arXiv subjects

Kenji Harada

Publications and source records attributed to Kenji Harada.

36 records · Page 2Linked to original sources

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↗

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

Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalization

The ground state of an S=1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4, is numerically studied. We apply a numerical variational method by using a tensor network with entanglement renormalization, which improves the capability of describing a quantum state. Magnetic ground states are identified for 0.7 <= J2/J1 <= 1 in the thermodynamic limit, where J1 and J2 denote the inner-chain and inter-chain coupling constants, respectively. Except for the isotropic case (J1=J2), the magnetic structure is spiral with an incommensurate wave vector that is different from the classical one. The quantum fluctuation weakens the effective coupling between chains, but the magnetic order remains in the thermodynamic limit. In addition, the incommensurate wave number is in good agreement with that of the series expansion method.

cond-mat.str-el↗

arXiv2011

Bayesian Inference in the Scaling Analysis of Critical Phenomena

To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes only the smoothness of a scaling function, and it does not need a form. We demonstrate this method for the finite-size scaling analysis of the Ising models on square and triangular lattices. Near the critical point, the method is comparable in accuracy to the least-square method. In addition, it works well for data to which we cannot apply the least-square method with a polynomial of low degree. By comparing the data on triangular lattices with the scaling function inferred from the data on square lattices, we confirm the universality of the finite-size scaling function of the two-dimensional Ising model.

cond-mat.stat-mech↗

arXiv2008

Diffusion in the Continuous-Imaginary-Time Quantum World-Line Monte Carlo Simulations with Extended Ensembles

The dynamics of samples in the continuous-imaginary-time quantum world-line Monte Carlo simulations with extended ensembles are investigated. In the case of a conventional flat ensemble on the one-dimensional quantum S=1 bi-quadratic model, the asymmetric behavior of Monte Carlo samples appears in the diffusion process in the space of the number of vertices. We prove that a local diffusivity is asymptotically proportional to the number of vertices, and we demonstrate the asymmetric behavior in the flat ensemble case. On the basis of the asymptotic form, we propose the weight of an optimal ensemble as $1/\sqrt{n}$, where $n$ denotes the number of vertices in a sample. It is shown that the asymmetric behavior completely vanishes in the case of the proposed ensemble on the one-dimensional quantum S=1 bi-quadratic model.

cond-mat.stat-mech↗

arXiv2006

Persistent spin helix in Rashba-Dresselhaus two-dimensional electron systems

A persistent spin helix (PSH) in spin-orbit-coupled two-dimensional electron systems was recently predicted to exist in two cases: [001] quantum wells (QWs) with equal coupling strengths of the Rashba and the Dresselhaus interactions (RD), and Dresselhaus-only [110] QWs. Here we present supporting results and further investigations, using our previous results [Phys. Rev. B 72, 153305 (2005)]. Refined PSH patterns for both RD [001] and Dresselhaus [110] QWs are shown, such that the feature of the helix is clearly seen. We also discuss the time dependence of spin to reexamine the origin of the predicted persistence of the PSH. For the RD [001] case, we further take into account the random Rashba effect, which is much more realistic than the constant Rashba model. The distorted PSH pattern thus obtained suggests that such a PSH may be more observable in the Dresselhaus [110] QWs, if the dopants cannot be regularly enough distributed.

cond-mat.mes-hall↗

arXiv2006

Dimer-Quadrupolar Quantum Phase Transition in the Quasi-One-Dimensional Heisenberg Model with Biquadratic Interaction

The quasi-one-dimensional S=1 Heisenberg antiferromagnet with a biquadratic term is investigated at zero temperature by quantum Monte Carlo simulation. As the magnitude of the inter-chain coupling is increased, the system undergoes a phase transition from a spontaneously dimerized phase to a Néel ordered or spin nematic phase. The numerical results suggest the possibility of an unconventional second-order transition in which the symmetry group characterizing one phase is not a subgroup of the other.

cond-mat.stat-mech↗

arXiv2004

Recent Developments of World-Line Monte Carlo Methods

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.

cond-mat.dis-nn↗

arXiv2003

A quantum Monte Carlo algorithm for softcore boson systems

An efficient Quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin quantum number. It is demonstrated, how this limit may be taken explicitly in the algorithm, eliminating the systematic errors. The efficiency of the algorithm is examined for the non-interacting lattice boson model and compared with the stochastic series expansion method with the heat-bath type scattering probability of the random walker.

cond-mat.stat-mech↗

arXiv2002

Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems

Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.

cond-mat.stat-mech↗

arXiv2002

Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets

The two-dimensional SU(N) quantum antiferromagnet, a generalization of the quantum Heisenberg model, is investigated by quantum Monte Carlo simulations. The ground state for $N\le 4$ is found to be of the Néel type with broken SU(N) symmetry, whereas it is of the Spin-Peierls type for $N\ge 5$ with broken lattice translational invariance. No intermediate spin-liquid phase was observed in contrast to previous numerical simulations on smaller lattices [Santoro et al., Phys. Rev. Lett. {\bf 83} 3065 (1999)].

cond-mat.supr-con↗

arXiv2001

Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction

Through Quantum Monte Carlo simulation, we study the biquadratic-interaction model with the SU(2) symmetry in two and three dimensions. The zero-temperature phase diagrams for the two cases are identical and exhibit an intermediate phase characterized by finite quadrupole moment, in agreement with mean-field type arguments and the semi-classical theory. In three dimensions, we demonstrate that the model in the quadrupolar regime has a phase transition at a finite temperature. In contrast to predictions by mean-field theories, the phase transition to the quadrupolar phase turns out to be of the second order. We also examine the critical behavior in the two marginal cases with the SU(3) symmetry.

cond-mat.mtrl-sci↗

arXiv2000

Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions

We present a new algorithm for quantum Monte Carlo simulation based on global updating with loops. While various theoretical predictions are confirmed in one dimension, we find, for S=1 systems on a square lattice with an antiferromagnetic biquadratic interaction, that the intermediate phase between the antiferromagnetic and the ferromagnetic phases is disordered and that the two phase transitions are both of the first order in contrast to the one-dimensional case. It is strongly suggested that the transition points coincide those at which the algorithm changes qualitatively.

cond-mat.stat-mech↗

arXiv2000

Short-time dynamics and magnetic critical behavior of two-dimensional random-bond Potts model

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two-dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents theta, beta/nu and z for the quenched disorered systems from the power-law behavior of the kth moments of magnetizations.

cond-mat.soft↗

arXiv1998

The Two-Dimensional S=1 Quantum Heisenberg Antiferromagnet at Finite Temperatures

The temperature dependence of the correlation length, susceptibilities and the magnetic structure factor of the two-dimensional spin-1 square lattice quantum Heisenberg antiferromagnet are computed by the quantum Monte Carlo loop algorithm (QMC). In the experimentally relevant temperature regime the theoretically predicted asymptotic low temperature behavior is found to be not valid. The QMC results however, agree reasonably well with the experimental measurements of La2NiO4 even without considering anisotropies in the exchange interactions.

cond-mat.stat-mech↗

arXiv1998

Kosterlitz-Thouless transition of quantum XY model in two dimensions

The two-dimensional $S=1/2$ XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to $128 \times 128$ near and below the critical temperature. The critical temperature is estimated as $T_{\rm KT} = 0.3427(2)J$. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.

cond-mat.stat-mech↗

arXiv1997

Universal Jump in the Helicity Modulus of the Two-Dimensional Quantum XY Model

The helicity modulus of the S=1/2 XY model is precisely estimated through a world line quantum Monte Carlo method enhanced by a cluster update algorithm. The obtained estimates for various system sizes and temperatures are well fitted by a scaling form with L replaced by \log(L/L_0), which is inferred from the solution of the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.

cond-mat.stat-mech↗