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arXiv:2009.00070 · Physical review. B./Physical review. B

Vestigial anyon condensation in kagome quantum spin liquids

Yan-Cheng Wang, Zheng Yan, Chenjie Wang, Yang Qi, Zi Yang Meng

Published Jan 6, 2021• 21 citations
arXivHTMLPDF

Abstract

We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a ${\mathbb{Z}}_{2}\ensuremath{\boxtimes}{\mathbb{Z}}_{2}$ topological order to a ${\mathbb{Z}}_{2}$ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.

DOI
10.1103/physrevb.103.014408

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We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a Z2\ensuremath⊠Z2{\mathbb{Z}}_{2}\ensuremath{\boxtimes}{\mathbb{Z}}_{2}Z2​\ensuremath⊠Z2​ topological order to a Z2{\mathbb{Z}}_{2}Z2​ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.
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Transitions between quantum spin liquids (QSLs) are fundamental problems lying beyond the Landau paradigm and requiring a deep understanding of the entanglement structures of QSLs called topological orders. The novel concept of anyon condensation has been proposed as a theoretical mechanism, predicting various possible transitions between topological orders, but it has long been elusive to confirm the mechanism in quantum spin systems. Here, we introduce a concrete spin model that incarnates the mechanism of the anyon condensation transition. Our model harbors two topological QSLs in different parameter regions, a non-Abelian Kitaev spin liquid (KSL) bilayer state and a resonating valence bond (RVB) state. The bilayer-KSL-to-RVB transition indeed occurs by the mechanism of anyon condensation, which we identify by using parton theories and exact diagonalization studies. Moreover, we observe “anyon confinement” phenomena in our numerical results, akin to the quark confinement in high-energy physics. Namely, non-Abelian Ising anyons of the bilayer KSL are confined in the transition to the RVB state. Implications and extensions of this study are discussed in various aspects such as (i) anyon-condensed multilayer construction of Kitaev's 16-fold way of anyon theories, (ii) an additional vison condensation transition from the RVB to a valence bond solid in the Kitaev bilayer system, (iii) dynamical anyon condensation in a non-Hermitian Kitaev bilayer, (iv) generalizations of our model to other lattice geometries, and (v) experimental realizations. This work puts together the two fascinating QSLs that are extensively studied in modern condensed matter and quantum physics into a concrete spin model, offering a comprehensive picture that unifies the anyon physics of the Kitaev spin liquids and the resonating valence bonds. Published by the American Physical Society 2024
We study the ground-state phase diagram of a two-dimensional kagome-lattice spin-1/2 XYXYXY model (JJJ) with a four-site ring-exchange interaction (KKK) using quantum Monte Carlo simulations. We find that the superfluid phase, existing in the regime of small ring exchange, undergoes a direct transition to a Z2{\mathbb{Z}}_{2}Z2​ quantum spin liquid phase at ${(K/J)}_{c}\ensuremath{\approx}22$, which is related to the phase proposed by L. Balents, M. P. A. Fisher, and S. M. Girvin [Phys. Rev. B 65, 224412 (2002)]. The quantum phase transition between the superfluid and the spin liquid phase has exponents zzz and $\ensuremath{\nu}$ falling in the three-dimensional XYXYXY universality class, making it a candidate for an exotic XYXYXY* quantum critical point, mediated by the condensation of bosonic spinons.
Evidence for a Z2_22​ topological ordered quantum spin liquid in a kagome-lattice antiferromagnet
A quantum spin liquid with a Z2Z_2Z2​ topological order has long been thought to be important for the application of quantum computing and may be related to high-temperature superconductivity. While a two-dimensional kagome antiferromagnet may host such a state, strong experimental evidences are still lacking. Here we show that the spin excitations from the kagome planes in magnetically ordered Cu4_44​(OD)6_66​FBr and non-magnetically ordered Cu3_33​Zn(OD)6_66​FBr are similarly gapped although the content of inter-kagome-layer Cu2+^{2+}2+ ions changes dramatically. This suggests that the spin triplet gap and continuum of the intrinsic kagome antiferromagnet are robust against the interlayer magnetic impurities. Our results show that the ground state of Cu3_33​Zn(OD)6_66​FBr is a gapped quantum spin liquid with Z2_22​ topological order.