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arXiv:2311.13393 · Physical review. B./Physical review. B

Thermodynamics of the spin- 12 Heisenberg antiferromagnet on the star lattice

Adrien Reingruber, Nils Caci, Stefan Weßel, Johannes Richter

Published Mar 11, 2024• 5 citations
arXivHTMLPDF

Abstract

Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.

DOI
10.1103/physrevb.109.125120

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Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.
We explore the frustrated spin-12\frac{1}{2}21​ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) intertriangle couplings (Je<0{J}_{e}<0Je​<0), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening Je{J}_{e}Je​, the system exhibits a universal scaling behavior either with or without a magnetic field hhh: the order parameter, the five critical fields that separate the ${J}_{e}\text{\ensuremath{-}}h$ ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on Je{J}_{e}Je​. Our work implies that the spin-1 VBCs can be stabilized by introducing small FM couplings in the geometrically frustrated spin-12\frac{1}{2}21​ systems.
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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.
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