arXiv subjects

Cassian Plorin

Publications and source records attributed to Cassian Plorin.

5 recordsLinked to original sources

arXiv2024

The antiferromagnetic $S=1/2$ Heisenberg model on the ${\text{C}}_{60}$ fullerene geometry

We solve the quantum-mechanical antiferromagnetic Heisenberg model with spins positioned on vertices of the truncated icosahedron using the density-matrix renormalization group (DMRG). This describes magnetic properties of the undoped C$_{60}$ fullerene at half filling in the limit of strong on-site interaction $U$. We calculate the ground state and correlation functions for all possible distances, the lowest singlet and triplet excited states, as well as thermodynamic properties, namely the specific heat and spin susceptibility. We find that unlike smaller C$_{20}$ or C$_{32}$ that are solvable by exact diagonalization, the lowest excited state is a triplet rather than a singlet, indicating a reduced frustration due to the presence of many hexagon faces and the separation of the pentagonal faces, similar to what is found for the truncated tetrahedron. This implies that frustration may be tuneable within the fullerenes by changing their size. The spin-spin correlations are much stronger along the hexagon bonds and exponentially decrease with distance, so that the molecule is large enough not to be correlated across its whole extent. The specific heat shows a high-temperature peak and a low-temperature shoulder reminiscent of the kagome lattice, while the spin susceptibility shows a single broad peak and is very close to the one of C$_{20}$.

cond-mat.str-el↗

arXiv2024

Kondo Screening and Indirect Magnetic Exchange through a Conventional Superconductor Studied by the Density-Matrix Renormalization Group

The competition between the Kondo screening and indirect magnetic exchange in systems with two magnetic impurities coupled to a conventional s-wave superconductor gives rise to a nontrivial ground-state phase diagram. Here, we utilize the density-matrix renormalization group (DMRG) method and exploit the non-abelian spin-SU(2) symmetry to study the phase diagram for two quantum-spin-$\frac12$ impurities locally exchange coupled to large one-dimensional chains. The nonlocal inter-impurity exchange is treated as an emergent Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling. We find qualitatively different phase diagrams for impurity spins coupled to sites with odd or even distances $d$ on the chain and a partial-Kondo-screened spin-doublet phase that extends over the whole range of local exchange couplings $J$ in the limit of weak superconducting pairing strength $Δ$. Our numerical studies are complemented by exact diagonalization of small (quantum-box) systems and by perturbative-in-$J$ computations of the $d$ and $Δ$ dependent RKKY interaction. It is thereby demonstrated that the specific system geometry is essential for our understanding of magnetic impurity interactions in superconducting hosts, and thus for insights into the control of quantum-state properties in nanoparticle systems and topological superconductivity.

cond-mat.str-el↗

arXiv2024

Matrix-product state approach to the generalized nuclear pairing Hamiltonian

We show that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix-product state) despite the presence of long-range interactions. The ground state can be obtained using the density-matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used BCS (Bardeen-Cooper-Schrieffer) approach, and does not suffer from any mean-field artifacts. We apply this framework to compute the even-odd mass differences of all known lead isotopes from $^{178}$Pb to $^{220}$Pb in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. We also treat pairing with non-zero angular momentum and determine the lowest excited states in the full configuration space of one major shell, which we demonstrate for the $N=126$, $Z\geq 82$ isotones. To demonstrate the capabilities of the method beyond low-lying excitations, we calculate the first 100 excited states of $^{208}$Pb with singlet pairing and the two-neutron removal spectral function of $^{210}$Pb, which relates to a two-neutron pickup experiment.

nucl-th↗

arXiv2023

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $\avg{\vec{S}_i}$, the spiral can be detected via the connected spin-spin correlations $\avg{\vec{S}_i\cdot\vec{S}_j}-\avg{\vec{S}_i}\cdot\avg{\vec{S}_j}$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.

cond-mat.str-el↗

arXiv2022

Magnetic properties of a capped kagome molecule with 60 quantum spins

We compute ground-state properties of the isotropic, antiferromagnetic Heisenberg model on the sodalite cage geometry. This is a 60-spin spherical molecule with 24 vertex-sharing tetrahedra which can be regarded as a molecular analogue of a capped kagome lattice and which has been synthesized with high-spin rare-earth atoms. Here, we focus on the $S=1/2$ case where quantum effects are strongest. We employ the SU(2)-symmetric density-matrix renormalization group (DMRG). We find a threefold degenerate ground state that breaks the spatial symmetry and that splits up the molecule into three large parts which are almost decoupled from each other. This stands in sharp contrast to the behaviour of most known spherical molecules. On a methodological level, the disconnection leads to "glassy dynamics" within the DMRG that cannot be targeted via standard techniques. In the presence of finite magnetic fields, we find broad magnetization plateaus at 4/5, 3/5, and 1/5 of the saturation, which one can understand in terms of localized magnons, singlets, and doublets which are again nearly decoupled from each other. At the saturation field, the zero-point entropy is $S=\ln(182)\approx 5.2$ in units of the Boltzmann constant.

cond-mat.str-el↗