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Ground-state and finite-temperature properties of a special class of exactly solvable Ising-Heisenberg planar models are examined using the generalized decoration-iteration and star-triangle mapping transformations. The investigated spin…
In this study, we show that any system consisting of magnetic dipoles forming ordered or disordered configurations can be simplified to a form mathematically equivalent to a system consisting of two magnetic dipoles. It is shown that the…
Magnetic frustration, the competition among exchange interactions, often leads to novel magnetic ground states with unique physical properties which can hinge on details of interactions that are otherwise difficult to observe. Such states…
The entanglement in many-electron states is investigated using a global entanglement measure, viz. average site mixedness. We have examined metallic states of noninteracting electrons, Nagaoka and Gutzwiller states of strongly-correlated…
We classify all possible 36 gap-opening instabilities in graphene-like structures in two dimensions, i.e., masses of Dirac Hamiltonian when the spin, valley, and superconducting channels are included. These 36 order parameters break up into…
Structures of excited states in $^{14}$C are investigated with a method of $\beta$-$\gamma$ constraint antisymmetrized molecular dynamics in combination with the generator coordinate method. Various excited states with the developed…
When electron correlations are important it is often necessary to use numerical methods to solve the Hamiltonian for a finite system (cluster) "exactly". Unfortunately, such methods are restricted to small systems. We propose to combine the…
We prove that Nagaoka's theorem, that the large-$U$ Hubbard model with exactly one hole is ferromagnetic, holds for any balanced Hamiltonian. Simply put, if a positive bond encodes friendship and a negative bond encodes enmity, then balance…
We investigate the geometry of the four qubit systems by means of algebraic geometry and invariant theory, which allows us to interpret certain entangled states as algebraic varieties. More precisely we describe the nullcone, i.e., the set…
The average number of constraints per particle $< C_{total} >$ in mechanically stable systems of Platonic solids (except cubes) approaches the isostatic limit at the jamming point ($< C_{total} > \rightarrow 12$), though average number of…
Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find…
Observations of galaxy clusters show that the intracluster medium (ICM) is likely to be turbulent and is certainly magnetized. The properties of this magnetized turbulence are determined both by fundamental nonlinear magnetohydrodynamic…
We study the geometric and physical effects of quadrupolar configurations of disclinations using a conformal metric approach in $(2+1)$ dimensions. Two cases are considered: a linear quadrupole, inducing anisotropic curvature with a…
We study the equilibrium properties of a model of magnetic diblock copolymer where each monomer is decorated with an Ising-like spin. Spins interact ferromagnetically within each block and antiferromagnetically across blocks, generating…
We investigate the emergence of altermagnetism -- a collinear magnetic phase characterized by large non-relativistic spin splitting and zero net magnetization -- driven by electronic correlations on 3x3 geometrically frustrated square…
Geometrically frustrated magnetic molecules have attracted a lot of interest in the field of molecular magnetism as well as frustrated Heisenberg antiferromagnets. In this article we demonstrate how an approximate diagonalization scheme can…
We classify the magnetic ground states of a 2D lattice of localized magnetic moments which are coupled to a superconducting substrate with Rashba-spin-orbit coupling. We discover a rich magnetic phase diagram with surprisingly complex…
The coherent dynamics of bubble clusters in liquid are of fundamental and industrial importance and are elusive due to the complex interactions of disordered bubble oscillations. Here we introduce and demonstrate unsupervised learning of…
Competing interactions in Quantum Materials induce novel states of matter such as frustrated magnets, an extensive field of research both from the theoretical and experimental perspectives. Here, we show that competing energy scales present…
In the triangular layered magnet PdCrO2 the intralayer magnetic interactions are strong, however the lattice structure frustrates interlayer interactions. In spite of this, long-range, 120$^\circ$ antiferromagnetic order condenses at $T_N =…