Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0711.2670

Spin waves and local magnetizations on the Penrose tiling

Attila Szallas·Anuradha Jagannathan
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider a Heisenberg antiferromagnet on the Penrose tiling, a quasiperiodic system having an inhomogeneous Neel-ordered ground state. Spin wave energies and wavefunctions are studied in the linear spin wave approximation. A linear dispersion law is found at low energies, as in other bipartite antiferromagnets, with an effective spin wave velocity lower than in the square lattice. Spatial properties of eigenmodes are characterized in several different ways. At low energies, eigenstates are relatively extended, and show multifractal scaling. At higher energies, states are more localized, and, depending on the energy, confined to sites of a specified coordination number. The ground state energy of this antiferromagnet, and local staggered magnetizations are calculated. Perpendicular space projections are presented in order to show the underlying simplicity of this "complex" ground state. A simple analytical model, the two-tier Heisenberg star, is presented to explain the staggered magnetization distribution in this antiferromagnetic system.

Explore related subjects

cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Attila Szallas, Anuradha Jagannathan. 2008-04-01. Spin waves and local magnetizations on the Penrose tiling. https://doi.org/10.1103/physrevb.77.104427

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Spontaneous Parity Breaking in Quantum Antiferromagnets on the Triangular Lattice

Frustration on the triangular lattice has long been a source of intriguing and often debated phases in many-body systems. Although symmetry analysis has been employed, the role of the seemingly trivial parity symmetry has received little attention. In this work, we show that phases induced by frustration are systematically shaped by an implicit rule-of-thumb associated with spontaneous parity breaking in weak longitudinal field. This principle enables us to anticipate and rationalize the regimes and conditions under which nontrivial phases emerge. For the spin-$S$ antiferromagnetic XXZ model, we demonstrate that a controversial parity-broken phase appears at intermediate values of $S$. In bilayer systems, enhanced frustration leads to additional phases, such as supersolids, whose properties can be classified by their characteristic parity features. Benefiting from our improved tensor network contraction techniques, we confirm these results through large-scale tensor-network calculations. This study offers an alternative viewpoint and a systematic approach for examining the interplay between spin, symmetry, and frustration in many-body systems.

cond-mat.str-el↗
arXiv2026

Directional Criticality and Higher-Order Flatness: Designing Van Hove Singularities in Three Dimensions

Van Hove singularities (VHSs) play a pivotal role in driving correlated electronic phenomena. Traditional classifications focus only on critical points where the band gradient vanishes in all directions. Here we establish a unified classification of VHSs in three-dimensional systems, characterized by the number of vanishing gradient components and Hessian eigenvalues: ordinary ($M$-type), higher-order ($T_1$, $T_2$, $T_3$), noncritical ordinary ($N_0$, $N_1$, $N_2$), and noncritical higher-order ($S_1$, $S_2$) types. Noncritical VHSs exhibit directional quenching: the gradient vanishes in a two-dimensional subspace while remaining finite along the orthogonal direction, yielding finite density-of-states enhancements with distinct energy dependencies. Using an $s$-orbital tight-binding model on the pyrochlore lattice with spin-orbit coupling, we demonstrate that all singularity classes emerge at distinct high-symmetry points through controlled tuning of the hopping ratio. This work establishes directional criticality and higher-order flatness as design principles for tailoring density-of-states enhancements in three-dimensional quantum materials.

cond-mat.str-el↗
arXiv2026

Quantum Rotors on the Fuzzy Sphere and the Cubic CFT

The three-dimensional cubic conformal field theory governs the critical behaviour of Heisenberg magnets with cubic anisotropy. Studying this theory non-perturbatively is challenging, because its most easily accessible observables are numerically very close to those of the more symmetric $O(3)$ model. In this work, we overcome this difficulty using the fuzzy sphere regularisation method. By adding a cubic-invariant two-body interaction to the quantum rotor Hamiltonian used for the $O(3)$ model, we break the continuous rotational symmetry by construction and unambiguously isolate the cubic critical point. Using exact diagonalisation and the density matrix renormalisation group, we calculate the scaling dimensions of several key operators, including the leading scalar singlets, and resolve the splitting of the $O(3)$ rank-two traceless symmetric tensor into the $E_g$ and $T_{2g}$ representations of the cubic group. Our results are consistent with existing Monte Carlo, conformal perturbation theory, and $\varepsilon$ expansion benchmarks, demonstrating the power of the fuzzy sphere in resolving closely spaced universality classes.

cond-mat.str-el↗