Related papers: Supersymmetric Valence Bond Solid States
We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys…
We use Monte Carlo simulations to study properties of Anderson's resonating-valence-bond (RVB) spin-liquid state on the square lattice (i.e., the equal superposition of all pairing of spins into nearest-neighbor singlet pairs) and compare…
The concept of valence bond resonance plays a fundamental role in the theory of the chemical bond and is believed to lie at the heart of many-body quantum physical phenomena. Here we show direct experimental evidence of a time-resolved…
This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper…
Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical…
We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the…
Using numerical results from a density matrix renormalization group study as a guide, we develop a resonating valence bond (RVB) theory for coupled Heisenberg chains. We argue that simple topological effects mandate a short-range RVB…
We propose a new class of ground states for doped Mott insulators in the electron second-quantization representation. They are obtained from a bosonic resonating valence bond (RVB) theory of the t-J model. At half filling, the ground state…
We construct a family of simple fermionic projected entangled pair states (fPEPS) on the square lattice with bond dimension $D=3$ which are exactly hole-doped resonating valence bond (RVB) wavefunctions with short-range singlet bonds. Under…
Various lattice geometries and boundaries are used to investigate valence-bond-solid (VBS) ordering in the ground state of an S=1/2 square-lattice quantum spin model---the J-Q model, in which 4- or 6-spin interactions Q are added to the…
We study maximal bipartite entanglement in valence-bond states and show that the average bipartite entanglement $E_v^2$, between a sub-system of two spins and the rest of the system, can be maximized through a homogenized superposition of…
We generalize the construction of the spin-1/2 SU(2) Resonating Valence Bond (RVB) state to the case of the self-conjugate $\bf 6$-representation of SU(4). As for the case of SU(2) [J-Y. Chen and D. Poilblanc, Phys. Rev. B $\textbf{97}$,…
Dicke's original thought experiment with two spins coupled to a photon mode has recently been experimentally realized. We propose extending this experiment to N spins and show that it naturally gives rise to highly entangled states. In…
We study resonating valence bond (RVB) states in the Projected Entangled Pair States (PEPS) formalism. Based on symmetries in the PEPS description, we establish relations between the toric code state, the orthogonal dimer state, and the…
In a recent Letter [Phys. Rev. Lett. 99, 170502 (2007); quant-ph/0703227], Chandran and coworkers study the entanglement properties of valence bond (VB) states. Their main result is that VB states do not contain (or only an insignificant…
We study generalizations of the singlet-sector amplitude-product (AP) states in the valence-bond basis of S=1/2 quantum spin systems. In the standard AP states, the weight of a tiling of the system into valence bonds (singlets of two spins)…
We introduce a general method to construct one-dimensional translationally invariant valence bond solid states with a built-in Lie group $G$ and derive their matrix product representations. The general strategies to find their parent…
We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin…
We consider the valence-bond-solid ground state of the q-deformed higher-spin AKLT model (q-VBS state). We investigate the eigenvalues and eigenvectors of a matrix (G matrix), which is constructed from the matrix product representation of…
Using a graphical presentation of the spin $S$ one dimensional Valence Bond Solid (VBS) state, based on the representation theory of the $SU(2)$ Lie-algebra of spins, we compute the spectrum of a mixed state reduced density matrix. This…