Research Highlights

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).

The quantum phase transition from the Neel order to the Valence Bond Solid (VBS) order can be realized in the 2D Heisenberg model with additional multi-spin interactions. As shown in the illustration (Figure 1), such interactions (also known as “singlet projectors”) induce valence bonds (singlets) in a crystaline pattern. When the multi-spin interaction is sufficiently strong, The candidate of the ground state of such model can be either in plaquette or columnar VBS phase. Based on quantum Monte Carlo calculation on a square lattice of relatively large size (64*64), we found the Neel–VBS transition is of second order, and this quantum phase transition complies with the Deconfined Quantum Critical Point (DQCP) theory proposed by Senthil, et. al.. Through finite size scaling analysis, we found that the transitions induced by 4-spin and 6-spin interactions are of the same universality class, as critical exponents derived are the same. This also supports the notion of DQCP. However, it is worth to mention that a very weak first order phase transition scenario can not be completely ruled out.

One salient feature of the DQCP theory is the emergence of U(1) symmetry near the critical point. On the other hand, the VBS phase is 4-fold symmetric spatially (Z4 symmetric). However it was not possible to study such crossover between U(1) and Z4 symmetries, due to the fact that strong VBS order can not be achieved in previous studies. In the Heisenberg model with 6-spin interactions, we are able to induce strong columnar VBS order and study such crossover (Shown in Figure 2). We also extend the symmetry of spins to SU(N). The order parameter of spatial Z4 symmetry (dimer order) is governed by a length scale Lambda which diverges faster than the spin correlation length.

（by Jie Lou）

Reference

1. J. Lou, A. W. Sandvik and N. Kawashima: Antferromagnetic to valence-bond-solid transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions. Phys. Rev. B 80, 180414(R) (2009).
2. A. W. Sandvik: Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions.  Phys. Rev. Lett. 98, 227202 (2007).

Two-dimensional Heisenberg dipolar lattices are investigated by Monte Carlo simulations. Simulations are performed on triangular, square, honeycomb, and kagome ́ lattices. Lattice-dependent magnetic structures and critical phenomena are observed. Although it is believed that two-dimensional Heisenberg dipolar lattices belong to the same universality class of two-dimensional XY dipolar lattices, results from the Monte Carlo simulations show considerable deviations in the critical exponent between the Heisenberg and XY models of triangular and square lattices. The Heisenberg dipolar honeycomb lattice exhibits unusual magnetic ordering in the form of arrays of vortices. Using finite-size scaling techniques, it is shown that the unusual order undergoes the Kosterlitz–Thouless transition. On the kagome ́ lattice, geometric frustration produces a peculiar ferromagnetic ordered state that is macroscopically degenerate. The degeneracy is expected to explain the missing magnetic entropy in ferromagnetic kagome ́, pyrochlore, and spinel substances.

(by Yusuke Tomita)

Reference

[1] K. Fukui and S. Todo: “Order-N cluster Monte Carlo method for spin systems with long-range interactions”, J. Comput. Phys. 228 (2009) 2629.

[2] Yusuke Tomita: “Monte Carlo Study of Two-Dimensional Heisenberg Dipolar Lattices”, J. Phys. Soc. Jpn 78 (2009) 114004.