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Finite-Temperature Phase Diagram and Algebraic Paramagnetic Liquid in the Spin-1/2 Kagom\'e Heisenberg Antiferromagnet

Xi Chen, Shi-Ju Ran, Tao Liu, Cheng Peng, Yizhen Huang, Gang Su

Published Nov 3, 2017• 1 citation
OpenAlex

Abstract

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-$1/2$ 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.

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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.
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.
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.
Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation is a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1J_1J1​-J2J_2J2​ kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing ∣J2∣/J1|J_2|/J_1∣J2​∣/J1​ causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.
Quantum spin liquids (QSL) are phases of matter which are distinguished not by the symmetries they break, but rather by the patterns of entanglement within them. Although these entanglement properties have been widely discussed for ground states, the way in which QSL form at finite temperature remains an open question. Here we introduce a method of characterizing both the depth and spatial structure of entanglement, and use this to explore how patterns of entanglement form as temperature is reduced in two widely studied models of QSL, the Kitaev honeycomb model, and the spin-1/2 Heisenberg antiferromagnet on a Kagome lattice. These results enable us to evaluate both the temperature at which spins within the high-temperature paramagnet first become entangled, and the temperature at which the system first develops the structured, multipartite entanglement characteristic of its QSL ground state.
Recent studies have revealed that the randomness-induced quantum spin liquid (QSL)-like state is stabilized in certain frustrated quantum magnets in two and three dimensions. In order to clarify the nature of this gapless QSL-like state, we investigate both zero- and finite-temperature properties of the random-bond one-dimensional (1D) s=12s=12s=12 Heisenberg model with the competing nearest-neighbor and next-nearest-neighbor antiferromagnetic interactions, J1J_1J1​ and J2J_2J2​, by means of the exact diagonalization, density-matrix renormalization-group and Hams--de Raedt methods. We find that, on increasing the frustration J2J_2J2​, the gapless nonmagnetic state stabilized in the unfrustrated model with J2=0J_2=0J2​=0, the {\it unfrustrated\} random-singlet (RS) state, exhibits a phase transition into different gapless nonmagnetic state, the {\it frustrated\} RS state. This frustrated RS state in 1D has properties quite similar to the randomness-induced QSL-like state recently identified in 2D and 3D frustrated magnets exhibiting the TTT-linear low-temperature (TTT) specific heat, while the unfrustrated RS state is more or less specific to the unfrustrated 1D system exhibiting the ∼1(log⁡T)3\sim 1(\log T)^3∼1(logT)3 low-TTT specific heat. Universal features and the robustness against perturbations of the frustrated RS state are emphasized.
We investigate the ground-state and finite-temperature properties of the bond-random s=1/2s=1/2s=1/2 Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions, J1J_1J1​ and J2J_2J2​, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration (J2/J1J_2/J_1J2​/J1​) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba3_33​CuSb2_22​O9_99​ and 6HB-Ba3_33​NiSb2_22​O9_99​ exhibiting the gapless QSL-like behaviors are discussed.