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Stability of the Nagaoka-type ferromagnetic state in a t 2 g orbital system on a cubic lattice
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Quantum many-body calculations using body-centered cubic lattices
It is often computationally advantageous to model space as a discrete set of points forming a lattice grid. This technique is particularly useful for computationally difficult problems such as quantum many-body systems. For reasons of simplicity and familiarity, nearly all quantum many-body calculations have been performed on simple cubic lattices. Since the removal of lattice artifacts is often an important concern, it would be useful to perform calculations using more than one lattice geometry. In this paper we show how to perform quantum many-body calculations using auxiliary-field Monte Carlo simulations on a three-dimensional body-centered cubic (BCC) lattice. As a benchmark test we compute the ground state energy of 33 spin-up and 33 spin-down neutrons in the unitary limit, which is an idealized limit where the interaction range is zero and scattering length is infinite. As a fraction of the free Fermi gas energy E FG , we find that the ground state energy is E 0 /E FG =0.369(2),0.371(2), using two different definitions of the finite-system energy ratio. This is in excellent agreement with recent results obtained on a cubic lattice [He et al., Phys. Rev. A 101, 063615 (2020)]. We find that the computational effort and performance on a BCC lattice is approximately the same as that for a cubic lattice with the same number of lattice points. We discuss how the lattice simulations with different geometries can be used to constrain the size of lattice artifacts in simulations of continuum quantum many-body systems.
Phase Transitions in the Antiferromagnetic Heisenberg Model on a Body-Centered Cubic Lattice with Allowance for the Next-Nearest-Neighbor Interactions
Based on the replica exchange Monte Carlo algorithm and histogram analysis of data, the phase transitions in the three-dimensional antiferromagnetic Heisenberg model on a body-centered cubic lattice with allowance for the next-nearest-neighbor interaction are studied. The study is performed for the nextnearest- neighbor exchange interaction ratio of r = 1. It is established that, for this model, the transition from the antiferromagnetic to paramagnetic phase is a first-order phase transition.
Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors
Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.
Ice rule for a ferromagnetic nanosite network on the face-centered cubic lattice
The magnetic properties of an inverse opal-like cobalt-based structure having the symmetry of the face-centered cubic lattice are studied. The magnetization reversal of the structure in a magnetic field applied along the [11̄0] axis is described using a phenomenological model, which uses the ice rule for the local magnetization of nanostructure elements. This description predicts the absence of a long-range magnetic order in two <111> directions that are normal to the magnetic field. The magnetic structure is analyzed by smallangle neutron diffraction. Neutron diffraction patterns are measured in an external magnetic field varying from −1.2 to 1.2 T and applied along the crystallographic [11̄0] direction. A magnetic contribution to the neutron scattering intensity is extracted. It is shown that this contribution is close to zero over the entire applied magnetic field range for all scattering planes that are normal to the field, which agrees well with the proposed model.
Studying Thermodynamic Properties of the Ising Model on a Body-Centered Cubic Lattice with Competing Exchange Interactions
Using the Monte Carlo method, magnetic structures of the ground state and thermodynamic properties of the antiferromagnetic Ising model on a body-centered cubic lattice with competing exchange interactions are studied. The investigations are carried out for the ratio of the exchange interactions of next and nearest neighbors r = J{sub 2}/J{sub 1} = 2/3. All possible magnetic structures of the ground state for this ratio of exchange interactions have been obtained. It has been shown that at r = 2/3 the competition of exchange interactions does not lead to the appearance of frustration and degeneracy of the ground state. Based on the histogram data analysis, it has been shown that the phase transition of the second kind is observed in the model under study at r = 2/3.
Phase Transitions and the Critical Properties of the Heisenberg Model on a Body-Centered Cubic Lattice
The Monte Carlo replica technique is used to study phase transitions and the thermodynamic and critical properties of the three-dimensional Heisenberg antiferromagnetic model on the body-centered cubic lattice with the inclusion of the interaction of the nearest and the next-nearest neighbors. The studies are performed for the proportions of the values of the exchange interactions of the nearest and the next-nearest neighbors in the range of values of k [0.0, 0.6]. The phase transition character is analyzed based on the histogram method. The overall set of static critical indices is calculated in terms of the theory of the finite-dimensional scaling. It is shown that the class of the critical behavior universality of this model is conserved in the above range of values of k.
Interaction of macroparticles localized in Wigner–Seitz cells of various types of cubic lattices in an equilibrium plasma
The interaction of two charged point macroparticles located in Wigner–Seitz cells of simple cubic (SC), body-centered cubic (BCC), or face-centered cubic (FCC) lattices in an equilibrium plasma has been studied within the Debye approximation or, more specifically, based on the linearized Poisson–Boltzmann model. The shape of the outer boundary is shown to exert a strong influence on the pattern of electrostatic interaction between the two macroparticles, which transforms from repulsion at small interparticle distances to attraction as the interparticle distance approaches half the length of the computational cell. The macroparticle pair interaction potential in an equilibrium plasma is shown to be nevertheless the Debye one and purely repulsive for likely charged macroparticles.
Reversible Nanoparticle Cubic Lattices in Blue Phase Liquid Crystals
Blue phases (BPs), a distinct class of liquid crystals (LCs) with 3D periodic ordering of double twist cylinders involving orthogonal helical director twists, have been theoretically studied as potential templates for tunable colloidal crystals. Here, we report the spontaneous formation of thermally reversible, cubic crystal nanoparticle (NP) assemblies in BPs. Gold NPs, functionalized to be highly miscible in cyanobiphenyl-based LCs, were dispersed in BP mixtures and characterized by polarized optical microscopy and synchrotron small-angle X-ray scattering (SAXS). The NPs assemble by selectively migrating to periodic strong trapping sites in the BP disclination lines. The NP lattice, remarkably robust given the small particle size (4.5 nm diameter), is commensurate with that of the BP matrix. At the BP I to BP II phase transition, the NP lattice reversibly switches between two different cubic structures. The simultaneous presence of two different symmetries in a single material presents an interesting opportunity to develop novel dynamic optical materials.
S U ( 2 ) principal chiral model with tensor renormalization group on a cubic lattice
We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean S U ( 2 ) principal chiral field model with the triad tensor renormalization group and the anisotropic tensor renormalization group methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step closer to studying finite-density quantum chromodynamics in four dimensions using tensor network methods. Published by the American Physical Society 2024
Barium titanate nanoparticles: Short-range lattice distortions with long-range cubic order
Barium titanate (BTO) nanoparticles (sizes 10 to 500 nm) exhibit a displacement of the Ti atom from the center of the Perovskite unit cell as inferred from synchrotron X-ray diffraction patterns (XRD) analyzed using atomic pair distribution functions (PDFs). Fits to PDFs acquired at temperatures of 20° to 220°C indicate that these Ti displacements (~ 0.1 Å) are comparable to or even greater than those in the bulk material. Moreover, these displacements persist at temperatures well above 120°C where the tetragonal to pseudo-cubic phase transition occurs in the bulk. Tetragonal Raman spectral lines were observed for all sizes of these BTO nanoparticles and confirm a distorted unit cell up to 120°C. Above 120°C, the small BTO nanoparticles (10, 50, 100 nm) continue to display tetragonal Raman lines, though with slowly decreasing amplitudes as the temperature rises. In contrast, the tetragonal Raman lines of large BTO nanoparticles (300, 400, 500 nm) disappear abruptly above 120°C, suggestive of bulk material. Indeed, fits to large-particle X-ray PDFs over the range 20-60 Å reveal a sharp, long-range structural change toward a cubic lattice at 120°C, again consistent with bulk material. This sharp, long-range structural change is absent in the small particles. In fact, laboratory XRD Bragg peak profiles for the small BTO particles appear to be singlets at 20°C, indicating that significant long-range cubic order already exists at room temperature. As temperature rises, this long-range cubic order is gradually reinforced as inferred from long-range fits of the small particle PDFs. By combining information from X-ray PDFs, Raman spectra, and Bragg peak profiles, we conclude that small BTO nanoparticles exhibit both short-range (unit-cell) distortion and long-range (mesoscale) cubic order from 20° to 220°C, while the large nanoparticles behave as bulk material, differing from small particles only by exhibiting long-range tetragonal order below 120°C and a mesoscale structural phase change at 120°C.
Structure of One-Dimensional Rubidium and Silver Iodide Crystals in the Channels of Single-Walled Carbon Nanotubes
The structures of one-dimensional (1D) RbI, AgI, and RbAg{sub 4}I{sub 5} crystals inside single-walled carbon nanotube (SWCNT) channels of 1D crystal@SWCNT nanocomposites formed by the capillary technique have been studied by high-resolution (scanning) transmission electron microscopy and computer modeling. 1D RbI crystals form a cubic lattice in a limited space, while 1D AgI crystals form a hexagonal lattice, as in their ternary compounds. The 1D RbAg{sub 4}I{sub 5} structure differs from known bulk analogs and can be described by a distorted cubic lattice formed in two different directions.
Monte Carlo simulations of lattice models for single polymer systems
Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length N∼O(10{sup 4}). Based on the standard simple cubic lattice model (SCLM) with fixed bond length and the bond fluctuation model (BFM) with bond lengths in a range between 2 and √(10), we investigate the conformations of polymer chains described by self-avoiding walks on the simple cubic lattice, and by random walks and non-reversible random walks in the absence of excluded volume interactions. In addition to flexible chains, we also extend our study to semiflexible chains for different stiffness controlled by a bending potential. The persistence lengths of chains extracted from the orientational correlations are estimated for all cases. We show that chains based on the BFM are more flexible than those based on the SCLM for a fixed bending energy. The microscopic differences between these two lattice models are discussed and the theoretical predictions of scaling laws given in the literature are checked and verified. Our simulations clarify that a different mapping ratio between the coarse-grained models and the atomistically realistic description of polymers is required in a coarse-graining approach due to the different crossovers to the asymptotic behavior.
Local and average structures of BaTiO[subscript 3]-Bi(Zn[subscript 1/2]Ti[subscript 1/2])O[subscript 3]
Abstract not provided
Classification of Arnold-Beltrami flows and their hidden symmetries
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold’s theorem stating that, for flows taking place on compact three manifolds ℳ{sub 3}, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★{sub g }d, which can be solved by using time-honored harmonic analysis. Taking for ℳ{sub 3}, a torus T {sup 3} constructed as ℝ{sup 3}/Λ, where Λ is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B {sub A }of three-vectors in the momentum lattice *Λ. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group GA{sub Λ} which contains all space groups as proper subgroups. We show that the ★{sub g }d eigenfunctions are naturally arranged into irreducible representations of GA{sub Λ} and by means of a systematic use of the branching rules with respect to various possible subgroups H{sub i}⊂GA{sub Λ} we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O{sub 24} and the Universal Classifying Group GA{sub cubic} is a finite group G{sub 1536} of order |G{sub 1536}| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O{sub 24} orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G{sub 1536}. In this way we obtain an exhaustive classification of all generalized ABC-flows and of their hidden symmetries. We make several conceptual comments about the need of a field-theory yielding Beltrami equation as a field equation and/or an instanton equation and on the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that are different from the non-linear one proposed by Arnold and possibly make contact with M-theory and the geometry of flux-compactifications.
Disordered Supersolids in the Extended Bose-Hubbard Model
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.
Publisher Correction: Disordered Supersolids in the Extended Bose-Hubbard Model
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But we also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.