Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2308.03509 · Physical Review A

Abelian and non-Abelian quantum spin liquids in a three-component Bose gas on optical kagome lattices

Kaiye Shi, Wei Zhang, Zheng-Xin Liu

Published Sep 8, 2023• 3 citations
arXivHTMLPDF

Abstract

The realization of non-Abelian anyons in topological phases is a crucial step toward topological quantum computation. We propose a scheme to realize a non-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas with contact interaction on optical kagome lattices. In the strong coupling regime, the system is described by an effective spin-1 model with two- and three-body interactions between neighboring spins. By mapping out the phase diagram via the variational Monte Carlo method, we find a non-Abelian chiral spin-liquid phase in which the Ising-type anyons obey non-Abelian braiding statistics. The gapless chiral edge states can be detected by measuring the spin-spin correlation from atomic population. Furthermore, an interesting ${Z}_{2}$ QSL phase is observed exhibiting both topological order and lattice symmetry-breaking order. Our scheme can be implemented in cold quantum gases of bosonic atoms.

DOI
10.1103/physreva.108.033308

Related papers

Non-Abelian chiral spin liquid in a spin-111 antiferromagnet on the square lattice

Xiao-Tian Zhang, Yuan Yang, D. N. Sheng +1 more

Non-Abelian chiral spin liquids (CSLs) host non-Abelian anyon excitations and are promising platforms for topological quantum computation. However, realizing non-Abelian CSLs in short-range interacting spin systems remains elusive. Here, we study a spin-$1$ square-lattice model with the first- and second-neighbor bilinear ($J_1,J_2$) and biquadratic interactions ($K_1,K_2$), as well as the three-spin scalar chiral coupling $J_χ$. Inspired by the evidence of the Moore-Read state in exact diagonalization and infinite Projected Entangled Pair States calculations, we fix $J_1=1.0$, $J_2/J_1=0.623$, $K_1/J_1=-0.176$, and obtain a quantum phase diagram for $0 \leq K_2/J_1 \leq 0.4$ and $0.3 \leq J_χ/J_1 \leq 0.6$ by using the density matrix renormalization group (DMRG) calculations. We identify a stripe antiferromagnetic phase, a Néel antiferromagnetic phase, a magnetically ordered chiral spin state phase, and a non-Abelian CSL phase emerging near the boundaries of the ordered phases. The unbiased DMRG results provide strong evidence for the Moore-Read state, including the three topological sectors, the quantized spin Chern number $C=1$, and the level counting of low-lying entanglement spectra which is consistent with the chiral SU(2)$_2$ conformal field theory. Our results may shed new light on searching for non-Abelian CSLs in other higher-spin ($S > 1/2$) systems with short-range couplings.

arXiv:2609.15061•Sep 14, 2026•0 citations

Non-Abelian S=1 chiral spin liquid on the kagome lattice

Zheng-Xin Liu, Hong-Hao Tu, Ying-Hai Wu +4 more

We study $S=1$ spin liquid states on the kagome lattice constructed by Gutzwiller-projected ${p}_{x}+i{p}_{y}$ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices $S$ and $T$, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the $SO{(3)}_{1}$ (or, equivalently, $SU{(2)}_{2}$) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the ${Z}_{2}$ Abelian spin liquid.

arXiv:1509.00391•Physical review. B./Physical review. B•May 31, 2018•24 citations

Non-Abelian Topological Order in s -Wave Superfluids of Ultracold Fermionic Atoms

Masatoshi Sato, Yoshiro Takahashi, Satoshi Fujimoto

It is proposed that in s-wave superfluids of cold fermionic atoms with laser-field-generated effective spin-orbit interactions, a topological phase with gapless edge states and Majorana fermion quasiparticles obeying non-Abelian statistics is realized in the case with a large Zeeman magnetic field. Our scenario provides a promising approach to the realization of quantum computation based on the manipulation of non-Abelian anyons via an s-wave Feshbach resonance.

arXiv:0901.4693•Physical Review Letters•Jul 6, 2009•737 citations

Compact localized fermions and Ising anyons in a chiral spin liquid

Tim Bauer, Johannes Reuther

Quasiparticle hybridization remains a major challenge to realizing and controlling exotic states of matter in existing quantum simulation platforms. We report the absence of hybridization for compact localized states (CLS) emerging in the chiral spin liquid described by the Yao-Kivelson model. The CLS form due to destructive quantum interference at fine-tuned coupling constants and populate perfectly flat quasiparticle bands on an effective kagome lattice. Using a formalism for general Majorana-hopping Hamiltonians, we derive exact expressions for CLS for various flux configurations and both for the topological and trivial phases of the model. In addition to finite-energy matter fermions with characteristic spin-spin correlations, we construct compact localized Majorana zero modes attached to $π$-flux excitations, which enable non-Abelian braiding of Ising anyons with minimal separation. Our results inform the quantum simulation of topologically ordered states of matter and open avenues for exploring flat-band physics in quantum spin liquids.

cond-mat.str-elCross-listedarXiv:2511.05105•Physical review. B./Physical review. B•Nov 10, 2025•0 citations

Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks

Yu-Hsueh Chen, Ching-Yu Huang, Ying-Jer Kao

We propose a unified scheme to identify phase transitions out of the ${\mathbb{Z}}_{2}$ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, and N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a ${\mathbb{Z}}_{2}$-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the $\ensuremath{\sigma}$ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian.

arXiv:2102.10980•Physical review. B./Physical review. B•Jul 20, 2021•4 citations

Anyonic braiding in optical lattices

Chuanwei Zhang, V. W. Scarola, Sumanta Tewari +1 more

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.

arXiv:quant-ph/0609101•Proceedings of the National Academy of Sciences•Nov 13, 2007•67 citations
The realization of non-Abelian anyons in topological phases is a crucial step toward topological quantum computation. We propose a scheme to realize a non-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas with contact interaction on optical kagome lattices. In the strong coupling regime, the system is described by an effective spin-1 model with two- and three-body interactions between neighboring spins. By mapping out the phase diagram via the variational Monte Carlo method, we find a non-Abelian chiral spin-liquid phase in which the Ising-type anyons obey non-Abelian braiding statistics. The gapless chiral edge states can be detected by measuring the spin-spin correlation from atomic population. Furthermore, an interesting Z2{Z}_{2}Z2​ QSL phase is observed exhibiting both topological order and lattice symmetry-breaking order. Our scheme can be implemented in cold quantum gases of bosonic atoms.
Non-Abelian chiral spin liquids (CSLs) host non-Abelian anyon excitations and are promising platforms for topological quantum computation. However, realizing non-Abelian CSLs in short-range interacting spin systems remains elusive. Here, we study a spin-111 square-lattice model with the first- and second-neighbor bilinear (J1,J2J_1,J_2J1​,J2​) and biquadratic interactions (K1,K2K_1,K_2K1​,K2​), as well as the three-spin scalar chiral coupling JχJ_χJχ​. Inspired by the evidence of the Moore-Read state in exact diagonalization and infinite Projected Entangled Pair States calculations, we fix J1=1.0J_1=1.0J1​=1.0, J2/J1=0.623J_2/J_1=0.623J2​/J1​=0.623, K1/J1=−0.176K_1/J_1=-0.176K1​/J1​=−0.176, and obtain a quantum phase diagram for 0≤K2/J1≤0.40 \leq K_2/J_1 \leq 0.40≤K2​/J1​≤0.4 and 0.3≤Jχ/J1≤0.60.3 \leq J_χ/J_1 \leq 0.60.3≤Jχ​/J1​≤0.6 by using the density matrix renormalization group (DMRG) calculations. We identify a stripe antiferromagnetic phase, a Néel antiferromagnetic phase, a magnetically ordered chiral spin state phase, and a non-Abelian CSL phase emerging near the boundaries of the ordered phases. The unbiased DMRG results provide strong evidence for the Moore-Read state, including the three topological sectors, the quantized spin Chern number C=1C=1C=1, and the level counting of low-lying entanglement spectra which is consistent with the chiral SU(2)2_22​ conformal field theory. Our results may shed new light on searching for non-Abelian CSLs in other higher-spin (S>1/2S > 1/2S>1/2) systems with short-range couplings.
We study S=1S=1S=1 spin liquid states on the kagome lattice constructed by Gutzwiller-projected px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices SSS and TTT, we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the SO(3)1SO{(3)}_{1}SO(3)1​ (or, equivalently, SU(2)2SU{(2)}_{2}SU(2)2​) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the Z2{Z}_{2}Z2​ Abelian spin liquid.
Quasiparticle hybridization remains a major challenge to realizing and controlling exotic states of matter in existing quantum simulation platforms. We report the absence of hybridization for compact localized states (CLS) emerging in the chiral spin liquid described by the Yao-Kivelson model. The CLS form due to destructive quantum interference at fine-tuned coupling constants and populate perfectly flat quasiparticle bands on an effective kagome lattice. Using a formalism for general Majorana-hopping Hamiltonians, we derive exact expressions for CLS for various flux configurations and both for the topological and trivial phases of the model. In addition to finite-energy matter fermions with characteristic spin-spin correlations, we construct compact localized Majorana zero modes attached to πππ-flux excitations, which enable non-Abelian braiding of Ising anyons with minimal separation. Our results inform the quantum simulation of topologically ordered states of matter and open avenues for exploring flat-band physics in quantum spin liquids.
We propose a unified scheme to identify phase transitions out of the Z2{\mathbb{Z}}_{2}Z2​ Abelian topological order, including the transition to a non-Abelian chiral spin liquid. Using loop gas and and string gas states [H.-Y. Lee, R. Kaneko, T. Okubo, and N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on the star lattice Kitaev model as an example, we compute the overlap of minimally entangled states through transfer matrices. We demonstrate that, similar to the anyon condensation, continuous deformation of a Z2{\mathbb{Z}}_{2}Z2​-injective projected entangled-pair state (PEPS) also allows us to study the transition between Abelian and non-Abelian topological orders. We show that the charge and flux anyons defined in the Abelian phase transmute into the $\ensuremath{\sigma}$ anyon in the non-Abelian topological order. Furthermore, we show that contrary to the claim in [Phys. Rev. B 101, 035140 (2020)], both the LG and SG states have infinite correlation length in the non-Abelian regime, consistent with the no-go theorem that a chiral PEPS has a gapless parent Hamiltonian.
Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.