arXiv subjects

Naoki Kawashima

Publications and source records attributed to Naoki Kawashima.

At least 91 records · Page 5Linked to original sources

arXiv2011

First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice

Using a Monte Carlo method, we study the finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with or without easy-plane anisotropy. The model takes account of competing interactions: a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third nearest-neighbor interaction $J_3$. As a result, the ground state is a spiral spin configuration for $-4 < J_1/J_3 < 0$. In this structure, global spin rotation cannot compensate for the effect of 120-degree lattice rotation, in contrast to the conventional 120-degree structure of the nearest-neighbor interaction model. We find that this model exhibits a first-order phase transition with breaking of the lattice rotation symmetry at a finite temperature. The transition is characterized as a $Z_2$ vortex dissociation in the isotropic case, whereas it can be viewed as a $Z$ vortex dissociation in the anisotropic case. Remarkably, the latter is continuously connected to the former as the magnitude of anisotropy decreases, in contrast to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. \textbf{79} (2010) 073001.] in which both the transitions were found to be continuous.

cond-mat.stat-mech↗

arXiv2011

Double-$\it q$ Order in a Frustrated Random Spin System

We use the three-dimensional Heisenberg model with site randomness as an effective model of the compound Sr(Fe$_{1-x}$Mn$_x$)O$_2$. The model consists of two types of ions that correspond to Fe and Mn ions. The nearest-neighbor interactions in the ab-plane are antiferromagnetic. The nearest-neighbor interactions along the c-axis between Fe ions are assumed to be antiferromagnetic, whereas other interactions are assumed to be ferromagnetic. From Monte Carlo simulations, we confirm the existence of the double-$\boldsymbol{q}$ ordered phase characterized by two wave numbers, $(πππ)$ and $(π\pi0)$. We also identify the spin ordering pattern in the double-$\boldsymbol{q}$ ordered phase.

cond-mat.stat-mech↗

arXiv2011

Phase Transition of Generalized Ferromagnetic Potts Model - Effect of Invisible States -

We investigate the nature of the phase transition of the ferromagnetic Potts model with invisible states. The ferromagnetic Potts model with invisible states can be regarded as straightforward extension of the standard ferromagnetic Potts model. The invisible states contribute the entropy, however they do not affect the internal energy. They also do not change the symmetry which breaks at the transition temperature. The invisible states stimulate a first-order phase transition. We confirm that the first-order phase transition with spontaneous $q$-fold symmetry breaking for $q=2,3$, and 4 takes place even on two-dimensional lattice by Monte Carlo simulation. We also find that the transition temperature decreases and the latent heat increases as the number of invisible states increases.

cond-mat.stat-mech↗

arXiv2010

Crossover Behavior from Decoupled Criticality

We study the thermodynamic phase transition of a spin Hamiltonian comprising two 3D magnetic sublattices. Each sublattice contains XY spins coupled by the usual bilinear exchange, while spins in different sublattices only interact via biquadratic exchange. This Hamiltonian is an effective model for XY magnets on certain frustrated lattices such as body centered tetragonal. By performing a cluster Monte Carlo simulation, we investigate the crossover from the 3D-XY fixed point (decoupled sublattices) and find a systematic flow toward a first-order transition without a separatrix or a new fixed point. This strongly suggests that the correct asymptotic behavior is a first-order transition.

cond-mat.str-el↗

arXiv2010

Reponse to Comment on "Direct mapping of the finite temperature phase diagram of strongly correlated quantum models"

Pollet et al have questioned our claim staked in Phys. Rev. Lett. 103, 085701 (2009) that from the location of sharp features in the compressibility in the trap, it is possible to map out the phase boundary between two phases within reasonable accuracy. We stand by it and use this reply to sharpen the conditions under which "sharp" features in compressibility reflect the effects of critical fluctuations.

cond-mat.quant-gas↗

arXiv2010

Quantum Monte Carlo method for pairing phenomena: Super-counter-fluid of two-species Bose gases in optical lattices

We study the super-counter-fluid(SCF) states in the two-component hardcore Bose-Hubbard model on the square lattice, using the quantum Monte Carlo method based on the worm(directed loop) algorithm. Since the SCF state is a state of a pair-condensation characterized by $< a^{\dagger} b > \neq 0, < a > = 0$, and $< b > = 0$, where $a$ and $b$ are the order parameters of the two components, it is important to study behaviors of the pair-correlation function $< a_{i} b_{i}^{\dagger} a_{j}^{\dagger} b_{j} >$. For this purpose, we propose a choice of the worm head for calculating the pair-correlation function. From this pair-correlation, we confirm the Kosterlitz-Thouless(KT) charactor of the SCF phase. The simulation efficiency is also improved in the SCF phase.

cond-mat.quant-gas↗

arXiv2010

Phase Transition in Potts Model with Invisible States

We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and the free energy, although they do not contribute to the internal energy. The internal energy and the number of degenerated ground states do not change, if invisible states are introduced into the standard Potts model. A second-order phase transition takes place at finite temperature in the standard $q$-state ferromagnetic Potts model on two-dimensional lattice for $q=2,3$, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous $q$-fold symmetry breaking ($q=2,3$, and 4) due to entropy effect of invisible states. We believe that our present model is a fundamental model for analysis of a first-order phase transition with spontaneous discrete symmetry breaking.

cond-mat.stat-mech↗

arXiv2010

Entanglement in valence-bond-solid states on symmetric graphs

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 $\ln 2$. 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.

quant-ph↗

arXiv2010

Finite-Temperature Transition in the Spin-Dimer Antiferromagnet BaCuSi2O6

We consider a classical XY-like Hamiltonian on a body-centered tetragonal lattice, focusing on the role of interlayer frustration. A three-dimensional (3D) ordered phase is realized via thermal fluctuations, breaking the mirror-image reflection symmetry in addition to the XY symmetry. A heuristic field-theoretical model of the transition has a decoupled fixed point in the 3D XY universality, and our Monte Carlo simulation suggests that there is such a temperature region where long-wavelength fluctuations can be described by this fixed point. However, it is shown using scaling arguments that the decoupled fixed point is unstable against a fluctuation-induced biquadratic interaction, indicating that a crossover to nontrivial critical phenomena with different exponents appears as one approaches the critical point beyond the transient temperature region. This new scenario clearly contradicts the previous notion of the 3D XY universality.

cond-mat.str-el↗

arXiv2009

Successive phase transitions and phase diagrams of the quasi-two-dimensional triangular antiferromagnet Rb4Mn(MoO4)3

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.

cond-mat.str-el↗

arXiv2009

Magnetic properties of the spin-1/2 XXZ model on the Shastry-Sutherland lattice: Effect of long-range interactions

We study magnetic properties of the $S=1/2$ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We investigate the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the 2D Ising model universality, although there is a single phase transition in the Ising limit case. Finally, we estimate the coupling ratio to explain the magnetization process observed in ${\rm TmB_4}$

cond-mat.str-el↗

arXiv2009

Finite-Size Scaling for Quantum Criticality above the Upper Critical Dimension: Superfluid-Mott-Insulator Transition in Three Dimensions

Validity of modified finite-size scaling above the upper critical dimension is demonstrated for the quantum phase transition whose dynamical critical exponent is $z=2$. We consider the $N$-component Bose-Hubbard model, which is exactly solvable and exhibits mean-field type critical phenomena in the large-$N$ limit. The modified finite-size scaling holds exactly in that limit. However, the usual procedure, taking the large system-size limit with fixed temperature, does not lead to the expected (and correct) mean-field critical behavior due to the limited range of applicability of the finite-size scaling form. By quantum Monte Carlo simulation, it is shown that the same holds in the case of N=1.

cond-mat.stat-mech↗

arXiv2009

Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies and correlation functions of the Bose Hubbard model is developed. We illustrate the general formalism, which includes all possible inhomogeneous effects in the formalism, such as disorder, or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third-order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator to superfluid transition along with a generalization of the RPA-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions; the accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling theory results are benchmarked against numerically exact QMC simulations in two and three dimensions and against DMRG calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

cond-mat.other↗

arXiv2009

Direct mapping of the finite temperature phase diagram of strongly correlated quantum models

Optical lattice experiments, with the unique potential of tuning interactions and density, have emerged as emulators of nontrivial theoretical models that are directly relevant for strongly correlated materials. However, so far the finite temperature phase diagram has not been mapped out for any strongly correlated quantum model. We propose a remarkable method for obtaining such a phase diagram for the first time directly from experiments using only the density profile in the trap as the input. We illustrate the procedure explicitly for the Bose Hubbard model, a textbook example of a quantum phase transition from a superfluid to a Mott insulator. Using "exact" quantum Monte Carlo simulations in a trap with up to $10^6$ bosons, we show that kinks in the local compressibility, arising from critical fluctuations, demarcate the boundaries between superfluid and normal phases in the trap. The temperature of the bosons in the optical lattice is determined from the density profile at the edge. Our method can be applied to other phase transitions even when reliable numerical results are not available.

cond-mat.supr-con↗

arXiv2008

First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model

We study a finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third-nearest-neighbor interaction $J_3$ using a Monte Carlo method. Apart from a trivial degeneracy corresponding to O(3) spin rotations,the ground state for $J_3 \neq 0$ has a threefold degeneracy corresponding to 120 degree lattice rotations. We find that this model exhibits a first-order phase transition with the breaking of the threefold symmetry when the interaction ratio is $J_3/J_1=-3$.

cond-mat.stat-mech↗

arXiv2008

Critical properties of edge-cubic spin model on square lattice

The edge-cubic spin model on square lattice is studied via Monte Carlo simulation with cluster algorithm. By cooling the system, we found two successive symmetry breakings, i.e., the breakdown of $O_h$ into the group of $C_{3h}$ which then freezes into ground state configuration. To characterize the existing phase transitions, we consider the magnetization and the population number as order parameters. We observe that the magnetization is good at probing the high temperature transition but fails in the analysis of the low temperature transition. In contrast the population number performs well in probing the low- and the high-$T$ transitions. We plot the temperature dependence of the moment and correlation ratios of the order parameters and obtain the high- and low-$T$ transitions at $T_h = 0.602(1)$ and $T_l=0.5422(2)$ respectively, with the corresponding exponents of correlation length $ν_h=1.50(1)$ and $ν_l=0.833(1)$. By using correlation ratio and size dependence of correlation function we estimate the decay exponent for the high-$T$ transition as $η_h=0.260(1)$. For the low-$T$ transition, $η_l = 0.267(1)$ is extracted from the finite size scaling of susceptibility. The universality class of the low-$T$ critical point is the same as the 3-state Potts model.

cond-mat.stat-mech↗

arXiv2007

Supersolid of Hardcore Bosons on the Face Centered Cubic Lattice

We investigate a supersolid state in hardcore boson models on the face-centered-cubic (FCC) lattice. The supersolid state is characterized by a coexistence of crystalline order and superfluidity. Using a quantum Monte Carlo method based on the directed-loop algorithm, we calculate static structure factors and superfluid density at finite temperature, from which we obtain the phase diagram. The supersolid phase exists at intermediate fillings between a three-quarter-filled solid phase and a half-filled solid phase. We also discuss the mechanism of the supersolid state on the FCC lattice.

cond-mat.supr-con↗

arXiv2007

Ground States of the SU(N) Heisenberg Model

The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N>=5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.

cond-mat.stat-mech↗