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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., 5 pages, 6 figures. +Supplemental Material

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., 6 pages, 9 figures

We performed inelastic neutron scattering measurements on a polycrystalline sample of a classical kagome antiferromagnet ${\mathrm{NaBa}}_{2}{\mathrm{Mn}}_{3}{\mathrm{F}}_{11}$ 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 ${\mathrm{NaBa}}_{2}{\mathrm{Mn}}_{3}{\mathrm{F}}_{11}$ is a good realization of the classical kagome antiferromagnet which exhibits a dispersionless mode lifted by the magnetic dipole-dipole interaction.

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

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.

We haved studied the ground state of the classical kagome antiferromagnet ${\mathrm{NaBa}}_{2}{\mathrm{Mn}}_{3}{\mathrm{F}}_{11}$. Strong magnetic Bragg peaks observed for $d$ spacings shorter than 6.0 \AA{} were indexed by the propagation vector of ${\mathbit{k}}_{0}=(0,0,0)$. Additional peaks with weak intensities in the $d$-spacing range above 8.0 \AA{} were indexed by the incommensurate vector of ${\mathbit{k}}_{1}=[0.3209(2),0.3209(2),0]$ and ${\mathbit{k}}_{2}=[0.3338(4),0.3338(4),0]$. Magnetic structure analysis unveils a ${120}^{\ensuremath{\circ}}$ structure with the tail-chase geometry having ${\mathbit{k}}_{0}$ modulated by the incommensurate vector. A classical calculation of the Heisenberg kagome antiferromagnet with antiferromagnetic second-neighbor interaction, for which the ground state a ${\mathbit{k}}_{0}\phantom{\rule{4pt}{0ex}}{120}^{\ensuremath{\circ}}$ degenerated structure, reveals that the magnetic dipole-dipole (MDD) interaction including up to the fourth neighbor terms selects the tail-chase structure. The observed modulation of the tail-chase structure is attributed to a small perturbation such as the long-range MDD interaction or the interlayer interaction.

We investigate the ground state properties of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ based on numerical calculations of the recently proposed 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 [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014)], we apply a two-dimensional density matrix renormalization group and an 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 ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ 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 ab initio value of ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ 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 ${A}_{2}{\mathrm{IrO}}_{3}$ 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 contributing to finding a route to realize the Kitaev spin liquid.

Novel magnetic phases are expected to occur in highly frustrated spin systems. Here, we study the structurally perfect kagome antiferromagnet $\mathrm{CdC}{\mathrm{u}}_{3}{(\mathrm{OH})}_{6}{({\mathrm{NO}}_{3})}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$ 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 kagome plane sets in at ${T}_{\mathrm{N}}\ensuremath{\sim}4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, well below the nearest-neighbor exchange interaction $J/{k}_{\mathrm{B}}=45\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This suggests that a unique ``$\mathbf{q}=0$'' type ${120}^{\ensuremath{\circ}}$ spin structure with ``negative'' (downward) vector chirality, which breaks the underlying threefold rotational symmetry of the kagome 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.

Transport and specific heat measurements on hydrothermally grown single crystals reveal the formation of a heavy-mass Fermi liquid in the LiV2O4 spinel, below a coherence temperature of T* = 20-30 K. A few observations which illustrate the uniqueness of this spinel are discussed in connection with the origin of the heavy mass, such as the anomalous absence of resistivity saturation above T* and the close proximity to a spin glass phase where the influence of the magnetic frustration is evident.

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($N$) N\'eel 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 $y \equiv 1/\nu$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field $\Psi^2$ for the SU(3) model., Comment: 5 pages, 5 figures

We have succeeded in synthesizing single crystals of the verdazyl radical $\ensuremath{\beta}$-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl. The $ab$ $initio$ molecular orbital calculation indicates the formation of an $S=1/2$ Heisenberg antiferromagnetic chain with fourfold magnetic periodicity consisting of three types of exchange interactions. We successfully explain the magnetic and thermodynamic properties based on the expected spin model by using the quantum Monte Carlo method. Furthermore, we reveal that the alternating and unique Ising ferromagnetic chains become effective in the specific field regions and observe a cooperative phenomenon caused by the magnetic order and quantum fluctuations. These results demonstrate that the verdazyl radical could form an unconventional spin model with interesting quantum behavior and provide a way to study a variety of quantum spin systems.

Motivated by the recent experiment on kagome-lattice antiferromagnets, we study the zero-field ordering behavior of the antiferromagnetic classical Heisenberg model on a uniaxially distorted kagome lattice by Monte Carlo simulations. A first-order transition, which has no counterpart in the corresponding undistorted model, takes place at a very low temperature. The origin of the transition is ascribed to a cooperative proliferation of topological excitations inherent to the model.

Ordering of the frustrated classical Heisenberg model on the triangular-lattice with an incommensurate spiral spin structure is studied under magnetic fields by means of a mean-field analysis and a Monte Carlo simulation. Several types of multiple-q states including the "skyrmion-lattice" state is observed in addition to the standard single-q state. In contrast to the Dzyaloshinskii-Moriya interaction driven system, the present model allows both skyrmions and anti-skyrmions, together with a new thermodynamic phase where skyrmion and anti-skyrmion lattices form a domain state., Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Lett

Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau et al. [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings. We apply this mean-field analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A 367, 435 (2006)]. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased and there are three phases: one egalitarian and two hierarchical states. We also highlight that the transition from the egalitarian phase to the first hierarchical phase is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.