Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch
SciPost Phys. 14, 052 (2023) ·
published 28 March 2023

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The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearestneighbour interactions $J$ and antiferromagnetic nextnearestneighbour 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 spinspin 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 finitesystem sizes typically employed in numerical simulations. A faithful treatment thus requires the use of stateoftheart 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 densitymatrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowestenergy 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

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We compute groundstate properties of the isotropic, antiferromagnetic Heisenberg model on the sodalite cage geometry. This is a 60spin spherical molecule with 24 vertexsharing tetrahedra which can be regarded as a molecular analogue of a capped kagome lattice and which has been synthesized with highspin rareearth atoms. Here, we focus on the $S=1/2$ case where quantum effects are strongest. We employ the SU(2)symmetric densitymatrix 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 zeropoint entropy is $S=\ln(182)\approx 5.2$ in units of the Boltzmann constant.
ShengHsuan Lin, Björn Sbierski, Florian Dorfner, Christoph Karrasch, Fabian HeidrichMeisner
SciPost Phys. 4, 002 (2018) ·
published 18 January 2018

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We study the finiteenergy 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 Luttingerliquid phase persists at weak disorder in the ground state, which is a wellknown result. We revisit the groundstate phase diagram and show that the recently introduced occupationspectrum discontinuity computed from the eigenspectrum of oneparticle density matrices is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization scheme to study the finitesize dependence of the conductance, which resolves the existence of the Luttinger liquid as well and is computationally cheap. Our main results concern the finiteenergy density case. Using exact diagonalization and by computing various established measures of the manybody localizationdelocalization transition, we argue that the zerotemperature Luttinger liquid smoothly evolves into a finiteenergy density ergodic phase without any intermediate phase transition.