arXiv subjects

Synge Todo

Publications and source records attributed to Synge Todo.

At least 73 records · Page 4Linked to original sources

arXiv2013

Path-integral Monte Carlo method for the local Z_2 Berry phase

We present a loop cluster algorithm Monte Carlo method for calculating the local Z_2 Berry phase of the quantum spin models. The Berry connection, which is given as the inner product of two ground states with different local twist angles, is expressed as a Monte Carlo average on the worldlines with fixed spin configurations at the imaginary-time boundaries. The "complex weight problem" caused by the local twist is solved by adopting the meron cluster algorithm. We present the results of simulation on the antiferromagnetic Heisenberg model on an out-phase bond-alternating ladder to demonstrate that our method successfully detects the change in the valence bond pattern at the quantum phase transition point. We also propose that the gauge-fixed local Berry connection can be an effective tool to estimate pricisely the quantum critical point.

cond-mat.str-el↗

arXiv2012

Geometric Allocation Approach for Transition Kernel of Markov Chain

We introduce a new geometric approach that constructs a transition kernel of Markov chain. Our method always minimizes the average rejection rate and even reduce it to zero in many relevant cases, which cannot be achieved by conventional methods, such as the Metropolis-Hastings algorithm or the heat bath algorithm (Gibbs sampler). Moreover, the geometric approach makes it possible to find not only a reversible but also an irreversible solution of rejection-free transition probabilities. This is the first versatile method that can construct an irreversible transition kernel in general cases. We demonstrate that the autocorrelation time (asymptotic variance) of the Potts model becomes more than 6 times as short as that by the conventional Metropolis-Hastings algorithm. Our algorithms are applicable to almost all kinds of Markov chain Monte Carlo methods and will improve the efficiency.

cond-mat.stat-mech↗

arXiv2012

Ordering and Excitation in Orbital Compass Model on a Checkerboard Lattice

We study an orbital compass model on a checkerboard lattice where orbital degree of freedom is represented by the pseudo-spin operator. Competition arises from an Ising interaction for the $z$ component of pseudo-spins along the vertical/horizontal bonds and an Ising interaction for the $x$ component along diagonal bonds. Classical and quantum compass models are analyzed by utilizing several analytical methods and numerical simulations. At a fully frustrated point where the two Ising interactions compete with each other, a macroscopic number of orbital configurations are degenerate in a classical ground state. This degeneracy is lifted by thermal and quantum fluctuations, and a staggered long-range order of the $z$ component of the pseudo-spin is realized. A tricritical point for this order appears due to competition between the bond dependent Ising interactions. Roles of geometrical frustration on excitation dynamics are also examined.

cond-mat.str-el↗

arXiv2012

Critical temperature and correlation length of an elastic interaction model for spin-crossover materials

It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical point. In the present paper, we study this property in a model of bistable molecules, whose size changes depending on the bistable states. The molecules can move in space, interacting via an elastic interaction. It is known that due to the different sizes, an effective long-range interaction between the spins appears, and thus this model has a mean-field type of phase transition. It is found that the scaling properties of the shift of the critical temperature from the pure short-range limit in the model with infinite-range and short-range interactions hold also in the present model, regarding the ratio of the size of the two states as a control parameter for the strength of the long-range interaction. By studying the structure factor, it is shown that the dependence of the cluster size at the critical temperature also shows the same scaling properties as a previously studied model with both infinite-range and short-range interactions. We therefore conclude that these scaling relations hold universally in hybrid models with both short-range and weak long-range interactions.

cond-mat.stat-mech↗

arXiv2010

Markov Chain Monte Carlo Method without Detailed Balance

We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.

cond-mat.stat-mech↗

arXiv2010

Orbital ordering in e_g orbital systems: Ground states and thermodynamics of the 120 degree model

Orbital degrees of freedom shape many of the properties of a wide class of Mott insulating, transition metal oxides with partially filled 3d-shells. Here we study orbital ordering transitions in systems where a single electron occupies the e_g orbital doublet and the spatially highly anisotropic orbital interactions can be captured by an orbital-only model, often called the 120 degree model. Our analysis of both the classical and quantum limits of this model in an extended parameter space shows that the 120 degree model is in close proximity to several T=0 phase transitions and various competing ordered phases. We characterize the orbital order of these nearby phases and their associated thermal phase transitions by extensive numerical simulations and perturbative arguments.

cond-mat.str-el↗

arXiv2008

Improved chain mean-field theory for quasi-one-dimensional quantum magnets

A novel mean-field approximation for quasi-one-dimensional (Q1D) quantum magnets is formulated. Our new mean-field approach is based on the Bethe-type effective-field theory, where thermal and quantum fluctuations between the nearest-neighbor chains as well as those in each chain are taken into account exactly. The self-consistent equation for the critical temperature contains the boundary-field magnetic susceptibilities of a multichain cluster, which can be evaluated accurately by some analytic or numerical methods, such as the powerful quantum Monte Carlo method. We show that the accuracy of the critical temperature of Q1D magnets as a function of the strength of interchain coupling is significantly improved, compared with the conventional chain mean-field theory. It is also demonstrated that our new approximation can predict nontrivial dependence of critical temperature on the sign (i.e., ferromagnetic or antiferromagnetic) of interchain coupling as well as on the impurity concentration in randomly diluted Q1D Heisenberg antiferromagnets.

cond-mat.str-el↗

arXiv2008

Green's function theory for spin-1/2 ferromagnets with an easy-plane exchange anisotropy

The many-body Green's function theory with the random-phase approximation is applied to the study of easy-plane spin-1/2 ferromagnets in an in-plane magnetic field. We demonstrate that the usual procedure, in which only the three Green's functions $<< S_i^μ;S_j^->>$ ($μ=+,-,z$) are used, yields unreasonable results in this case. Then the problem is discussed in more detail by considering all combinations of Green's functions. We can derive one more equation, which cannot be obtained by using only the set of the above three Green's functions, and point out that the two equations contradict each other if one demands that the identities of the spin operators are exactly satisfied. We discuss the cause of the contradiction and attempt to improve the method in a self consistent way. In our procedure, the effect of the anisotropy can be appropriately taken into account, and the results are in good agreement with the quantum Monte Carlo calculations.

cond-mat.str-el↗

arXiv2008

Successive phase transitions at finite temperatures of the supersolid in the three-dimensional extended Bose-Hubbard model

We study the finite temperature properties of the extended Bose-Hubbard model on a cubic lattice. This model exhibits the so-called supersolid state. To start with, we investigate ordering processes by quantum Monte Carlo simulations, and find successive superfluid and solid phase transitions. There, we find that the two order parameters compete with each other. We obtain the finite temperature phase diagram, which contains the superfluid, the solid, the supersolid and the disordered phase. We develop a mean-field theory to analyze the ordering processes and compare the result with that obtained by simulations, and discuss the mechanism of the competition of these two orders. We also study how the supersolid region shrinks as the on-site repulsion becomes strong.

cond-mat.stat-mech↗

arXiv2008

Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions

An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The realized stochastic dynamics is equivalent to that of the conventional Swendsen-Wang algorithm, which requires O(N^2) operations per Monte Carlo sweep if applied to long-range interacting models. In addition, it is shown that the total energy and the specific heat can also be measured in O(N) time. We demonstrate the efficiency of our algorithm over the conventional method and the O(N log N) algorithm by Luijten and Bloete. We also apply our algorithm to the classical and quantum Ising chains with inverse-square ferromagnetic interactions, and confirm in a high accuracy that a Kosterlitz-Thouless phase transition, associated with a universal jump in the magnetization, occurs in both cases.

cond-mat.stat-mech↗

arXiv2006

Universal Reduction of Effective Coordination Number in the Quasi-One-Dimensional Ising Model

Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, L times infty or L times L times infty. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-1/2 transverse-field Ising model.

cond-mat.stat-mech↗

arXiv2006

Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number $n\_ω$ of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirm the parity law and the gapless character of the ribbon for even $n\_ω$.

cond-mat.str-el↗

arXiv2006

Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets

Bond-dilution effects on the ground state of the square-lattice antiferromagnetic Heisenberg model, consisting of coupled bond-alternating chains, are investigated by means of the quantum Monte Carlo simulation. It is found that, when the ground state of the non-diluted system is a non-magnetic state with a finite spin gap, a sufficiently weak bond dilution induces a disordered state with a mid gap in the original spin gap, and under a further stronger bond dilution an antiferromagnetic long-range order emerges. While the site-dilution-induced long-range order is induced by an infinitesimal concentration of dilution, there exists a finite critical concentration in the case of bond dilution. We argue that this essential difference is due to the occurrence of two types of effective interactions between induced magnetic moments in the case of bond dilution, and that the antiferromagnetic long-range-ordered phase does not appear until the magnitudes of the two interactions become comparable.

cond-mat.dis-nn↗

arXiv2005

Quantum phase transitions of spin chiral nanotubes

Recently many interesting magnetic nanostructures have been fabricated and much attention is arising on the rich magnetic properties that originate in the quantum effects eminent in the nanoscale world. One of the peculiar aspects of the quantum effects is the spin excitation gap. In the spin-1/2 low-dimensional systems, the spin gap often appears when the lattice dimerization or the frustration in the spin-spin interaction are introduced. In the present study, we investigate the ground-state property of the spin-1/2 antiferromagnetic spin chiral nanotubes with the spatial modulation in the spin-spin interaction. The ground-state phase diagrams of them are determined by observing the behavior of the expectation value of the Lieb-Schultz-Mattis slow-twist operator calculated by the quantum Monte Carlo method with the continuous-time loop algorithm. We discuss the relation between the characteristic of the topology of the phase diagram and the chiral vector of the nanotubes.

cond-mat.str-el↗

arXiv2005

Randomness-driven quantum phase transition in bond-alternating Haldane chain

The effect of bond randomness on the spin-gapped ground state of the spin-1 bond-alternating antiferromagnetic Heisenberg chain is discussed. By using the loop cluster quantum Monte Carlo method, we investigate the stability of topological order in terms of the recently proposed twist order parameter [M. Nakamura and S. Todo: Phys. Rev. Lett. 89 (2002) 077204]. It is observed that the dimer phases as well as the Haldane phase of the spin-1 Heisenberg chain are robust against a weak randomness, though the valence-bond-solid-like topological order in the latter phase is destroyed by introducing a disorder stronger than the critical value.

cond-mat.dis-nn↗

arXiv2003

Quantum Phase Transitions of Quasi-One-Dimensional Heisenberg Antiferromagnets

We study the ground-state phase transitions of quasi-one-dimensional quantum Heisenberg antiferromagnets by the quantum Monte Carlo method with the continuous-time loop algorithm and finite-size scaling. For a model which consists of S=1 chains with bond alternation coupled on a square lattice, we determine the ground state phase diagram and the universality class of the quantum phase transitions.

cond-mat.str-el↗

arXiv2002

Ground state of antiferromagnetic Heisenberg two-leg ladder in terms of the valence-bond solid picture

We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder.

cond-mat.str-el↗

arXiv2002

Dilution Effects on Two-Dimensional Heisenberg Antiferromagnets with Non-Magnetic Spin-Gapped Ground State

Dilution effects on spin-1/2 quantum Heisenberg antiferromagnets with a non-magnetic spin-gapped ground state are studied by means of the qunatum Monte Carlo simulation. In the site-diluted system, an antiferromagnetic long-range order (AF-LRO) is induced at an infinitesimal concentration of dilution due to an effective coupling $\tilde{J}_{mn}$ between induced magnetic moments. In the bond-diluted case, on the other hand, the AF-LRO is not induced up to a certain concentration of dilution due to singlet pairs reformed by an AF coupling $\tilde{J}_{\rm af}$ between the edge spins of the diluted bond through the two-dimensional shortest paths. The competition between $\tilde{J}_{mn}$ and $\tilde{J}_{\rm af}$ yields peculiar phenomena in the bond-diluted system.

cond-mat.dis-nn↗