We construct a short-range resonating-valence-bond (RVB) state on the ruby lattice, using projected entangled-pair states with bond dimension $D=3$ . By introducing nonlocal moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining a nonzero topological contribution, $\ensuremath{\gamma}=\ensuremath{-}\mathrm{ln}\phantom{\rule{4pt}{0ex}}2$, consistent with that of a ${\mathbb{Z}}_{2}$ topological quantum spin liquid. We also calculate the ground-state energy of the spin- $\frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.We construct a short-range resonating-valence-bond (RVB) state on the ruby lattice, using projected entangled-pair states with bond dimension $D=3$. By introducing nonlocal moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining a nonzero topological contribution, $\ensuremath{\gamma}=\ensuremath{-}\mathrm{ln}\phantom{\rule{4pt}{0ex}}2$, consistent with that of a ${\mathbb{Z}}_{2}$ topological quantum spin liquid. We also calculate the ground-state energy of the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

arXiv:1912.06215Physical review. B./Physical review. BMar 9, 202013 citations

Analytic evaluation of resonating valence bond states

Walter Metzner

The European Physical Journal BJun 1, 19919 citations

Resonating valence bond states beyond mean field approximation

Ma Benkun, Shiping Feng

Journal of Beijing Normal UniversityJan 1, 19910 citations

Resonating Valence Bond Wave Functions and Classical Interacting Dimer Models

Kedar Damle, Deepak Dhar, Kabir Ramola

We relate properties of nearest-neighbor resonating valence-bond (NNRVB) wave functions for $SU(g)$ spin systems on two-dimensional bipartite lattices to those of fully packed interacting classical dimer models on the same lattice. The interaction energy can be expressed as a sum of $n$ -body potentials ${V}_{n}$ , which are recursively determined from the NNRVB wave function on finite subgraphs of the original lattice. The magnitude of the $n$ -body interaction ${V}_{n}$ ( $n>1$ ) is of order $\mathcal{O}({g}^{\ensuremath{-}(n\ensuremath{-}1)})$ for small ${g}^{\ensuremath{-}1}$. The leading term is a two-body nearest-neighbor interaction ${V}_{2}(g)$ favoring two parallel dimers on elementary plaquettes. For $SU(2)$ spins, using our calculated value of ${V}_{2}(g=2)$ , we find that the long-distance behavior of the bond-energy correlation function is dominated by an oscillatory term that decays as $1/|\stackrel{\ensuremath{\rightarrow}}{r}{|}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}1.22$. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give $\ensuremath{\alpha}\ensuremath{\approx}1.20$.We relate properties of nearest-neighbor resonating valence-bond (NNRVB) wave functions for $SU(g)$ spin systems on two-dimensional bipartite lattices to those of fully packed interacting classical dimer models on the same lattice. The interaction energy can be expressed as a sum of $n$-body potentials ${V}_{n}$, which are recursively determined from the NNRVB wave function on finite subgraphs of the original lattice. The magnitude of the $n$-body interaction ${V}_{n}$ ($n>1$) is of order $\mathcal{O}({g}^{\ensuremath{-}(n\ensuremath{-}1)})$ for small ${g}^{\ensuremath{-}1}$. The leading term is a two-body nearest-neighbor interaction ${V}_{2}(g)$ favoring two parallel dimers on elementary plaquettes. For $SU(2)$ spins, using our calculated value of ${V}_{2}(g=2)$, we find that the long-distance behavior of the bond-energy correlation function is dominated by an oscillatory term that decays as $1/|\stackrel{\ensuremath{\rightarrow}}{r}{|}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}1.22$. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give $\ensuremath{\alpha}\ensuremath{\approx}1.20$.

arXiv:1112.4917Physical Review LettersJun 15, 201230 citations

Resonating valence-bond physics on the honeycomb lattice

Pranay Patil, Ishita Dasgupta, Kedar Damle

We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large- $g$ expansion approach to relate bond-energy correlators of the $\mathrm{SU}(g)$ wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting $g=2$ , we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for $g=3,4,10$ and find that the bond-energy correlations in the $\mathrm{SU}(g)$ wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large-$g$ expansion approach to relate bond-energy correlators of the $\mathrm{SU}(g)$ wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting $g=2$, we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for $g=3,4,10$ and find that the bond-energy correlations in the $\mathrm{SU}(g)$ wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.

arXiv:1408.4374Physical Review BDec 15, 201412 citations

The New Resonating Valence Bond Method for Ab-Initio Electronic Simulations

Sandro Sorella, Andrea Zen

arXiv:1310.0845Mathematical physics studiesJan 1, 20145 citations

We construct a short-range resonating-valence-bond (RVB) state on the ruby lattice, using projected entangled-pair states with bond dimension

D=3

. By introducing nonlocal moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining a nonzero topological contribution, $\ensuremath{\gamma}=\ensuremath{-}\mathrm{ln}\phantom{\rule{4pt}{0ex}}2$, consistent with that of a

{\mathbb{Z}}_{2}

topological quantum spin liquid. We also calculate the ground-state energy of the spin-

\frac{1}{2}

antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.

We relate properties of nearest-neighbor resonating valence-bond (NNRVB) wave functions for

SU(g)

spin systems on two-dimensional bipartite lattices to those of fully packed interacting classical dimer models on the same lattice. The interaction energy can be expressed as a sum of

n

-body potentials

{V}_{n}

, which are recursively determined from the NNRVB wave function on finite subgraphs of the original lattice. The magnitude of the

n

-body interaction

{V}_{n}

(

n>1

) is of order $\mathcal{O}({g}^{\ensuremath{-}(n\ensuremath{-}1)})$ for small ${g}^{\ensuremath{-}1}$. The leading term is a two-body nearest-neighbor interaction

{V}_{2}(g)

favoring two parallel dimers on elementary plaquettes. For

SU(2)

spins, using our calculated value of

{V}_{2}(g=2)

, we find that the long-distance behavior of the bond-energy correlation function is dominated by an oscillatory term that decays as $1/|\stackrel{\ensuremath{\rightarrow}}{r}{|}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\approx}1.22$. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give $\ensuremath{\alpha}\ensuremath{\approx}1.20$.

We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric

S=1/2

antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large-

g

expansion approach to relate bond-energy correlators of the

\mathrm{SU}(g)

wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting

g=2

, we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for

g=3,4,10

and find that the bond-energy correlations in the

\mathrm{SU}(g)

wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.