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arXiv:2211.16932 · Physical review. B./Physical review. B

Tensor network study of the spin- 12 Heisenberg antiferromagnet on the shuriken lattice

Philipp Schmoll, Augustine Kshetrimayum, Jan Naumann, Jens Eisert, Yasir Iqbal

Published Feb 7, 2023• 21 citations
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Abstract

We investigate the ground state of the spin $S=\frac{1}{2}$ Heisenberg antiferromagnet on the shuriken lattice, also in the presence of an external magnetic field. To this end, we employ two-dimensional tensor network techniques based on infinite projected entangled pair and simplex states considering states with different sizes of the unit cells. We show that a valence bond crystal with resonances over length six loops emerges as the ground state (at any given finite bond dimension) yielding the lowest reported estimate of the ground state energy ${E}_{0}/J=\ensuremath{-}0.4410\ifmmode\pm\else\textpm\fi{}0.0001$ for this model, estimated in the thermodynamic limit. We also study the model in the presence of an external magnetic field and find the emergence of 0, $\frac{1}{3}$, and $\frac{2}{3}$ magnetization plateaus. The $\frac{1}{3}$ and $\frac{2}{3}$ plateau states respect translation and point group symmetries and feature loop-four plaquette resonances.

DOI
10.1103/physrevb.107.064406

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We investigate the ground state of the spin S=12S=\frac{1}{2}S=21​ Heisenberg antiferromagnet on the shuriken lattice, also in the presence of an external magnetic field. To this end, we employ two-dimensional tensor network techniques based on infinite projected entangled pair and simplex states considering states with different sizes of the unit cells. We show that a valence bond crystal with resonances over length six loops emerges as the ground state (at any given finite bond dimension) yielding the lowest reported estimate of the ground state energy E0/J=\ensuremath−0.4410\ifmmode±\else\textpm\fi0.0001{E}_{0}/J=\ensuremath{-}0.4410\ifmmode\pm\else\textpm\fi{}0.0001E0​/J=\ensuremath−0.4410\ifmmode±\else\textpm\fi0.0001 for this model, estimated in the thermodynamic limit. We also study the model in the presence of an external magnetic field and find the emergence of 0, 13\frac{1}{3}31​, and 23\frac{2}{3}32​ magnetization plateaus. The 13\frac{1}{3}31​ and 23\frac{2}{3}32​ plateau states respect translation and point group symmetries and feature loop-four plaquette resonances.
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.
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We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on projected entangled simplex states. The nature of the ground state varies strongly with the spin quantum number SSS. For S=12S=\frac{1}{2}S=21​, it is an algebraic (gapless) quantum spin liquid. For S=1S=1S=1, it is a gapped, nonmagnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For S=2S=2S=2, it is a simplex-solid state with a spin gap and no symmetry breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For S=32S=\frac{3}{2}S=23​, and indeed for all spin values $S\ensuremath{\ge}\frac{5}{2}$, the ground states have ${120}^{\ensuremath{\circ}}$ antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of SSS, there is always a plateau in the magnetization at m=13m=\frac{1}{3}m=31​.
Quantum spin models on two-dimensional corner-sharing triangular arrangements, e.g., the kagome lattice, are fertile playgrounds for realizing exotic phases. Following the recent report of a gapless spin liquid in KCu6{}_{6}6​AlBiO4{}_{4}4​(SO4{}_{4}4​)5{}_{5}5​Cl, wherein the Cu2+{}^{2+}2+ spin-\textonehalf{} ions form a perfect two-dimensional shuriken lattice, the authors employ state-of-the-art quantum many-body approaches to reveal a pinwheel valence-bond-crystal ground state of the isotropic Heisenberg antiferromagnet. This work thus points to the important role of spatial anisotropy in triggering the gapless spin liquid, in contrast to the kagome material herbertsmithite.
Frustrated quantum antiferromagnetism is an important physical phenomena leading to many of the key properties of quantum matter, such as quantum spin liquids and topological order. Here, the authors employ novel techniques based on tensor network methods for the triangle-honeycomb lattice in order to compute ground-state properties of a frustrated quantum antiferromagnet on the star lattice, with high accuracy, in the thermodynamic limit. Importantly, their findings contradict some of the existing results in the literature on this model. In particular, they find a new resonating valence-bond solid (VBS) phase that had not been observed before, as well as a different VBS structure at the isotropic point than the one previously conjectured by other methods. Moreover, by using tensor network techniques, they also determine the existence of a continuous quantum phase transition in the system between different VBS orders.