Models of non-Abelian quantum spin liquids

Quantum spin liquids are elusive states of matter, which have been predicted more than four decades ago but have not so far been conclusively sighted in nature. In this paper the authors study the so called `extended Kitaev model', which has a number of different quantum spin-liquid phases including one with non-Abelian excitations. They present a solution of a long standing problem for this model, namely, the problem of obtaining the dynamical response function. Using a rarely available exact calculation, they find that there are indeed clear signatures in the spin structure factor betraying the presence of spin-liquids and their fractionalized quasi-particles, including those with non-Abelian statistics.Quantum spin liquids are elusive states of matter, which have been predicted more than four decades ago but have not so far been conclusively sighted in nature. In this paper the authors study the so called `extended Kitaev model', which has a number of different quantum spin-liquid phases including one with non-Abelian excitations. They present a solution of a long standing problem for this model, namely, the problem of obtaining the dynamical response function. Using a rarely available exact calculation, they find that there are indeed clear signatures in the spin structure factor betraying the presence of spin-liquids and their fractionalized quasi-particles, including those with non-Abelian statistics.

arXiv:1507.02865Physical Review BSep 14, 2015162 citations

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

Kaiye Shi, Wei Zhang, Zheng-Xin Liu

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.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.

arXiv:2308.03509Physical Review ASep 8, 20233 citations

Introduction to Quantum Spin Liquids

C. Lhuillier, Grégoire Misguich

Springer series in solid-state sciencesSep 29, 201011 citations

An introduction to Quantum Spin Liquids

Subhro Bhattacharjee

Texts and readings in physical sciencesJan 1, 20172 citations

Global quantum phase diagram and non-Abelian chiral spin liquid in a spin- 32 square-lattice antiferromagnet

Weiwei Luo, Yixuan Huang, D. N. Sheng +1 more

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin- $\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin- $\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin- $\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-$\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin-$\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.

arXiv:2212.14223Physical review. B./Physical review. BJul 17, 20234 citations

{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.

Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-

\frac{1}{2}

systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-

\frac{3}{2}

Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Our numerical discovery of an exotic quantum spin liquid in a spin-

\frac{3}{2}

system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.