Research Highlights

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.

             

(by Naoki Kawashima)

[Reference]

[1] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).

[2] Y. Yamaji, Y. Nomura, M. Kurita, R. Arita, and M. Imada, Phys. Rev. Lett. 113, 107201 (2014).

[3] Tsuyoshi Okubo, Kazuya Shinjo, Youhei Yamaji, Naoki Kawashima, Shigetoshi Sota, Takami Tohyama, and Masatoshi Imada, Phys. Rev. B 96, 054434 (2017)

Two-dimensional Ising models on the honeycomb lattice and the square lattice with striped random impurities are studied to obtain their phase diagrams. Assuming bimodal distributions of the random impurities where all the non-zero couplings have the same magnitude, exact critical values for the fraction \(p\) of ferromagnetic bonds at the zero-temperature \(T=0\) are obtained. The critical lines in the \(p-T\) plane are drawn by numerically evaluating the Lyapunov exponent of random matrix products.

 

 

Reference

[1] S. Morita and S. Suzuki: J. Stat. Phys. 162, 123 (2016).

The $\mathrm{SU}\left(N\right)$ symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) 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 either the Néel or the VBS 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.

(by Tsuyoshi Okubo)

Reference:

T. Okubo, K. Harada, J. Lou and N. Kawashima: Phys. Rev. B 92, 134404 (2015).

We propose a scaling relation for critical phenomena in which a symmetry-breaking field is dangerously irrelevant. We confirm its validity on the six-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. (Abstract of Ref. [1])

Reference

[1] T. Okubo, K. Oshikawa, H. Watanabe and N. Kawashima: Phys. Rev. B 91, 174417 (2015).

When you uncork a bottle of champagne, you will observe nuclei of bubbles and coarsening of them (Ostwald ripening). Ostwald ripening of bubbles is also observed in a power-generating turbine. While Ostwald ripening of bubbles is common and important in our life, this is highly non-trivial problem, since the interaction between bubbles is much stronger than that in other systems involving coarsening.

A mathematical framework describing coarsening processes was developed by Lifshitz and Slyozov, which was followed by Wagner. Now the theory is called LSW theory [1,2]. While the theory successfully explains the behaviors of coarsening processes for various systems, it is highly non-trivial whether the theory works for bubble systems. Especially, the mean-field treatment assumed in the theory should be verified for bubble systems, since the interactions between bubbles via the ambient liquid are much stronger than those in other systems, such as alloy, droplets, etc. Therefore, we perform molecular dynamics simulations of the cavitation process in order to study the validity of the LSW theory in homogeneous nuclei of bubbles.

In order to investigate the coarsening process of bubbles from the molecular levels, a huge number of particles are required. Recent development in computational power, however, enables us to treat hundreds of millions of particles. We perform molecular dynamics simulations involving 700 million particles on 4,000 processors on the K computer, which is the largest computer in Japan. We observe the behavior of the total number of bubbles and find a crossover from the interface-limited (Wagner limit) to the diffusion-limited process (Lifshitz-Slyozov limit) as temperature increases. In both regimes, the exponents of the time evolution are well predicted by the theory. Our findings imply that the time scales between the relaxation time of the pressure in the ambient liquid and the coarsening rates are clearly separated, and therefore, the mean-field treatment is well justified.

（by H. Watanabe）

Reference

[1] I. Lifshitz and V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961).
[2] C. Wagner, Z. Elektrochem. 65, 581 (1961).
[3] H. Watanabe, M. Suzuki, H. Inaoka, and N. Ito, J. Chem. Phys. 141 234703 (2014).

Press release by AIP publishing: How the Physics of Champagne and Soda Bubbles May Help Address the World’s Future Energy Needs

Based on the worm algorithm in the path-integral representation, we propose a general quantum Monte Carlo algorithm suitable for parallelizing on a distributed-memory computer by domain decomposition. Of particular importance is its application to large lattice systems of bosons and spins. A large number of worms are introduced and its population is controlled by a fictitious transverse field. For a benchmark, we study the size dependence of the Bose-condensation order parameter of the hard-core Bose-Hubbard model with L×L×βt=10240×10240×16, using 3200 computing cores, which shows good parallelization efficiency.

Reference

[1] N. Prokof’ev, B. Svistunov and I. Tupitsyn, Sov. Phys. JETP 87, 310 (1998) .
[2] O. F. Syljuasen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2012).
[3] A. Masaki-Kato, T. Suzuki, K. Harada, S. Todo and N. Kawashima, Phys. Rev. Lett. 112, 140603 (2014).

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.

    

(by Tsuyoshi Okubo)

Reference

[1] P. Mendels and F. Bert, J. Phys. Soc. Jpn. 79, 011001 (2010), Z. Hiroi, et al, J. Phys.:Conf. Ser. 320, 012003 (2011), Y. Okamoto, J. Phys. Soc. Jpn. 78, 033701 (2009).

[2] H. Masuda, T. Okubo, and H. Kawamura, Phys. Rev. Lett 109, 057201 (2012).

Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a commensurate filling factor \(1/2\) (a commensurate supersolid) in the soft-core Bose-Hubbard model with nearest-neighbor repulsions on a cubic lattice. In conventional cases, supersolids are realized at incommensurate filling factors by a doped-defect-condensation mechanism, where particles (holes) doped into a perfect crystal act as interstitials (vacancies) and delocalize in the crystal order. However, in the model, a supersolid state is stabilized even at the commensurate filling factor \(1/2\) without doping. By performing grand canonical simulations, we obtain a ground-state phase diagram that suggests the existence of a supersolid at a commensurate filling. To obtain direct evidence of the commensurate supersolid, we next perform simulations in canonical ensembles at a particle density \(\rho = 1/2\) and exclude the possibility of phase separation. From the obtained snapshots, we discuss its microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order. (Abstract of Ref.[2])

(by T. Ohgoe)

Reference

[1] A. F. Andreev and I. M. Lifshitz, Sov. Phys. JETP 29, 1107 (1969).
[2] T. Ohgoe, T. Suzuki, and N. Kawashima, Phys. Rev. Lett. 108, 185302 (2012).
[3] T. Ohgoe, T. Suzuki, and N. Kawashima, Phys. Rev. B 86, 054520 (2012).

We study quantum entanglement in the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model defined on two-dimensional graphs with reflection and/or inversion symmetry. The ground state of this spin model is known as the valence-bond-solid state. We investigate the properties of reduced density matrix of a subsystem which is a mirror image of the other one. Thanks to the reflection symmetry, the eigenvalues of the reduced density matrix can be obtained by numerically diagonalizing a real symmetric matrix whose elements are calculated by Monte Carlo integration. We calculate the von Neumann entropy of the reduced density matrix. The obtained results indicate that there is some deviation from the naive expectation that the von Neumann entropy per valence bond on the boundary between the subsystems is ln2. This deviation is interpreted in terms of the hidden spin chain along the boundary between the subsystems. In some cases where graphs are on ladders, the numerical results are analytically or algebraically confirmed.

(by Shu Tanaka)

Reference

[1] Hosho Katsura, Naoki Kawashima, Anatol N. Kirillov, Vladimir E. Korepin and Shu Tanaka, J. Phys. A: Math. Theor. 43 (2010) 255303.

 

Comprehensive experimental studies by magnetic, thermal and neutron measurements have clarified that Rb₄Mn(MoO₄)₃ is a model system of a quasi-2D triangular Heisenberg antiferromagnet with an easy-axis anisotropy, exhibiting successive transitions across an intermediate collinear phase. As a rare case for geometrically frustrated magnetism, quantitative agreement between experiment and theory is found for complete, anisotropic phase diagrams as well as magnetic properties.

(by Shu Tanaka)

Reference

[1]Rieko Ishii, Shu Tanaka, Keisuke Onuma, Yusuke Nambu, Masashi Tokunaga, Toshiro Sakakibara, Naoki Kawashima, Yoshiteru Maeno, Collin Broholm, Dixie P. Gautreaux, Julia Y. Chan, and Satoru Nakatsuji, Europhysics Letters 94, 17001 (2011).