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arXiv:1308.3988 · Physical Review B

Featureless quantum spin liquid, 13 -magnetization plateau state, and exotic thermodynamic properties of the spin- 12 frustrated Heisenberg antiferromagnet on an infinite Husimi lattice

Tao Liu, Shi-Ju Ran, Wei Li, Xin Yan, Yang Zhao, Gang Su

Published Feb 24, 2014• 20 citations
arXivHTMLPDF

Abstract

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 $1/3$-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.

DOI
10.1103/physrevb.89.054426

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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 e0=\ensuremath−0.4343(1){e}_{0}=\ensuremath{-}0.4343(1)e0​=\ensuremath−0.4343(1), which is very close to that [e0=\ensuremath−0.4386(5){e}_{0}=\ensuremath{-}0.4386(5)e0​=\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.
We investigate the ground state and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnet on an infinite octa-kagome lattice by utilizing state-of-the-art tensor network-based numerical methods. It is shown that the ground state has a vanishing local magnetization and possesses a 1/21/21/2-magnetization plateau with an up-down-up-up spin configuration. A quantum phase transition at the critical coupling ratio Jd/Jt=0.6{J}_{d}/{J}_{t}=0.6Jd​/Jt​=0.6 is found. When 0<Jd/Jt<0.60<{J}_{d}/{J}_{t}<0.60<Jd​/Jt​<0.6, the system is in a valence bond state, where an obvious zero-magnetization plateau is observed, implying a gapful spin excitation; when Jd/Jt>0.6{J}_{d}/{J}_{t}>0.6Jd​/Jt​>0.6, the system exhibits a gapless excitation, in which the dimer-dimer correlation is found decaying in a power law, while the spin-spin and chiral-chiral correlation functions decay exponentially. At the isotropic point (Jd/Jt=1{J}_{d}/{J}_{t}=1Jd​/Jt​=1), we unveil that at low temperature TTT, the specific heat depends linearly on TTT, and the susceptibility tends to a constant for $T\ensuremath{\rightarrow}0$, giving rise to a Wilson ratio around unity, implying that the system under interest is a fermionic algebraic quantum spin liquid.
Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the sqrt[3]×sqrt[3] state (i.e., the state with 120^{∘} spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m_{s}=1/3,23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T^{2} behavior, and the susceptibility approaches a finite constant as T→0. Our TN results of thermodynamic properties are compared with those from high-temperature series expansion. In addition, we disclose a quantum phase transition between q=0 state (i.e., the state with 120^{∘} spin configuration within a unit cell containing three sites) and sqrt[3]×sqrt[3] state in a spin-3/2 kagome XXZ model at the critical point Δ_{c}=0.54. This study provides reliable and useful information for further explorations on high-spin kagome physics.
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​.
The nature of the 1/9-magnetization plateau of the spin-12\frac{1}{2}21​ kagome Heisenberg antiferromagnet remains controversial due to the exotic physical properties and high complexity induced by the geometrical frustration. Instead of a Z3{\mathbb{Z}}_{3}Z3​ quantum spin liquid revealed on a cylinder, we show on an infinite-size lattice that the 1/9 plateau can be described by a valence bond crystal (VBC) that breaks spatial translational invariance. Consistent results are achieved by two accurate tensor network methods, namely the full-update infinite projected-entangled pair states and the projected-entangled simplex states. The VBC exhibits an hourglass pattern with $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spatial symmetry, demonstrated by magnetizations, bond energies, and three-body correlators. The spatial inversion symmetry in the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ VBC is instantly broken with the presence of the difference between the coupling strengths in the up and down triangles, suggesting the existence of gapless excitations. The gapless nature of the 1/9 plateau is further indicated by the scaling behaviors of the entanglement entropy and the correlation length, which indicate a c=1c=1c=1 conformal field theory.
Quantum fluctuations from frustration can trigger quantum spin liquids (QSLs) at zero temperature. However, it is unclear how thermal fluctuations affect a QSL. We employ state-of-the-art tensor network-based methods to explore the spin-1/21/21/2 kagom\'e Heisenberg antiferromagnet (KHA). Its ground state is shown to be a gapless U(1) QSL. By studying the behaviors of specific heat and magnetic susceptibility, we propose a finite-temperature phase diagram for the spin-1/2 KHA in a magnetic field. It is unveiled that there exists an algebraic paramagnetic liquid (APL) that possesses both paramagnetic and algebraic behaviors inherited from the QSL. The APL is induced under the interplay between quantum fluctuations from geometrical frustration and thermal fluctuations. Our work suggests that even when the QSL at zero temperature is frozen into a solid state by a magnetic field, proper thermal fluctuations could melt the system into a liquid-like state. We speculate that an APL phase could generally emerge after proper thermal fluctuations intervene in a gapless QSL.
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.