We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor $\mathrm{SO}(N)$ singlet projectors on the kagome lattice. Our model shares some features with the popular $S=1/2$ kagome antiferromagnet but is specifically designed to be free of the sign problem of quantum Monte Carlo. In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large- $N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${\mathbb{Z}}_{2}$ topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor $\mathrm{SO}(N)$ singlet projectors on the kagome lattice. Our model shares some features with the popular $S=1/2$ kagome antiferromagnet but is specifically designed to be free of the sign problem of quantum Monte Carlo. In our numerical analysis, we find as a function of $N$ a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-$N$ generalization suggests that the quantum spin liquid in our original model is a gapped ${\mathbb{Z}}_{2}$ topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.

arXiv:1906.06246Physical review. B./Physical review. BJan 9, 202020 citations

Topological entanglement entropy of Z2 spin liquids and lattice Laughlin states

Yi Zhang, Tarun Grover, Ashvin Vishwanath

We study entanglement properties of candidate wave functions for SU(2) symmetric gapped spin liquids and Laughlin states. These wave functions are obtained by the Gutzwiller projection technique. Using topological entanglement entropy $\ensuremath{\gamma}$ as a tool, we establish topological order in chiral spin liquid and ${\mathbb{Z}}_{2}$ spin liquid wave functions, as well as a lattice version of the Laughlin state. Our results agree very well with the field theoretic result $\ensuremath{\gamma}=\mathrm{log}D$ where $D$ is the total quantum dimension of the phase. All calculations are done using a Monte Carlo technique on a $12\ifmmode\times\else\texttimes\fi{}12$ lattice enabling us to extract $\ensuremath{\gamma}$ with small finite-size effects. For a chiral spin liquid wave function, the calculated value is within $4%$ of the ideal value. We also find good agreement for a lattice version of the Laughlin $\ensuremath{\nu}=1/3$ phase with the expected $\ensuremath{\gamma}=\mathrm{log}\sqrt{3}$.We study entanglement properties of candidate wave functions for SU(2) symmetric gapped spin liquids and Laughlin states. These wave functions are obtained by the Gutzwiller projection technique. Using topological entanglement entropy $\ensuremath{\gamma}$ as a tool, we establish topological order in chiral spin liquid and ${\mathbb{Z}}_{2}$ spin liquid wave functions, as well as a lattice version of the Laughlin state. Our results agree very well with the field theoretic result $\ensuremath{\gamma}=\mathrm{log}D$ where $D$ is the total quantum dimension of the phase. All calculations are done using a Monte Carlo technique on a $12\ifmmode\times\else\texttimes\fi{}12$ lattice enabling us to extract $\ensuremath{\gamma}$ with small finite-size effects. For a chiral spin liquid wave function, the calculated value is within $4%$ of the ideal value. We also find good agreement for a lattice version of the Laughlin $\ensuremath{\nu}=1/3$ phase with the expected $\ensuremath{\gamma}=\mathrm{log}\sqrt{3}$.

arXiv:1106.0015Physical Review BAug 9, 2011102 citations

Topological entanglement entropy of a Bose–Hubbard spin liquid

Sergei V. Isakov, Matthew B. Hastings, Roger G. Melko

arXiv:1102.1721Nature PhysicsJul 10, 2011264 citations

Computing Entanglement Entropy in Quantum Monte Carlo

Roger G. Melko

Bulletin of the American Physical SocietyFeb 29, 20120 citations

Topological entanglement entropy in Gutzwiller projected spin liquids

Jiquan Pei, Steve Han, Haijun Liao +1 more

The topological entanglement entropy (TEE) of Gutzwiller projected RVB state is studied with Monte Carlo simulation. With tricks to speed up the convergence of TEE, we are able to show that the spin liquid state studied in Zhang et al. [Phys. Rev. B 84, 075128 (2011)] actually does not support ${Z}_{2}$ topological order. We find that both an approximate Marshall sign structure and a long-ranged RVB amplitude are responsible for the suppression of the vison gap in this spin liquid state. On the other hand, a TEE of $\mathrm{ln}2$ is clearly demonstrated for a short range RVB state on triangular lattice proposed in Yunoki et al. [Phys. Rev. B 74, 014408 (2006)]. We find the TEE of the RVB wave function is mainly determined by its phase rather than its amplitude. Our results indicate that the effective field theory misses some key information for the topological property of a RVB state.The topological entanglement entropy (TEE) of Gutzwiller projected RVB state is studied with Monte Carlo simulation. With tricks to speed up the convergence of TEE, we are able to show that the spin liquid state studied in Zhang et al. [Phys. Rev. B 84, 075128 (2011)] actually does not support ${Z}_{2}$ topological order. We find that both an approximate Marshall sign structure and a long-ranged RVB amplitude are responsible for the suppression of the vison gap in this spin liquid state. On the other hand, a TEE of $\mathrm{ln}2$ is clearly demonstrated for a short range RVB state on triangular lattice proposed in Yunoki et al. [Phys. Rev. B 74, 014408 (2006)]. We find the TEE of the RVB wave function is mainly determined by its phase rather than its amplitude. Our results indicate that the effective field theory misses some key information for the topological property of a RVB state.

arXiv:1212.2703Physical Review BSep 25, 20136 citations

We present a study of a simple model antiferromagnet consisting of a sum of nearest-neighbor

\mathrm{SO}(N)

singlet projectors on the kagome lattice. Our model shares some features with the popular

S=1/2

kagome antiferromagnet but is specifically designed to be free of the sign problem of quantum Monte Carlo. In our numerical analysis, we find as a function of

N

a quadrupolar magnetic state and a wide range of a quantum spin liquid. A solvable large-

N

generalization suggests that the quantum spin liquid in our original model is a gapped

{\mathbb{Z}}_{2}

topological phase. Supporting this assertion, a numerical study of the entanglement entropy in the sign free model shows a quantized topological contribution.

{\mathbb{Z}}_{2}

spin liquid wave functions, as well as a lattice version of the Laughlin state. Our results agree very well with the field theoretic result $\ensuremath{\gamma}=\mathrm{log}D$ where

D

is the total quantum dimension of the phase. All calculations are done using a Monte Carlo technique on a $12\ifmmode\times\else\texttimes\fi{}12$ lattice enabling us to extract $\ensuremath{\gamma}$ with small finite-size effects. For a chiral spin liquid wave function, the calculated value is within

4%

of the ideal value. We also find good agreement for a lattice version of the Laughlin $\ensuremath{\nu}=1/3$ phase with the expected $\ensuremath{\gamma}=\mathrm{log}\sqrt{3}$.

{Z}_{2}

topological order. We find that both an approximate Marshall sign structure and a long-ranged RVB amplitude are responsible for the suppression of the vison gap in this spin liquid state. On the other hand, a TEE of

\mathrm{ln}2

is clearly demonstrated for a short range RVB state on triangular lattice proposed in Yunoki et al. [Phys. Rev. B 74, 014408 (2006)]. We find the TEE of the RVB wave function is mainly determined by its phase rather than its amplitude. Our results indicate that the effective field theory misses some key information for the topological property of a RVB state.