arXiv subjects

Takafumi Suzuki

Publications and source records attributed to Takafumi Suzuki.

30 records · Page 2Linked to original sources

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↗

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↗

arXiv2014

Spinor and twistor formulations of massless particles with rigidity

The 4-dimensional model of a massless particle with rigidity whose Lagrangian is proportional to its world-line curvature is reformulated in terms of spinor and twistor variables. We begin with a first-order Lagrangian that is equivalent to the original Lagrangian proportional to the extrinsic curvature of a particle world-line. The first-order Lagrangian is written in terms of spacetime and spinor variables, leading to a spinor representation of the Lagrangian. Then its corresponding action is expressed in terms of twistor variables, leading to the gauged Shirafuji action.

hep-th↗

arXiv2014

Canonical formalism and quantization of a massless spinning bosonic particle in four dimensions

A twistor model of a free massless spinning particle in 4-dimensional Minkowski space is studied in terms of spacetime and spinor variables. This model is specified by a simple action, referred to here as the gauged Shirafuji action, that consists of twistor variables and gauge fields on the 1-dimensional parameter space. We consider the canonical formalism of the model by following the Dirac formulation for constrained Hamiltonian systems. In the subsequent quantization procedure, we obtain a plane-wave solution with momentum spinors. From this solution and coefficient functions, we construct positive-frequency and negative-frequency spinor wave functions defined on complexified Minkowski space. It is shown that the Fourier-Laplace transforms of the coefficient functions lead to the spinor wave functions expressed as the Penrose transforms of the corresponding holomorphic functions on twistor space. We also consider the exponential generating function for the spinor wave functions and derive a novel representation for each of the spinor wave functions.

hep-th↗

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

Long distance entanglement in one-dimensional quantum systems under sinusoidal deformation

We investigate entanglement generation in one-dimensional quantum spin systems with the sinusoidal deformation. In the system, the energy scale of each local term in the Hamiltonian is modified according to a position-dependent function \sin^α[\fracπ{N} (x - \frac{1}{2})], where x is the position of the local term and N is the length of the system. We show that at zero temperature the system with α\ge 2 is able to generate a sizable entanglement between two spins at open edges even when the two spins are infinitely far apart. This long-distance entanglement is rather robust against thermal fluctuations and survives up to a temperature that decays with the system size slowly, in an algebraic form.

quant-ph↗

arXiv2012

Gapless edge states and their stability in two-dimensional quantum magnets

We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin-1/2 antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region of the dimerized phases, and the critical exponent of spin correlators along the edge deviates from the value of Tomonaga-Luttinger (TL) liquid universality in large but finite systems at low temperatures. We also demonstrate that the gapless nature at edges is stable against several perturbations such as external magnetic field, easy-plane XXZ anisotropy, Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions. The edge states exhibit non TL-liquid behavior, depending strongly on model parameters and kinds of perturbations. Possible ways of detecting these edge states are discussed. Properties of edge states we show in this paper could also be used as reference points to study other edge states of more exotic gapped magnetic phases such as spin liquids.

cond-mat.str-el↗

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↗

arXiv2011

Single-ion anisotropy in Haldane chains and form factor of the O(3) nonlinear sigma model

We consider spin-1 Haldane chains with single-ion anisotropy, which exists in known Haldane chain materials. We develop a perturbation theory in terms of anisotropy, where magnon-magnon interaction is important even in the low temperature limit. The exact two-particle form factor in the O(3) nonlinear sigma model leads to quantitative predictions on several dynamical properties including dynamical structure factor and electron spin resonance frequency shift. These agree very well with numerical results, and with experimental data on the Haldane chain material Ni(C$_5$H$_{14}$N$_2$)$_2$N$_3$(PF$_6$).

cond-mat.stat-mech↗