arXiv subjects

Tsuyoshi Okubo

Publications and source records attributed to Tsuyoshi Okubo.

At least 37 records · Page 2Linked to original sources

arXiv2022

Optimized Implementation for Calculation and Fast-Update of Pfaffians Installed to the Open-Source Fermionic Variational Solver mVMC

In this article, we present a high performance, portable and well templated implementation for computing and fast-updating Pfaffian and inverse of an even-ranked skew-symmetric (antisymmetric) matrix. It is achieved with a skew-symmetric, blocked variant of the Parlett-Reid algorithm and a blocked update scheme based on the Woodbury matrix identity. Installation of this framework into the geminal-wavefunction-based many-variable Variational Monte Carlo (mVMC) code boosts sampling performance to up to more than $6$ times without changing Markov chain's behavior. The implementation is based on an extension of the BLAS-like instantiation software (BLIS) framework which has optimized kernel for many state-of-the-art processors including Intel Skylake-X, AMD EPYC Rome and Fujitsu A64FX.

physics.comp-ph↗

arXiv2020

Bond-weighted Tensor Renormalization Group

We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the conventional TRG and the higher-order tensor renormalization group with the same bond dimension, while its computation time is almost the same as that of TRG. Furthermore, BTRG can have non-trivial fixed-point tensors at an optimal hyperparameter. We demonstrate that the singular value spectrum obtained by BTRG is invariant under the renormalization procedure in the case of the two-dimensional Ising model at the critical point. This property indicates that BTRG performs the tensor contraction with high accuracy while keeping the scale-invariant structure of tensors.

cond-mat.stat-mech↗

arXiv2020

Zero-energy excitation in the classical kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$

We performed inelastic neutron scattering measurements on a polycrystalline sample of a classical kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$ to investigate the possibility of a dispersionless zero-energy excitation associated with rotation of spins along the chains. The observed spectra indeed exhibit such an excitation with strong intensity at low energy, as well as dispersive excitations with weak intensity at high energy. Combining the measurements with calculations from linear spin-wave theory reveals that NaBa$_{2}$Mn$_{3}$F$_{11}$ is a good realization of the classical kagome antiferromagnet which exhibits a dispersionless mode lifted by the magnetic dipole-dipole interaction.

cond-mat.str-el↗

arXiv2020

Phase Shift in Skyrmion Crystals

The skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phases among the constituent waves. Although the phase degree of freedom is relevant to not only magnetism but also transport properties, its effect has not been elucidated thus far. We here theoretically show that a phase shift can occur in the skyrmion crystals to stabilize tetra-axial vortex crystals with staggered scalar spin chirality. This leads to spontaneous breaking of the lattice symmetry, which results in nonreciprocal transport phenomena even without the relativistic spin-orbit coupling. We show that such a phase shift is driven by long-range chirality interactions or thermal fluctuations in spin-charge coupled systems.

cond-mat.str-el↗

arXiv2020

Magnetic field induced quantum phases in a tensor network study of Kitaev magnets

Recent discovery of the half quantized thermal Hall conductivity in $α$-RuCl$_3$, a candidate material for the Kitaev spin liquid, suggests the presence of a highly entangled quantum state in external magnetic fields. This field induced phase appears between the low field zig-zag magnetic order and the high field polarized state. Motivated by this experiment, we study possible field induced quantum phases in theoretical models of the Kitaev magnets, using the two dimensional tensor network approach or infinite tensor product states. We find various quantum ground states in addition to the chiral Kitaev spin liquid occupying a small area in the phase diagram. They form a band of emergent quantum phases in an intermediate window of external magnetic fields, somewhat reminiscent of the experiment. We discuss the implications of these results in view of the experiment and previous theoretical studies.

cond-mat.str-el↗

arXiv2020

Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

We provide new insights into the Abelian and non-Abelian chiral Kitaev spin liquids on the star lattice using the recently proposed loop gas (LG) and string gas (SG) states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)]. Those are compactly represented in the language of tensor network. By optimizing only one or two variational parameters, accurate ansatze are found in the whole phase diagram of the Kitaev model on the star lattice. In particular, the variational energy of the LG state becomes exact(within machine precision) at two limits in the model, and the criticality at one of those is analytically derived from the LG feature. It reveals that the Abelian CSLs are well demonstrated by the short-ranged LG while the non-Abelian CSLs are adiabatically connected to the critical LG where the macroscopic loops appear. Furthermore, by constructing the minimally entangled states and exploiting their entanglement spectrum and entropy, we identify the nature of anyons and the chiral edge modes in the non-Abelian phase with the Ising conformal field theory.

cond-mat.str-el↗

arXiv2019

Multiple-$q$ states of the $J_1$-$J_2$ classical honeycomb-lattice Heisenberg antiferromagnet under magnetic fields

Motivated by the recent theoretical study by Okubo $et \ al$ [Phys. Rev. Lett. ${\bf 108}$, 017206 (2012)] on the possible realization of the frustration-induced $ symmetric$ skyrmion-lattice state in the $J_1$-$J_2$ (or $J_1$-$J_3$) triangular-lattice Heisenberg model without the Dzyaloshinskii-Moriya interaction, we investigate the ordering of the classical $J_1$-$J_2$ honeycomb-lattice Heisenberg antiferromagnet under magnetic fields by means of a Monte Carlo simulation, a mean-field analysis and a low-temperature expansion. The model has been known to have an infinite ring-like degeneracy in the wavevector space in its ground state for $1/6<J_2/J_1<0.5$, in distinction with the triangular-lattice model. As reported by Okumura $et \ al$ [J. Phys. Soc. Jpn. ${\bf 79}$, 114705 (2010)], such a ring-like degeneracy gives rise to exotic spin liquid states in zero field, $e.g$, the "ring-liquid" state and the "pancake-liquid" state. In this paper, we study the in-field ordering properties of the model paying attention to the possible appearance of exotic multiple-$q$ states. Main focus is made on the $J_2/J_1=0.3$ case, where we observe a rich variety of multiple-$q$ states including the single-$q$, double-$q$ and triple-$q$ states. While the skyrmion-lattice triple-$q$ state observed in the triangular-lattice model is not realized, we instead observe an exotic double-$q$ state consisting of meron/antimeron lattice textures.

cond-mat.str-el↗

arXiv2019

Anisotropic Tensor Renormalization Group

We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor Renormalization Group (HOTRG) algorithm, i.e., it preserves the lattice topology after the renormalization. In comparison with HOTRG, both of the computation cost and the memory footprint of our method are drastically reduced, especially in higher dimensions, by renormalizing tensors in an anisotropic way after the singular value decomposition. We demonstrate the ability of ATRG for the square lattice and the simple cubic lattice Ising models. Although the accuracy of the present method degrades when compared with HOTRG of the same bond dimension, the accuracy with fixed computation time is improved greatly due to the drastic reduction of the computation cost.

cond-mat.stat-mech↗

arXiv2019

Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks

We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the language of tensor network(TN). Without introducing Majorana fermion, most of the features of the KSL including the symmetries, gauge structure, criticality and vortex-freeness are explained in a compact TN representation. Our construction reveals a hidden string gas structure of the KSL. With only two variational parameters to adjust, we obtain an accurate KSL ansatz with the bond dimension D = 8 in a compact form, where the energy is about 0.007% higher than the exact one. In addition, the opening of gap and non-Abelian phase driven by a magnetic field are naturally understood in our construction.

cond-mat.str-el↗

arXiv2018

Magnetic State Selected by Magnetic Dipole Interaction in Kagome Antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$

We have studied the ground state of the classical Kagome antiferromagnet NaBa$_{2}$Mn$_{3}$F$_{11}$. Strong magnetic Bragg peaks observed in the $d$-spacing shorter than 6.0 Å were indexed by the propagation vectors of $\boldsymbol{k}_{0} = (0,0,0)$. Additional peaks with weak intensities in the range of the $d$-spacing longer than 8.0 Å were indexed by the incommensurate vectors of $\boldsymbol{k}_{1}=(0.3209(2),0.3209(2),0)$ and $\boldsymbol{k}_{2}=(0.3338(4),0.3338(4),0)$. Magnetic structure analysis exhibits that the 120$^{\circ}$ structure with the {\it tail-chase} geometry having $\boldsymbol{k}_0$ is modulated by the incommensurate vectors. The classical calculation of the Kagome Heisenberg antiferromagnet having the antiferromagnetic 2nd-neighbor interaction, the ground state of which is degenerated 120$^{\circ}$ structures with $\boldsymbol{k}_0$, reveals that the magnetic dipole-dipole (MDD) interaction including up to the 4th neighbor terms selects the tail-chase structure. The observed modulation of the tail-chase structure is indicated to be due to a small perturbation such as the long-range MDD interaction or the interlayer interaction.

cond-mat.str-el↗

arXiv2017

Quantum phase transitions driven by rhombic-type single-ion anisotropy in the S=1 Haldane chain

The spin-1 Haldane chain is an example of the symmetry-protected-topological (SPT) phase in one dimension. Experimental realization of the spin chain materials usually involves both the uniaxial-type, $D(S^z)^2$, and the rhombic-type, $E[(S^x)^2-(S^y)^2]$, single-ion anisotropies. Here, we provide a precise ground-state phase diagram for spin-1 Haldane chain with these single-ion anisotropies. Using quantum numbers, we find that the $\mathbb{Z}_2$ symmetry breaking phase can be characterized by double degeneracy in the entanglement spectrum. Topological quantum phase transitions take place on particular paths in the phase diagram, from the Haldane phase to the Large-$E_x$, Large-$E_y$, or Large-$D$ phases. The topological critical points are determined by the level spectroscopy method with a newly developed parity technique in the density matrix renormalization group [Phys. Rev. B 86, 024403 (2012)], and the Haldane-Large-$D$ critical point is obtained with an unprecedentedly precision, $(D/J)_c=0.9684713(1)$. Close to this critical point, a small rhombic single-ion anisotropy $|E|/J\ll1$ can destroy the Haldane phase and bring the system into a $y$-Néel phase. We propose that the compound [Ni(HF$_2$)(3-Clpy)$_4$]BF$_4$ is a candidate system to search for the $y$-Néel phase.

cond-mat.str-el↗

arXiv2017

Weak ferromagnetic order breaking the threefold rotational symmetry of the underlying kagomé lattice in CdCu$_3$(OH)$_6$(NO$_3$)$_2\cdot$H$_2$O

Novel magnetic phases are expected to occur in highly frustrated spin systems. Here we study the structurally perfect kagomé antiferromagnet CdCu$_3$(OH)$_6$(NO$_3$)$_2\cdot$H$_2$O by magnetization, magnetic torque, and heat capacity measurements using single crystals.An antiferromagnetic order accompanied by a small spontaneous magnetization that surprisingly is confined in the kagomé plane sets in at $T_\mathrm{N}\approx$4 K, well below the nearest-neighbor exchange interaction $J / k_B$ = 45 K.This suggests that a unique $\bf q = 0$ type 120$^\circ$ spin structure with "negative" (downward) vector chirality, which breaks the underlying threefold rotational symmetry of the kagomé lattice and thus allows a spin canting within the plane, is exceptionally realized in this compound rather than a common one with "positive" (upward) vector chirality. The origin is discussed in terms of the Dzyaloshinskii-Moriya interaction.

cond-mat.str-el↗

arXiv2016

Ground state properties of $\mathrm{Na_2IrO_3}$ determined from $\textit{ab initio}$ Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

We investigate the ground state properties of $\mathrm{Na_2IrO_3}$ based on numerical calculations of the recently proposed {\it ab initio} Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study (Yamaji $\textit{et al.}$, Phys. Rev. Lett. $\textbf{113}$, 107201 (2014)), we apply two-dimensional density matrix renomalization group, and infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of $\mathrm{Na_2IrO_3}$ is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the $\textit{ab initio}$ value of $\mathrm{Na_2IrO_3}$ controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in $120$ degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a $16$-site unit-cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in $A_\mathrm{2}\mathrm{IrO_3}$ compounds for $A$ other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contribute to find a route to realize the Kitaev spin liquid.

cond-mat.str-el↗

arXiv2015

SU(N) Heisenberg model with multi-column representations

The $\mathrm{SU}(N)$ symmetric antiferromagnetic Heisenberg model with multi-column representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of Young diagram with two columns, we confirm that a valence-bond solid order appears as soon as the Néel order disappears at $N = 10$ indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for both of the Néel and the valence-bond solid ordering for $N\ge 15$. This is actually consistent with the large-$N$ theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.

cond-mat.str-el↗

arXiv2014

A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields

We propose a scaling relation for critical phenomena in which a symmetry-breaking field is dengerously irrelevant. We confirm its validity on the 6-state clock model in three and four dimensions by numerical simulation. In doing so, we point out the problem in the previously-used order parameter, and present an alternative evidence based on the mass-dependent fluctuation.

cond-mat.stat-mech↗

arXiv2014

Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems

We investigate the eigenvalue distribution of the snapshot density matrix (SDM) generated by Monte Carlo simulation for two-dimensional classical spin systems. We find that the distribution in the high-temperature limit is well explained by the random-matrix theory, while that in the low-temperature limit can be characterized by the zero-eigenvalue condensation. At the critical point, we obtain the power-law distribution with a nontrivial exponent $α\equiv(2-η)/(1-η)$ and the asymptotic form of the snapshot entropy, on the basis of the relationship of the SDM with the correlation function matrix. The aspect-ratio dependence of the SDM spectrum is also mentioned.

cond-mat.stat-mech↗

arXiv2014

Kagome-Triangular Lattice Antiferromagnet NaBa2Mn3F11

A new type of magnetically frustrated lattice is found in the layered fluoride NaBa2Mn3F11. A kagome-type array of regular triangles composed of Mn2+ ions (spin 5/2) deforms so as to generate the next-nearest-neighbor interaction J2 between three out of six spins in the hexagon of a normal kagome lattice, in addition to the nearest-neighbor interaction J1. As a function of |J2/J1|, this lattice can interconnect the kagome (J2 = 0) and the triangular (J2 = J1) lattices and thus is called the kagome-triangular (KT) lattice. Magnetic susceptibility and heat capacity measurements performed on a polycrystalline sample of NaBa2Mn3F11 show an intensive short-range antiferromagnetic correlation below 14 K probably due to the specific magnetic frustration of the KT lattice. In addition, a long-range order at 2.0 K is observed, which is significantly low compared with the antiferromagnetic Weiss temperature of 32.3 K. Theoretical considerations of Heisenberg spins in the KT lattice reveal unique non-coplanar magnetic orders in the case of ferromagnetic J1 and antiferromagnetic J2. NaBa2Mn3F11 may actually exist in this regime according to the results of our analysis based on classical Monte-Carlo simulation.

cond-mat.mtrl-sci↗

arXiv2013

Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) Néel and valence-bond solid phases is characterized for $N=2,3,$ and $4$ on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y \equiv 1/ν$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field $Ψ^2$ for the SU(3) model.

cond-mat.str-el↗