Contributor info: Prof. Christoph Karrasch

Roman Rausch, Christoph Karrasch

SciPost Phys. Core 9, 003 (2026) · published 20 January 2026 | Toggle abstract · pdf

Highly-symmetric molecules often exhibit degenerate tight-binding states at the Fermi edge. This typically results in a magnetic ground state if small interactions are introduced in accordance with Hund's rule. In some cases, Hund's rule may be broken, which signals pair binding and goes hand-in-hand with an attractive pair-binding energy. We investigate pair binding and Hund's rule breaking for the Hubbard model on high-symmetry fullerenes C$_{20}$, C$_{20}$, C$_{40}$, and C$_{60}$ by using large-scale density-matrix renormalization group calculations. We exploit the SU(2) spin symmetry, the U(1) charge symmetry, and optionally the $\mathbb{Z}_N$ spatial rotation symmetry of the problem. For C$_{20}$, our results agree well with available exact-diagonalization data, but our approach is numerically much cheaper. We find a Mott transition at $U_c\sim2.2t$, which is much smaller than the previously reported value of $U_c\sim4.1t$ that was extrapolated from a few datapoints. We compute the pair-binding energy for arbitrary values of $U$ and observe that it remains overall repulsive. For larger fullerenes, we are not able to evaluate the pair binding energy with sufficient precision, but we can still investigate Hund's rule breaking. For C$_{28}$, we find that Hund's rule is fulfilled with a magnetic spin-2 ground state that transitions to a spin-1 state at $U_{c,1}\sim 5.4t$ before the eventual Mott transition to a spin singlet takes place at $U_{c,2}\sim 11.6t$. For C$_{40}$, Hund's rule is broken in the singlet ground state at half filling, but is restored if the system is doped with one electron. Hund's rule is also broken for C$_{60}$, and the doping with two or three electrons results in a minimum-spin state. Our results are consistent with an electronic mechanism of superconductivity for C$_{60}$ lattices. We speculate that the high geometric frustration of small fullerenes is detrimental to pair binding.

Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch

SciPost Phys. 14, 052 (2023) · published 28 March 2023 | Toggle abstract · pdf

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 $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spin-spin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>-\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ 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.

Roman Rausch, Matthias Peschke, Cassian Plorin, Christoph Karrasch

SciPost Phys. 12, 143 (2022) · published 2 May 2022 | Toggle abstract · pdf

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.

Sheng-Hsuan Lin, Björn Sbierski, Florian Dorfner, Christoph Karrasch, Fabian Heidrich-Meisner

SciPost Phys. 4, 002 (2018) · published 18 January 2018 | Toggle abstract · pdf

We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of one-particle density matrices is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization scheme to study the finite-size dependence of the conductance, which resolves the existence of the Luttinger liquid as well and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.