-J_2$, the $χ^{(h)}_F$ data were cast into the crossover-scaling formula, and the multi-critical exponent for $χ_F^{(h)}$ is estimated. The result is cross-checked by the numerically evaluated $β$-function behavior.

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arXiv2025

Two-dimensional transverse-field $XY$ model with the in-plane anisotropy and Dzyaloshinskii-Moriya interaction: Anisotropy-driven transition

The two-dimensional (2D) quantum spin-$S=1/2$ $XY$ model with the transverse-field $H$, in-plane-anisotropy $γ$, and Dzyaloshinskii-Moriya (DM) $D$ interactions was investigated by means of the exact diagonalization method, which enables us to treat the $D$-mediated complex-valued Hermitian matrix elements. According to the preceding real-space renormalization group analysis at $H=0$, the $γ$-driven phase transition occurs generically for $D\ne 0$ in contrast to the 1D $XY$ model where both $γ$- and $D$-induced phases are realized for $γ>D$ and $ γ<D$, respectively. In this paper, we evaluated the $β$ function $β(γ)$, namely, the differential of $γ$ with respect to the concerned energy scale, and from its behavior in proximity to $γ=0$, we observed an evidence of the $γ$-driven phase transition; additionally, $γ$'s scaling dimension is estimated from $β(γ)$'s slope. It was also determined how the value of the DM interaction influences the order-disorder phase boundary $H_c(γ)$ around the multi-critical point, $γ\to 0$.

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arXiv2024

$XY$-VBS phase boundary for the square-lattice $J_1$-$J_2$ $XXZ$ model with the ring exchange

The square-lattice $J_1$-$J_2$ $XXZ$ model with the ring-exchange interaction $K$ was investigated numerically. As for the hard-core-boson model with the nearest-neighbor hopping $J_1/2$, namely, the $J_1$-$K$ $XY$ model, it has been reported that the ring exchange leads to a variety of exotic phases such as the valence-bond-solid (VBS) phase. In this paper, we extend the parameter space in order to investigate the phase boundary between the $XY$ (superfluid) and VBS phases. A notable feature is that the phase boundary terminates at the fully-frustrated point, $J_2/J_1 \to 0.5^-$. As a scaling parameter for the multi-criticality, the distance from the multi-critical point $δ(\ge 0)$ is introduced. In order to detect the phase transition, we employed the high-order fidelity susceptibility $χ^{(3)}_F$, which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of $δ$, the $XY$-VBS criticality was analyzed by the probe $χ^{(3)}_F$. Thereby, with properly scaling $δ$, the $χ^{(3)}_F$ data were cast into the crossover-scaling formula to determine the multi-criticality.

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arXiv2023

Transverse-field $XY$ spin chain with the competing long-range interactions: Multi-criticality around the $XX$-symmetric point

The transverse-field $XY$ spin chain with competing antiferromagnetic long-range interactions, $J_r \propto 1/r^α$ ($r$: distance between spins), and the exponent $α$ was investigated numerically. The main concern is to clarify the character of the transverse-field-driven phase transition for the small-$α$ regime around the $XX$-symmetric point, $η=0$ ($η$: $XY$-anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility $χ_F$. Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the $XX$-symmetric point in a systematic manner. As a preliminary survey, with $η=0.5$ and $α=2$ fixed, we made the scaling analysis of $χ_F$. The scaling behavior of $χ_F$ shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled $η$, the $χ_F$ data is cast into the crossover scaling formula for the small-$α$ regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

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arXiv2023

End-point singularity of the $XY$-paramagnetic phase boundary for the $(2+1)$D $S=1$ square-lattice $J_1$-$J_2$ $XY$ model with the single-ion anisotropy

The two-dimensional quantum spin-$S=1$ square-lattice $J_1$-$J_2$ $XY$ model with the single-ion anisotropy $D$ was investigated numerically, placing an emphasis on the end-point singularity of the phase boundary separating the $XY$ and paramagnetic phases in proximity to the fully frustrated point, $J_2/J_1 \to 0.5^{-}$. We employed the exact diagonalization method to circumvent the negative sign problem of the quantum Monte Carlo method, and evaluated the fidelity susceptibility $χ_F$ as a probe to detect the phase transition. As a preliminary survey, for an intermediate value of $J_2/J_1$, the $D$-driven $XY$-paramagnetic phase transition was investigated via the probe $χ_F$. It turned out that the criticality belongs to the $3$D-$XY$ universality class. Thereby, the $χ_F$ data were cast into the crossover-scaling formula with the properly scaled distance from the multi-critical point, $0.5-J_2/J_1$. The set of multi-critical indices were obtained, and compared to those of the quantum Lifshitz criticality.

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arXiv2022

Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition

The two-dimensional ($2$D) spin-$S=1$ $XY$ model was investigated numerically as a realization of the $(2+1)$D superfluid-Mott-insulator (SF-MI) transition. The interaction parameters are extended so as to suppress corrections to finite-size scaling. Thereby, the external field of a unit flux quantum ($Φ=2π$) is applied to the 2D cluster by incorporating the phase factor $e^{iϕ_{ij}}$ ($ϕ_{ij}$: gauge angle between the $i$ and $j$ sites) into the hopping amplitudes. Taking the advantage in that the exact-diagonalization method allows us to treat such a complex-valued matrix element, we evaluated the excess energy cost $ΔE(2π)$ due to the magnetic flux $Φ=2π$ explicitly in the SF ($XY$) phase. As a result, we found that the amplitude ratio $ρ_s / ΔE(2π)$ ($ρ_s$: spin stiffness) makes sense in proximity to the critical point, exhibiting a notable plateau in the SF-phase side. The plateau height is estimated, and compared to the related studies.

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arXiv2021

Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality

The transverse-field $XY$ chain with the long-range interactions was investigated by means of the exact-diagonalization method. The algebraic decay rate $σ$ of the long-range interaction is related to the effective dimensionality $D(σ)$, which governs the criticality of the transverse-field-driven phase transition at $H=H_c$. According to the large-$N$ analysis, the phase boundary $H_c(η)$ exhibits a reentrant behavior within $2 2$.

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arXiv2021

Two-dimensional easy-plane SU$(3)$ magnet with the transverse field: Anisotropy-driven multicriticality

The two-dimensional easy-plane SU$(3)$ magnet subjected to the transverse field was investigated with the exact-diagonalization method. So far, as to the $XY$ model (namely, the easy-plane SU$(2)$ magnet), the transverse-field-driven order-disorder phase boundary has been investigated with the exact-diagonalization method, and it was claimed that the end-point singularity (multicriticality) at the $XX$-symmetric point does not accord with large-$N$-theory's prediction. Aiming to reconcile the discrepancy, we extend the internal symmetry to the easy-plane SU$(3)$ with the anisotropy parameter $η$, which interpolates the isotropic ($η=0$) and fully anisotropic ($η=1$) cases smoothly. As a preliminary survey, setting $η=1$, we analyze the order-disorder phase transition through resorting to the fidelity susceptibility $χ_F$, which exhibits a pronounced signature for the criticality. Thereby, with $η$ scaled carefully, the $χ_F$ data are cast into the crossover-scaling formula so as to determine the crossover exponent $ϕ$, which seems to reflect the extension of the internal symmetry group to SU(3).

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arXiv2020

Fidelity-susceptibility analysis of the honeycomb-lattice Ising antiferromagnet under the imaginary magnetic field

The honeycomb-lattice Ising antiferromagnet subjected to the imaginary magnetic field $H=iθT /2$ with the "topological" angle $θ$ and temperature $T$ was investigated numerically. In order to treat such a complex-valued statistical weight, we employed the transfer-matrix method. As a probe to detect the order-disorder phase transition, we resort to an extended version of the fidelity $F$, which makes sense even for such a non-hermitian transfer matrix. As a preliminary survey, for an intermediate value of $θ$, we investigated the phase transition via the fidelity susceptibility $χ_F^{(θ)}$. The fidelity susceptibility $χ_F^{(θ)}$ exhibits a notable signature for the criticality as compared to the ordinary quantifiers such as the magnetic susceptibility. Thereby, we analyze the end-point singularity of the order-disorder phase boundary at $θ=π$. We cast the $χ_F^{(θ)}$ data into the crossover-scaling formula with $δθ= π-θ$ scaled carefully. Our result for the crossover exponent $ϕ$ seems to differ from the mean-field and square-lattice values, suggesting that the lattice structure renders subtle influences as to the multi-criticality at $θ=π$.

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arXiv2020

Imaginary-field-driven phase transition for the $2$D Ising antiferromagnet: A fidelity-susceptibility approach

The square-lattice Ising antiferromagnet subjected to the imaginary magnetic field $H=i θT /2 $ with the "topological" angle $θ$ and temperature $T$ was investigated by means of the transfer-matrix method. Here, as a probe to detect the order-disorder phase transition, we adopt an extended version of the fidelity susceptibility $χ_F^{(θ)}$, which makes sense even for such a non-hermitian transfer matrix. As a preliminary survey, for an intermediate value of $θ$, we examined the finite-size-scaling behavior of $χ_F^{(θ)}$, and found a pronounced signature for the criticality; note that the magnetic susceptibility exhibits a weak (logarithmic) singularity at the Néel temperature. Thereby, we turn to the analysis of the power-law singularity of the phase boundary at $θ=π$. With $θ-π$ scaled properly, the $χ_F^{(θ)}$ data are cast into the crossover scaling formula, indicating that the phase boundary is shaped concavely. Such a feature makes a marked contrast to that of the mean-field theory.

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arXiv2019

Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field $XY$ model

The two-dimensional quantum $XY$ model with a transverse magnetic field was investigated with the exact diagonalization method. Upon turning on the magnetic field $h$ and the $XY$-plane anisotropy $η$, there appear a variety of phase boundaries, which meet at the multicritical point $(h,η)=(2,0)$. We devote ourselves to the Ising-universality branch, placing an emphasis on the multicritical behavior. As a probe to detect the underlying phase transitions, we adopt the fidelity susceptibility $χ_F$. The fidelity susceptibility does not rely on any presumptions as to the order parameter involved. We made a finite-size-scaling analysis of $χ_F$ for $η=1$ (Ising limit), where a number of preceding results are available. Thereby, similar analyses with $η$ scaled were carried out around the multicritical point. We found that the $χ_F$ data are described by the crossover scaling theory. A comparison with the preceding studies of the multicriticality is made.

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arXiv2019

Criticality of the Higgs mass for the long-range quantum $XY$ chain: Amplitude ratio between the Higgs and paramagnetic gaps

The quantum $XY$ spin chain with the interactions decaying as a power law $1/r^{1+ σ}$ of the distance between spins $r$ was investigated with the exact diagonalization method. Here, the constituent spin is set to $S=1$, which enables us to incorporate the biquadratic interactions so as to realize the order-disorder transition with the O$(2)$ symmetry maintained. Thereby, in the ordered phase, we resolved the Higgs mass $m_H$ out of the Goldstone-excitation continuum by specifying Higgs-particle's quantum numbers to adequate indices. We then turn to the analysis of the critical amplitude ratio $m_H / Δ$ ($Δ$: paramagnetic gap in the disordered phase). As the power of the algebraic decay $σ$ increases, the amplitude ratio $m_H/Δ$ gets enhanced gradually in agreement with the $ε(=4-D)$-expansion-renormalization-group result; here, we resort to the $σ\leftrightarrow D$ relation advocated recently in order to establish a relationship between the renormalization-group result and ours.

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arXiv2018

Criticality of the magnon-bound-state hierarchy for the quantum Ising chain with the long-range interactions

The quantum Ising chain with the interaction decaying as a power law $1/r^{1+σ}$ of the distance between spins $r$ was investigated numerically. A particular attention was paid to the low-energy spectrum, namely, the single-magnon and two-magnon-bound-state masses, $m_{1,2}$, respectively, in the ordered phase. It is anticipated that for each $σ$, the scaled bound-state mass $m_2/m_1$ should take a universal constant (critical amplitude ratio) in the vicinity of the critical point. In this paper, we calculated the amplitude ratio $m_2/m_1$ with the exact diagonalization method, which yields the spectral information such as $m_{1,2}$ directly. As a result, we found that the scaled mass $m_2/m_1$ exhibits a non-monotonic dependence on $σ$; that is, the bound state is stabilized by an intermediate value of $σ$. Such a feature is accordant with a recent observation based on the non-perturbative-renormalization-group method.

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arXiv2017

Hierarchy of the low-lying excitations for the $(2+1)$-dimensional $q=3$ Potts model in the ordered phase

The $(2+1)$-dimensional $q=3$ Potts model was simulated with the exact diagonalization method. In the ordered phase, the elementary excitations (magnons) are attractive, forming a series of bound states in the low-energy spectrum. We investigate the low-lying spectrum through a dynamical susceptibility, which is readily tractable with the exact diagonalization method via the continued-fraction expansion. As a result, we estimate the series of (scaled) mass gaps, $m_{2,3,4}/m_1$ ($m_1$: single-magnon mass), in proximity to the transition point.

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arXiv2016

Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase

In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, $m_2<m_3 < \dots$. Each ratio $m_{2,3,\dots}/m_1$ ($m_1$: the single-magnon mass) is expected to be a universal constant in the vicinity of the critical point. In this paper, we devote ourselves to the $(2+1)$-dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including $m_{2,3,4}$, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

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arXiv2016

Universal scaled Higgs-mass gap for the bilayer Heisenberg model in the ordered phase

The spectral properties for the bilayer quantum Heisenberg model were investigated with the numerical diagonalization method. In the ordered phase, there appears the massive Higgs excitation embedded in the continuum of the Goldstone excitations. Recently, it was claimed that the properly scaled Higgs mass is a universal constant in proximity to the critical point. Diagonalizing the finite-size cluster with $N \le 36$ spins, we calculated the dynamical scalar susceptibility $χ_s"(ω)$, which is rather insensitive to the Goldstone mode. A finite-size-scaling analysis of $χ_s "(ω)$ is made, and the universal (properly scaled) Higgs mass is estimated.

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arXiv2015

Critical behavior of the Higgs- and Goldstone-mass gaps for the two-dimensional S=1 XY model

Spectral properties for the two-dimensional quantum S=1 XY model were investigated with the exact diagonalization method. In the symmetry-broken phase, there appear the massive Higgs and massless Goldstone excitations, which correspond to the longitudinal and transverse modes of the spontaneous magnetic moment, respectively. The former excitation branch is embedded in the continuum of the latter, and little attention has been paid to the details, particularly, in proximity to the critical point. The finite-size-scaling behavior is improved by extending the interaction parameters. An analysis of the critical amplitude ratio for these mass gaps is made.

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arXiv2015

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 ν=0.88 (3).

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