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arXiv:1711.01001 · 中国科学通报：英文版

Thermodynamics of spin-1/2 Kagomé Heisenberg antiferromagnet: algebraic paramagnetic liquid and finite-temperature phase diagram

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

Published Nov 22, 2018• 58 citations
arXivHTMLPDF
DOI
10.1016/j.scib.2018.11.007

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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-$1/2$ 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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A Phenomenological Theory for the Z2Z_2Z2​ Spin-Liquid Phase of the S=1/2S=1/2S=1/2 Kagome Heisenberg Antiferromagnet
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.
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.
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.