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arXiv:2312.01783 · Nano Letters

Designer Spin Models in Tunable Two-Dimensional Nanographene Lattices

J. C. G. Henriques, Mar Ferri-Cortés, Joaquín Fernández-Rossier

Published Mar 1, 2024• 7 citations
arXivHTMLPDF

Abstract

High Resolution Image Download MS PowerPoint Slide Motivated by recent experimental breakthroughs, we propose a strategy for designing two-dimensional spin–lattices with competing interactions that lead to nontrivial emergent quantum states. We consider S = 1 / 2 nanographenes with C 3 symmetry as building blocks, and we leverage the potential to control both the sign and the strength of exchange with first neighbors to build a family of spin models. Specifically, we consider the case of a Heisenberg model in a triangle-decorated honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions whose ratio can be varied in a wide range. On the basis of the exact diagonalization of both Fermionic and spin models, we predict a quantum phase transition between a valence bond crystal of spin singlets with triplon excitations living in a Kagomé lattice and a Néel phase of effective S = 3 / 2 in the limit of dominant ferromagnetic interactions.

DOI
10.1021/acs.nanolett.3c04915

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High Resolution Image Download MS PowerPoint Slide Motivated by recent experimental breakthroughs, we propose a strategy for designing two-dimensional spin–lattices with competing interactions that lead to nontrivial emergent quantum states. We consider S = 1 / 2 nanographenes with C 3 symmetry as building blocks, and we leverage the potential to control both the sign and the strength of exchange with first neighbors to build a family of spin models. Specifically, we consider the case of a Heisenberg model in a triangle-decorated honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions whose ratio can be varied in a wide range. On the basis of the exact diagonalization of both Fermionic and spin models, we predict a quantum phase transition between a valence bond crystal of spin singlets with triplon excitations living in a Kagomé lattice and a Néel phase of effective S = 3 / 2 in the limit of dominant ferromagnetic interactions.
We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks.
The interplay of frustrated interactions and lattice geometry can lead to a variety of exotic quantum phases. Here we unearth a particularly rich phase diagram of the Kitaev-Heisenberg model on the star lattice, a triangle decorated honeycomb lattice breaking sublattice symmetry. In the antiferromagnetic regime, the interplay of Heisenberg coupling and geometric frustration leads to the formation of valence bond solid (VBS) phases—a singlet VBS and a bond selective triplet VBS stabilized by the Kitaev exchange. We show that the ratio of the Kitaev versus Heisenberg exchange tunes between these VBS phases and chiral quantum spin-liquid regimes. Remarkably, the VBS phases host a whole variety of chiral triplon excitations with high Chern numbers in the presence of a weak magnetic field. We discuss our results in light of a recently synthesized star lattice material and other decorated lattice systems. Published by the American Physical Society 2024
Magnetic nanographenes are emerging as versatile building blocks for artificial spin lattices, enabling the exploration of flagship one-dimensional quantum-magnetism models with unprecedented control. The spin-1 Heisenberg model, including bilinear and biquadratic exchange, was first realized using [3]-triangulenes, revealing the Haldane phase. More recently, Clar’s goblets enabled the spin-1/2 Heisenberg model with exchange alternation, uncovering additional topological phases. Here we show that spin-1 nanographenes can be used to explore bond-alternating chains both in the Haldane phase and beyond it, in a dimerized phase with emergent edge spin-1. We use density matrix renormalization group (DMRG) to analyze how biquadratic exchange, which is known to be large in spin-1 nanographenes, determines the phase transition boundary. Combining multiconfigurational and first-principles calculations, we identify two realistic candidates to realize these two different phases: the recently synthesized extended Clar’s goblet and a passivated [4]-triangulene. We demonstrate how to distinguish these phases experimentally using inelastic electron tunneling spectroscopy, paving the way for their observation.
The quantum spin liquid is an emergent state of matter, which has attracted a lot of recent attention. I will review recent numerical progress based on the density matrix renormalization calculations in identifying gapped spin liquid in twodimensional frustrated spin systems. I will first focus on extended model with Heisenberg exchange couplings on kagome lattice and demonstrate a topological state with fractionalized spinon and emergent gauge field clearly shown in numerical simulations. I will present concrete results on the quantum phase diagram of the extended kagome Heisenberg model, and compare that with the phase diagrams of the square and honeycomb lattice models with the dominant plaquette valence bond phase in nonmagnetic region. I will discuss numerical effort and theoretical challenge in fully pinning down the nature of the gapped topological phase, and also the nature of the quantum phase transitions in these Heisenberg systems.
We study the ground-state phase diagram of the quantum spin-1/2\text{spin-}1/2spin-1/2 Heisenberg model on the kagome lattice with first- (J1<0)({J}_{1}<0)(J1​<0), second- (J2<0)({J}_{2}<0)(J2​<0), and third-neighbor interactions (Jd>0)({J}_{d}>0)(Jd​>0) by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the Jd-dominant{J}_{d}\text{-dominant}Jd​-dominant regime in terms of three sets of spin chains weakly coupled by the ferromagnetic interchain interactions J1,2{J}_{1,2}J1,2​. When either J1{J}_{1}J1​ or J2{J}_{2}J2​ is much stronger than the other one, the model is found to support one of two cuboctohedral phases, cuboc1, and cuboc2. These cuboc states host noncoplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime ${J}_{1}\ensuremath{\simeq}{J}_{2}$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional quantum antiferromagnet. We find no evidence of either the one-dimensional gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean-field theories.
We study the ground-state phase diagram of the spin-1/21/21/2 antiferromagnetic Heisenberg model on the square-kagome lattice using infinite projected entangled-pair states (iPEPS). By systematically varying the ratio of exchange couplings on triangular and square plaquettes, we establish a complete quantum phase diagram in the thermodynamic limit. In the intermediate-coupling regime, we identify four distinct nonmagnetic phases that are unambiguously characterized as valence-bond crystals (VBCs) by their symmetry-inequivalent patterns of strong and weak spin-spin correlations. These include a plaquette crossed-dimer VBC, a loop-six VBC stabilized around the isotropic point, a generalized pinwheel VBC with reduced rotational symmetry, and a decorated loop-six VBC proximate to ferrimagnetic order. We determine the phase boundaries using a combination of bond-resolved correlation functions, entanglement entropy, and magnetization. For transitions not accompanied by sharp entanglement signatures, we extract the spin gap from finite-field simulations, allowing us to distinguish gapped and gapless VBC phases. At larger coupling ratios, the system undergoes transitions into imperfect and perfect ferrimagnetic states. Our results resolve long-standing ambiguities in the square-kagome Heisenberg model and provide a quantitatively reliable reference for future theoretical and experimental studies of frustrated quantum magnets.