Triangular-lattice Model Research Articles

Uniaxial compression on the superconductivity of β-BDA-TTP salts

The β-type BDA-TTP superconductors attract attention due to the high transition temperature Tc at ambient pressure for organic superconductors. In order to get insight into the superconductivity in terms of the dimerized anisotropic triangular lattice model, Tc of β-(BDA-TTP)2X [X = SbF6, X = AsF6] is studied under uniaxial compression by resistivity measurements. Under compression parallel to the donor stack, Tc increases gradually up to 3 (X = SbF6), 5 (X = AsF6) kbar, and decreases under further piston pressure. Under compression perpendicular to the donor stack, Tc decreases gradually up to 2.5 (X = SbF6), 4 (X = AsF6) kbar and then decreases rapidly under further pressure. Only for X = AsF6, a Tc minimum at 3 kbar is found for both direction. These trends in Tc are understood as an interplay between the enhancement of antiferromagnetic spin fluctuation and frustration on the triangular lattice. By the interplane compression, Tc increased by 0.5 K up to 2 kbar for both salts, demonstrating the importance of the interlayer interaction.

Vacancy diffusion in the triangular-lattice dimer model

We study vacancy diffusion on the classical triangular-lattice dimer model, subject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e., a monomer, in an otherwise fully packed lattice, is always localized in a treelike structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16+/-0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: x over 2 proportional variant tbeta, with beta=0.46+/-0.06 . We also find that the same exponent beta governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic mechanism allowing large-scale transport at low monomer densities. We further identify a "swap-tunneling" mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves (translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to their axes) plays an essential role.

Critical intermediate phase and phase transitions in a triangular-lattice three-spin interaction model: Level-spectroscopy approach

We investigate infinite-order phase transitions like the Berezinskii–Kosterlitz–Thouless transition observed in a triangular-lattice three-spin interaction model. Based on a field theoretical description and the operator-production-expansion technique, we perform the renormalization-group analysis, and then clarify properties of marginal operators near the phase transition points. The results are utilized to establish criteria to determine the transition points and some universal relations among excitation levels to characterize the transitions. We verify these predictions via the numerical analysis on eigenvalue structures of the transfer matrix. Also, we discuss an enhancement of symmetry at the end points of a critical intermediate phase in connection with a transition observed in the ground state of the bilinear-biquadratic spin-1 chain.

Numerical study on the anisotropic triangular-lattice Hubbard model at quarter filling: Charge fluctuations with three-fold periodicity

We study the extended Hubbard model at quarter filling defined on the anisotropic triangular lattices. We use the density-matrix renormalization group (DMRG) method to determine the ground-state phase diagram and the dynamical DMRG and Lanczos exact-diagonalization methods to calculate the excitation spectra. We find that the charge fluctuation with the three-fold periodicity, as well as the vertical and diagonal charge stripes, appears in realistic parameter ranges. We also find that, in the charge excitation spectra, there appear the low-energy collective modes in the entire Brillouin zone, together with the low-energy Drude-like peak separated from the high-energy broad features in the optical conductivity spectra, indicating the presence of the anomalous charge excitations in the state with the three-fold charge fluctuations.

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z ( T , B ) of the Ising model on L × L triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B, are evaluated exactly for L < 12 (using microcanonical transfer matrix) and approximately for L ⩾ 12 (using Wang–Landau Monte Carlo algorithm). From Z ( T , B ) , the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B ≠ 0 are obtained and discussed for the first time. The critical points a N ( x ) and the thermal scaling exponents y t ( x ) of the triangular-lattice Ising antiferromagnet, for various values of x = e − 2 β B , are estimated using the partition function zeros.

Exact diagonalization study on the extended Hubbard model in an anisotropic triangular lattice

A half-filled-band extended Hubbard model on an anisotropic triangular lattice is studied, using an exact diagonalization method, with κ -(BEDT-TTF) 2X in mind. In the isotropic case, the charge fluctuation of ( 2 π / 3 , 2 π / 3 ) is enhanced by the introduction of off-site Coulomb interaction ( V). In the case of V = 0 , the antiferromagnetic (AF) fluctuation is sizable for small frustration. However, when V is introduced, the AF fluctuation is rapidly suppressed and becomes substantially small, irrespective of the strength of frustration. Thus, it is revealed that both spin and charge fluctuations are sensitive to the shifts of t ′ / t and V / t .

Odd-frequency superconductivity in the 2D extended Hubbard model

It is an intriguing problem to clarify whether the odd-frequency superconducting state can be derived from a microscopic model or not, where the pairing function has odd parity in frequency. We study the instability of even-frequency and odd-frequency pairings on the extended Hubbard model in a 2D triangular lattice, with off-site Coulomb interaction V and on-site Coulomb interaction U . By using the random phase approximation (RPA), we find that the instability of odd-frequency spin-triplet s -wave pairing can be dominant with increasing V .

Chiral entanglement in triangular lattice models

We consider the low-energy spectrum of spin-$\frac{1}{2}$ two-dimensional triangular lattice models subject to a ferromagnetic Heisenberg interaction and a three spin chiral interaction of variable strength. Initially, we consider quasi-one-dimensional ladder systems of various geometries. Analytical results are derived that yield the behavior of the ground states, their energies, and the transition points. The entanglement properties of the ground state of these models are examined and we find that the entanglement depends on the lattice geometry due to frustration effects. To this end, the chirality of a given quantum state is used as a witness of tripartite entanglement. Finally, the two-dimensional model is investigated numerically by means of exact diagonalization and indications are presented that the low energy sector is a chiral spin liquid.

Long-range antiferromagnetic ordering in theS=12ordered rocksalt oxideLi5OsO6: Comparison with the isoelectronic and isostructural spin glassLi4MgReO6

${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$ and ${\mathrm{Li}}_{5}\mathrm{Re}{\mathrm{O}}_{6}$ polycrystalline samples were synthesized by conventional solid state methods. Employing powder neutron diffraction data, the crystal structure of ${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$ was reinvestigated. ${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$ crystallizes in $C2∕m$ in an ordered NaCl structure type, where $a=5.0472(1)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, $b=8.7827(2)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, $c=5.0079(1)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, $\ensuremath{\beta}=109.777(2)\ifmmode^\circ\else\textdegree\fi{}$ and $V=208.90(1)\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{3}$. Magnetic susceptibility and heat capacity data indicate an antiferromagnetic long-range order below $40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, although there is evidence for low dimensional short-range order below $80\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. As well, the frustration index, $f=\ensuremath{\mid}\ensuremath{\theta}\ensuremath{\mid}∕{T}_{N}\ensuremath{\sim}1$, in contrast to the isostructural and isoelectronic compound, ${\mathrm{Li}}_{4}\mathrm{Mg}\mathrm{Re}{\mathrm{O}}_{6}$, which is a spin glass below $12\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and has $f\ensuremath{\sim}14$. An attempt was made to rationalize these differences using spin dimer analysis. The key results are that the spin exchange interactions in the Re-based compound are stronger and are consistent with a frustrated triangular lattice model, while a low dimensional short-range order model is better for ${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$. The main reason for this is a strong Jahn-Teller distortion in the $\mathrm{Os}{\mathrm{O}}_{6}$ octahedron material which constrains the unpaired electron to occupy the ${d}_{xy}$ orbital.

Effective Field Theory of Triangular-Lattice Three-Spin Interaction Model

We discuss an effective field theory of a triangular-lattice three-spin interaction model defined by the Z p variables. Based on the symmetry properties and the ideal-state graph concept, we show that the vector dual sine-Gordon model describes the long-distance properties for p ≥5; we then compare its predictions with the previous argument. To provide the evidences, we numerically analyze the eigenvalue structure of the transfer matrix for p = 6, and we check the criticality with the central charge c = 2 of the intermediate phase and the quantization condition of the vector charges.

Supersolidity and phase diagram of soft-core bosons on a triangular lattice

We study the softcore extended Bose Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground state phase diagram of the system exhibits a very fruitful structure. Except the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\rho=1/3,2/3$ and $\rho=1$ are identified. Two of them (CDW II and CDW III) are newly predicted. In incommensurate fillings, superfluid, spuersolid as well as phase separation states are detected . As in the case for the hardcore bosons, a supersolid phase exists in $1/3<\rho<2/3$ while it is unstable towards the phase separation in $\rho<1/3$. However, this instability is refrained in $2/3<\rho<1$ due to the softening of the bosons and then a supersolid phase survives.

New universality class of the Ising model on curved geometry

We have considered critical properties of the heptagonal and triangular Ising lattice models defined on negatively curved surfaces. Finite-size scaling analyze reveal that several critical exponents take values distinct from those for the two-dimensional Ising model on a flat plane. This deviation originates from non-Euclidean property of the curved surface that leads to an alteration in global symmetries of the mounted system. Besides, it indicates the occurrence of a novel universality class of the Ising model induced by negative surface curvature.

Spin-triplet f-wave superconductivity in one-dimensional triangular-lattice Hubbard models

The Hubbard model at quarter filling defined on the one-dimensional (1D) triangular lattice (i.e., three chains coupled with interchain zigzag bonds) is studied by the density-matrix renormalization group method in order to clarify the symmetry of the Cooper-pair wave function of our proposed spin-triplet superconductivity induced by the ring-exchange mechanism. We calculate the rotational symmetry of the pair correlation function and show that the pairing occurs predominantly in the spin-triplet f-wave channel. Possible experimental relevance is discussed.

EFFECTIVE COMPUTATIONAL REUSE FOR ENERGY EVALUATIONS IN PROTEIN FOLDING

Predicting native conformations using computational protein models requires a large number of energy evaluations even with simplified models such as hydrophobic-hydrophilic (HP) models. Clearly, energy evaluations constitute a significant portion of computational time. We hypothesize that given the structured nature of algorithms that search for candidate conformations such as stochastic methods, energy evaluation computations can be cached and reused, thus saving computational time and effort. In this paper, we present a caching approach and apply it to 2D triangular HP lattice model. We provide theoretical analysis and prediction of the expected savings from caching as applied this model. We conduct experiments using a sophisticated evolutionary algorithm that contains elements of local search, memetic algorithms, diversity replacement, etc. in order to verify our hypothesis and demonstrate a significant level of savings in computational effort and time that caching can provide.

Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach

We investigate the triangular-lattice antiferromagnetic Ising model with a spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was first discussed by Kitatani and Oguchi. By employing the effective geometric factor, we analyze the scaling dimensions of the operators around the Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the global phase diagram. Our numerical data exhibit that two types of BKT-transition lines separate the intermediate critical region from the ordered and disordered phases, and they do not merge into a single curve in the antiferromagnetic region. We also estimate the central charge and perform some consistency checks among scaling dimensions in order to provide the evidence of the six-state clock universality. Further, we provide an analysis of the shapes of boundaries based on the crossover argument.

Charge order, spin order and superconductivity in two-dimensional electron systems: Effect of nearest-neighbor Coulomb interaction

Motivated by the charge order (CO) and superconductivity (SC) in θ - ( ET ) 2 X salts, we study the extended Hubbard model in a two-dimensional triangular lattice with variational Monte Carlo method. We show that the nearest-neighbor Coulomb interaction V induces charge fluctuation and the 3-fold CO state is stabilized. We also discuss the possibility of next-nearest-neighbor f-wave SC induced by charge fluctuation.

Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Néel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs2CuCl4.

Triangular lattice model of two-dimensional defect melting

We set up a harmonic lattice model for two-dimensional defect melting which, in contrast to earlier simple cubic models, resides on a triangular lattice. Integer-valued plastic defect gauge fields allow for the thermal generation of dislocations and disclinations. The model produces universal formulas for the melting temperature expressed in terms of the elastic constants, which are different from those derived for square lattices. They determine a Lindemann-like parameter for two-dimensional melting. In contrast to the square crystal which underwent a first-order melting transition, the triangular model melts in two steps. Our results are applied to the melting of Lennard-Jones and electron lattices.

Nature of phase transitions in the striped phase of a triangular-lattice Ising antiferromagnet

Different scenarios of the fluctuation-induced disordering of the striped phase which is formed at low temperatures in the triangular-lattice Ising model with the antiferromagnetic interaction of nearest and further neighbors are analyzed and compared. The dominant mechanism of the disordering is related to the formation of a network of domain walls, which is characterized by an extensive number of zero modes and has to appear via the first-order phase transition. In principle, this first-order transition can be preceded by a continuous one, related to the spontaneous formation of double domain walls and a partial restoration of the broken symmetry, but the realization of such a scenario requires the fulfillment of rather special relations between the coupling constants.

Crack propagation simulation of concrete with the regular triangular lattice model

This paper discusses 2D lattice models of beams for simulating the fracture of brittle materials. A simulation of an experiment on a concrete beam subjected to bending, in which two overlapping cracks occur, is used to study the effect of individual beam characteristics and different arrangements of the beams in the overall lattice. It was found that any regular orientation of the beams influences the resulting crack patterns. Methods to implement a wide range of Poisson's ratios are also developed, and the use of the lattice to study arbitrary micro-structures is outlined. The crack patterns that are obtained with lattice are in good agreement with the experimental results. Also, numerical simulations of the tests were performed by means of a lattice model, and non-integer dimensions were measured on the predicted lattice damage patterns.