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arXiv:1510.08655 · Physical review. B./Physical review. B

Heisenberg antiferromagnet on the Husimi lattice

Haijun Liao, Z. Y. Xie, J. Chen, Xiaoyang Han, Haidong Xie, Bruce Normand, Tao Xiang

Published Feb 29, 2016• 18 citations
arXivHTMLPDF

Abstract

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 $S$. For $S=\frac{1}{2}$, it is an algebraic (gapless) quantum spin liquid. For $S=1$, it is a gapped, nonmagnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For $S=2$, 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 $S=\frac{3}{2}$, 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 $S$, there is always a plateau in the magnetization at $m=\frac{1}{3}$.

DOI
10.1103/physrevb.93.075154

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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≥52S\ensuremath{\ge}\frac{5}{2}S\ensuremath≥25​, the ground states have 120\ensuremath∘{120}^{\ensuremath{\circ}}120\ensuremath∘ 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​.
Spin-SSS Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to S=2S=2S=2 directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the $\frac{1}{3}\mathrm{th},\left(1\ensuremath{-}\frac{2}{9S}\right)\mathrm{th}$, and $\left(1\ensuremath{-}\frac{1}{9S}\right)\mathrm{th}$ of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-12\frac{1}{2}21​ 19\frac{1}{9}91​ plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation U(1)U(1)U(1) symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the S=2S=2S=2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.
The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S=1/2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.
By utilizing tensor-network-based methods, we investigate the zero- and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnetic (HAF) model on an infinite Husimi lattice that contains 3/2 sites per triangle. The ground state of this model is found to possess vanishing local magnetization and is featureless; the spin-spin and dimer-dimer correlation functions are verified to decay exponentially, and its ground-state energy per site is determined to be ${e}_{0}=\ensuremath{-}0.4343(1)$, which is very close to that [${e}_{0}=\ensuremath{-}0.4386(5)$] of the intriguing kagome HAF model. The magnetization curve shows the absence of a zero-magnetization plateau, implying a gapless excitation. A 1/31/31/3-magnetization plateau with spin-up-up-down state is observed, which is selected and stabilized by quantum fluctuations. A ground-state phase diagram under magnetic fields is presented. Moreover, both magnetic susceptibility and the specific heat are studied, whose low-temperature behaviors reinforce the conclusion that the HAF model on the infinite Husimi lattice owns a gapless and featureless spin-liquid ground state.
The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S ¼ 1=2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date.We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement.By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid.We discuss the comparison with other numerical studies and the physical interpretation of this result.
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 ${E}_{0}/J=\ensuremath{-}0.4410\ifmmode\pm\else\textpm\fi{}0.0001$ 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, 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 investigate the spin-1/21/21/2 Heisenberg antiferromagnet on the ruby lattice with uniform first- and second-neighbor interactions, which forms a two-dimensional network of corner-sharing tetrahedra. Using infinite projected entangled pair states (iPEPS), we study the ground state of the system to find that it assumes a gapped threefold-degenerate simplex crystal ground state, with strong singlets formed on pairs of neighboring triangles. We argue that the formation of the simplex singlet ground state at the isotropic point relates to the weak inter-triangle coupling limit where an effective spin-chirality Hamiltonian on the honeycomb lattice exhibits an extensively degenerate ground state manifold of singlet coverings at the mean-field level. Under an applied Zeeman field, the iPEPS simulations uncover magnetization plateaus at m/ms=0,1/3,1/2,m/m_s = 0, 1/3, 1/2,m/ms​=0,1/3,1/2, and 2/32/32/3, separated by intermediate supersolid phases, all breaking the sixfold rotational symmetry of the lattice. Unlike the checkerboard lattice, these plateaus cannot be described by strongly localized magnons.