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arXiv:1807.00318 · Physical review. B./Physical review. B

Spin- 12 Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks

Saeed S. Jahromi, Román Orús

Published Oct 3, 2018• 39 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.98.155108

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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.
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
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Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor J1{J}_{1}J1​ and second-neighbor J2{J}_{2}J2​ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. N\'eel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio J2/J1{J}_{2}/{J}_{1}J2​/J1​, we find strong evidence for a continuous transition to a nonmagnetic phase at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For $0.23\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.36$, a gapless Z2{Z}_{2}Z2​ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the N\'eel order melts, this ordered state becomes clearly favored only for ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.3$. Finally, for $0.36\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the N\'eel antiferromagnet from the plaquette valence-bond solid.
Using a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q . We confirm the existence of a phase transition separating antiferromagnetism at J / Q > J c / Q from a valence bond solid (VBS) state at J / Q < J c / Q . Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80 2 , we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J / Q > J c / Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J / Q < J c / Q and we show that long but finite antiferromagnetic correlations are still present.
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