arXiv subjects

Naoki Kawashima

Publications and source records attributed to Naoki Kawashima.

At least 73 records · Page 4Linked to original sources

arXiv2017

Quantum Lattice Model Solver ${\mathcal H}Φ$

${\mathcal H}Φ$ [$aitch$-$phi$] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, ${\mathcal H}Φ$ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, ${\mathcal H}Φ$ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of ${\mathcal H}Φ$. We also show the benchmark results of ${\mathcal H}Φ$ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

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↗

arXiv2016

Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na$_2$IrO$_3$

Contrary to the original expectation, Na$_2$IrO$_3$ is not a Kitaev's quantum spin liquid (QSL) but shows a zig-zag-type antiferromagnetic order in experiments. Here we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka $et$ $al$. in Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na$_2$IrO$_3$ proposed by Yamaji $et$ $al$. in Phys. Rev. Lett. 113, 107201 (2014), by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Neel temperatures: (1) Two peaks in the temperature dependence of specific heat at $T_{\ell}$ and $T_h$ caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, prominent plateau or shoulder pinned at $(R/2)\ln 2$ in the temperature dependence of entropy, where $R$ is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio $T_{\ell}/T_h$ close to or less than 0.03. According to the proposed criteria, Na$_2$IrO$_3$ is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na$_2$IrO$_3$ on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ and other related materials are also discussed.

cond-mat.str-el↗

arXiv2015

Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices

We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical $XY$ model with a $Z_4$ symmetry-breaking field and the 3-state Potts model, respectively. In the square-lattice case, the thermal exponent, $ν$, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, $η$ and $γ/ν$, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the $Z_4$ symmetry-breaking field is always marginal. In contrast, $ν$ in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the $Z_3$ field remains relevant in the SU(3) and SU(4) cases.

cond-mat.stat-mech↗

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

Parallelized Quantum Monte Carlo Algorithm with Nonlocal Worm Updates

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 hardcore Bose-Hubbard model with $L\times L\times βt = 10240\times 10240\times 16$, using 3200 computing cores, which shows good parallelization efficiency.

cond-mat.stat-mech↗

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↗

arXiv2013

Phase Transitions with Discrete Symmetry Breaking in Antiferromagnetic Heisenberg Models on a Triangular Lattice

We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two cases in which a phase transition with discrete symmetry breaking occurs. The first is that the order parameter space is SO(3)$\times C_3$. In this case, a first-order phase transition, with threefold symmetry breaking, occurs. The second has the order parameter space SO(3)$\times Z_2$. In this case, a second-order phase transition occurs with twofold symmetry breaking. To investigate finite-temperature properties of these phase transitions from a microscopic viewpoint, we introduce a method to make the connection between continuous frustrated spin systems and the Potts model with invisible states.

cond-mat.stat-mech↗

arXiv2013

Second-order phase transition in the Heisenberg model on a triangular lattice with competing interactions

We discover an example where the dissociation of the Z2 vortices occurs at the second-order phase transition point. We investigate the nature of phase transition in a classical Heisenberg model on a distorted triangular lattice with competing interactions. The order parameter space of the model is SO(3)xZ2. The dissociation of the Z2 vortices which comes from SO(3) and a second-order phase transition with Z2 symmetry breaking occur at the same temperature. We also find that the second-order phase transition belongs to the universality class of the two-dimensional Ising model.

cond-mat.stat-mech↗

arXiv2012

Quantum phases of hard-core bosons on 2D lattices with anisotropic dipole-dipole interaction

By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the $y$ direction on the two-dimensional (2D) $xy$ plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an O(N) Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multi plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.

cond-mat.quant-gas↗

arXiv2012

Study of the Shastry Sutherland Model Using Multi-scale Entanglement Renormalization Ansatz

We performed variational calculation based on the multi-scale entanglemnt renormalization ansatz, for the antiferromagnetic Heisenberg model on a Shastry Sutherland lattice (SSL). Our results show that at coupling ratio J'/J= 0.687(3), the system undergoes a quantum phase transition from the orthogonal dimer order to the plaquette valence bond solid phase, which then transits into the antiferromagnetic order above J'/J=0.75. In the presence of an external magnetic field, our calculations show clear evidences of various magnetic plateaux in systems with different coupling ratios range from 0.5 to 0.69. Our calculations are not limited to the small coupling ratio region, and we are able to show strong evidence of the presence of several supersolid phases, including ones above 1/2 and 1/3 plateaux. Such supersolid phases, which feature the coexistence of compressible superfluidity and crystalline long range order in triplet excitations, emerge at relatively large coupling ratio (J'/J>0.5). A schematic phase diagram of the SSL model in the presence of magnetic field is provided.

cond-mat.str-el↗

arXiv2012

Ground-State Phase Diagram of the Two-Dimensional Extended Bose-Hubbard Model

We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to the previous study[P. Sengupta {\it et. al.}, Phys. Rev. Lett. {\bf 94}, 207202 (2005)], we present the ground-state phase diagrams up to large hopping parameters. As a result, in addition to the known supersolid above half-filling, we find supersolid even below and at half-filling for large hopping parameters. Furthermore, for the strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. The results are in qualitative agreement with that obtained by the Gutzwiller mean-field approximation[M. Iskin, Phys. Rev. A {\bf 83}, 051606(R) (2011) and T. Kimura, Phys. Rev. A {\bf 84}, 063630 (2011)].

cond-mat.quant-gas↗

arXiv2012

Commensurate Supersolid of Three-Dimensional Lattice Bosons

Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a {\it commensurate} filling factor 1/2 (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 above model, a supersolid state is stabilized even at the commensurate filling factor 1/2 {\it 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 $ρ=1/2$ and exclude the possibility of phase separation. From the obtained snapshots, we discuss the microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order.

cond-mat.quant-gas↗

arXiv2012

A Method to Control Order of Phase Transition: Invisible States in Discrete Spin Models

It is an important topic to investigate nature of the phase transition in wide area of science such as statistical physics, materials science, and computational science. Recently it has been reported the efficiency of quantum adiabatic evolution/quantum annealing for systems which exhibit a phase transition, and we cannot obtain a good solution in such systems. Thus, to control the nature of the phase transition has been also attracted attention in quantum information science. In this paper we review nature of the phase transition and how to control the order of the phase transition. We take the Ising model, the standard Potts model, the Blume-Capel model, the Wajnflasz-Pick model, and the Potts model with invisible states for instance. Until now there is no general method to avoid the difficulty of annealing method in systems which exhibit a phase transition. It is a challenging problem to propose a method how to erase or how to control the nature of the phase transition in the target system.

cond-mat.stat-mech↗

arXiv2012

Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence

We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys an area law and the non-universal prefactor of the leading term is strictly less than $\ln 2$. The analysis of entanglement spectra for various lattices reveals that the reduced density matrix associated with the VBS state is closely related to a thermal density matrix of a {\it holographic} spin chain, whose spectrum is reminiscent of that of the spin-1/2 Heisenberg chain. This correspondence is further supported by comparing the entanglement entropy in the holographic spin chain with conformal field theory predictions.

cond-mat.str-el↗

arXiv2011

Random Fan-Out State Induced by Site-Random Interlayer Couplings

We study the low-temperature properties of a classical Heisenberg model with site-random interlayer couplings on the cubic lattice. This model is introduced as a simplified effective model of Sr(Fe$_{1-x}$Mn$_{x}$)O$_2$, which was recently synthesized. In this material, when $x=0.3$, $(πππ)$ and $(π\pi0)$ mixed ordering is observed by neutron diffraction measurements. By Monte Carlo simulations, we find an exotic bulk spin structure that explains the experimentally obtained results. We name this spin structure the "random fan-out state". The mean-field calculations provide an intuitive understanding of this phase being induced by the site-random interlayer couplings. Since Rietveld analysis assuming the random fan-out state agrees well with the neutron diffraction pattern of Sr(Fe$_{0.7}$Mn$_{0.3}$)O$_2$, we conclude that the random fan-out state is reasonable for the spin-ordering pattern of Sr(Fe$_{0.7}$Mn$_{0.3}$)O$_2$ at the low-temperature phase.

cond-mat.mtrl-sci↗

arXiv2011

Novel Mechanism of Supersolid of Ultracold Polar Molecules in Optical Lattices

We study the checkerboard supersolid of the hard-core Bose-Hubbard model with the dipole-dipole interaction. This supersolid is different from all other supersolids found in lattice models in the sense that superflow paths through which interstitials or vacancies can hop freely are absent in the crystal. By focusing on repulsive interactions between interstitials, we reveal that the long-range tail of the dipole-dipole interaction have the role of increasing the energy cost of domain wall formations. This effect produces the supersolid by the second-order hopping process of defects. We also perform exact quantum Monte Carlo simulations and observe a novel double peak structure in the momentum distribution of bosons, which is a clear evidence for supersolid. This can be measured by the time-of-flight experiment in optical lattice systems.

cond-mat.quant-gas↗