We have performed Diffusion Quantum Monte Carlo simulations of Li clusters showing that Resonating-Valence-Bond (RVB) pairing correlations between electrons provide a substantial contribution to the cohesive energy. The RVB effects are identified in terms of electron transfers from s- to p-like character, constituting a possible explanation for the breakdown of the Fermi liquid picture observed in recent high resolution Compton scattering experiments for bulk Li.
We show that the mean-field resonating valence bond approximation proposed in 1987 by Baskaran, Zou, and Anderson describes gapless charge pair excitations confined to the boundaries of the spinon Brillouin zone. The existence of such pairs accounts for all the essential anomalous electronic properties of cuprates, with superconductivity arising due to the charge drag by the spinon superflow. This mechanism may be relevant to other unconventional superconductors.
We discuss how orbital degeneracy, which is usually removed by a cooperative Jahn-Teller distortion, could under appropriate circumstances lead rather to a Resonating Valence Bond spin-orbital liquid. The key points are: i) The tendency to form spin-orbital dimers, a tendency already identified in several cases; ii) The mapping onto Quantum Dimer Models, which have been shown to possess Resonating Valence Bond phases on the triangular lattice. How this program can be implemented is explained in some details starting from a microscopic model of LiNiO$_2$.
Short-range resonating-valence bond states in an orbitally degenerate magnet on a honeycomb lattice is studied. A quantum-dimer model is derived from the Hamiltonian which represents the superexchange interaction and the dynamical Jahn-Teller (JT) effect. We introduce two local units termed "spin-orbital singlet dimer", where two spins in a nearest-neighbor bond form a singlet state associated with an orbital polarization along the bond, and "local JT singlet", where an orbital polarization is quenched due to the dynamical JT effect. A derived quantum-dimer model consists of the hopping of the…
We develop a quantum spin liquid theory for quantum magnets with easy-plane ferromagnetic exchange. These strongly entangled quantum states are obtained by dimer coverings of 2D lattices with triplet $S = 1, m_z = 0$ bonds, forming a triplet resonating valence bond (tRVB) state. We discuss the conditions and the procedure to transfer well-known results from conventional singlet resonating valence bond theory to tRVB. Additionally, we present mean field theories of Abrikosov fermions on 2D triangular and square lattices, which can be controlled in an appropriate large $N$ limit. We also incorpo…
The Hubbard model in the strong-coupling regime is studied by the Kondo-lattice theory. If no symmetry is broken at a sufficiently low temperature in sufficiently low dimensions, an electron liquid is stabilized by the Fock-type exchange effect of the superexchange interaction. Since the stabilization mechanism is none other than the resonating-valence-bond (RVB) mechanism, the electron liquid is none other than an RVB electron liquid. The RVB electron liquid in the Hubbard model is adiabatically connected to the RVB spin liquid in the Heisenberg model.
We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in s…
We propose and study an SU(3) trimer resonating-valence-bond (tRVB) state with $C_{4v}$ point-group symmetry on the square lattice. By devising a projected entangled-pair state representation, we show that all (connected) correlation functions between local operators in this SU(3) tRVB state decay exponentially, indicating its gapped nature. We further calculate the modular $S$ and $T$ matrices by constructing all nine topological sectors on a torus and establish the existence of $\mathbb{Z}_3$ topological order in this SU(3) tRVB state.
We show that short-range resonating-valence-bond correlations and long-range order can coexist in the ground state (GS) of a frustrated spin system. Our study comprises a comprehensive investigation of the quantum magnetism on the structurally disorder-free single crystal of Cu$_2$(OH)$_3$NO$_3$, which realizes the $s$ = 1/2 Heisenberg model on a spatially anisotropic triangular lattice. Competing exchange interactions determined by fitting the magnetization measured up to 55 T give rise to an exotic GS wavefunction with coexistence of the dominant short-range resonating-valence-bond correlati…
The Resonating Valence Bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough ``quantum frustration''. This scenario, proposed long time ago but never confirmed by microscopic calculations, is very strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the $J_1{-}J_2$ Heisenberg model for $0.4 \lesssim J_2/J_1\lesssim 0.5$. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.
Gutzwiller variational method is applied to an effective two-dimensional Hubbard model to examine the recently proposed gossamer superconductor by Laughlin. The ground state at half filled electron density is a gossamer superconductor for smaller intra-site Coulomb repulsion U and a Mott insulator for larger U. The gossamer superconducting state is similar to the resonant valence bond superconducting state, except that the chemical potential is approximately pinned at the mid of the two Hubbard bands away from the half filled.
We use an effective Hamiltonian for two-dimensional Hubbard model including an antiferromagnetic spin-spin coupling term to study recently proposed gossamer superconductivity. We formulate a renormalized mean field theory to approximately take into account the strong correlation effect in the partially projected Gutzwiller wavefucntions. At the half filled, there is a first order phase transition to separate a Mott insulator at large Coulomb repulsion U from a gossamer superconductor at small U. Away from the half filled,the Mott insulator is evolved into an resonating valence bond state, whic…
We apply a variational wave function capable of describing qualitatively and quantitatively the so called "resonating valence bond" in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekulé and Dewar contributions to the chemical bond of the benzene molecule, and we establish the corresponding resonating valence bond energy of these well known structures ($\simeq 0.01$eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene and show that this picture remains …
We propose resonating valence bond wave functions for a spin-1 system on the torus that realize a non-Abelian chiral spin liquid. The wave functions take the form of infinite dimensional matrix product states constructed from conformal blocks of the $\mathrm{SO}(3)_{1}$ Wess-Zumino-Witten model. This means that they are lattice analogues of the bosonic Moore-Read state introduced in fractional quantum Hall systems. The topological order of this system is revealed by explicit construction of three-fold degenerate ground states and analytical computation of the modular S and T matrices.
With extensive variational Monte Carlo simulation, we show that the uniform resonating valence bond state(U-RVB) on square lattice is actually antiferromagnetic long range ordered. The ordered moment is estimated to be $m\approx 0.17$. Finite size scaling analysis on lattice up to lattice size of $50\times 50$ shows that the spin structure factor at the antiferromagnetic ordering wave vector follows perfectly the $\mathrm{S}_{\mathrm{q}=(π,π)} \simeq S_{0}+α(1/L)^{5/4}$ behavior, where $L$ is linear scale of the lattice. Such a behavior is quite unexpected from the slave Boson mean field treat…
Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids (QSL). Here, we show that excitations related to singlet breaking on nearest-neighbor bonds describe the high-energy part of the excitation spectrum in YbMgGaO4, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering (INS) study, we demonstrate that nearest-neighbor RVB excitations account fo…
We consider the simplest generalizations of the valence bond physics of SU(2) singlets to SU(N) singlets that comprise objects with N sites -- these are SU(N) singlet plaquettes with N=3 and N=4 in three spatial dimensions. Specifically, we search for a quantum mechanical liquid of such objects -- a resonating singlet valence plaquette phase that generalizes the celebrated resonating valence bond phase for SU(2) spins. We extend the Rokhsar-Kivelson construction of the quantum dimer model to the simplest SU(4) model for valence plaquette dynamics on a cubic lattice. The phase diagram of the re…
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 obstacle overcome is the fact that different "dimer" configurations in the spin model are not orthogonal to each other. We show that the physics depends on how dimers are related to the spins, and find a Hamiltonian that may be quantum critical.
Projected-BCS wave functions have been proposed as the paradigm for the understanding of disordered spin states (spin liquids). Here we investigate the properties of these wave functions showing how Luttinger liquids, dimerized states, and gapped spin liquids may be described by the same class of wave functions, which, therefore, represent an extremely flexible variational tool. A close connection between spin liquids and
We investigate the entanglement properties of resonating-valence-bond states on two and higher dimensional lattices, which play a significant role in our understanding of various many-body systems. We show that these states are genuinely multipartite entangled, while there is only a negligible amount of two-site entanglement. We comment on possible physical implications of our findings.
The spin-orbital model for triply degenerate t_2g electrons on a triangular lattice has been shown to be dominated by dimers: the phase diagram contains both strongly resonating, compound spin-orbital dimer states and quasi-static, spin-singlet valence-bond (VB) states. To elucidate the nature of the true ground state in these different regimes, the model is mapped to a number of quantum dimer models (QDMs), each of which has three dimer colors. The generic multicolored QDM, illustrated for the two- and three-color cases, possesses a topological color structure, "color vison" excitations, and …
On the triangular and kagome lattices, short-ranged resonating valence bond (RVB) wave functions can be sampled without the sign problem using a recently-developed Pfaffian Monte Carlo scheme. In this paper, we study the Renyi entanglement entropy in these wave functions using a replica-trick method. Using various spatial bipartitions, including the Levin-Wen construction, our finite-size scaled Renyi entropy gives a topological contribution consistent with $γ= \text{ln}(2)$, as expected for a gapped $\mathbb{Z}_{2}$ quantum spin liquid. We prove that the mutual statistics are consistent with …
The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix metho…
Within the $t$--$J$ model Hamiltonian we present a RVB mean field theory directly in terms of dopant particles. We apply this theory to $\mathrm{Na}_{x}\mathrm{CoO_{2}}\cdot y% \mathrm{H_{2}0}$ and show that the resulting phase diagram $T_c$ versus doping is in qualitative agreement with the experimental results.
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 the valence-bond states. Our derived maximal $E_v^2$ rapidly increases with system size and saturates at its maximum allowed value. We also demonstrate that our maximal $E^2_v$ states are ground states of an infinite range Heisenberg model (IRHM) and represent a new class of resonating-valence-bond (RVB) states. The entangled RVB states produced from our IRHM…
We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on timescale smaller than typical experimental decoherence times.
We propose a new exactly solvable model of strongly correlated electrons. The model is based on a $d$-$p$ model of the CuO$_2$ plane with infinitely large repulsive interactions on Cu-sites, and it contains additional correlated-hopping, pair-hopping and charge-charge interactions of electrons. For even numbers of electrons less than or equal to 2/3-filling, we construct the exact ground states of the model, all of which have the same energy and each of which is the unique ground state for a fixed electron number. It is shown that these ground states are the resonating-valence-bond states whic…
We investigate the behavior of bipartite as well as genuine multipartite entanglement of a resonating valence bond state on a ladder. We show that the system possesses significant amounts of bipartite entanglement in the steps of the ladder while no substantial bipartite entanglement is present in the rails. Genuine multipartite entanglement present in the system is negligible. The results are in stark contrast with the entanglement properties of the same state on isotropic lattices in two and higher dimensions, indicating that the geometry of the lattice can have important implications on the…
The nature of the kagome Heisenberg antiferromagnet (HAFM) is under ongoing debate. While recent evidence points towards a Z_2 topological spin liquid, the exact nature of the topological phase is still unclear. In this paper, we introduce semionic Resonating Valence Bond (RVB) states, this is, Resonating Valence Bond states which are in the Z_2 ordered double-semion phase, and study them using Projected Entangled Pair States (PEPS). We investigate their physics and study their suitability as an ansatz for the HAFM, as compared to a conventional RVB state which is in the Toric Code Z_2 topolog…
Superconductivity in an uncompensated boron doped diamond, a very recent observation, is strikingly close to an earlier observation of Anderson-Mott insulator to metal transition, prompting us to suggest an electron correlation driven superconductivity in an impurity band. Random coulomb potential remove a three fold orbital degeneracy of boron acceptor states, resulting in an effective single, narrow, tight binding and half filled band of holes. Singlet coupling between spins of neighboring neutral acceptors $B^0-B^0$ is the seed of pairing. Across the insulator to metal transition, a small a…
Implementation of the hardcore-dimer Hilbert space in cold Rydberg-atom simulators opens a new route of investigating real-time dynamics of dimer liquids under Hamiltonian quench. Here, we consider an initial Resonating Valence Bond (RVB) state on the square lattice realizing a critical Coulomb phase with algebraic and dipolar correlations. Using its representation as a special point of a broad manifold of SU($2$)-symmetric, translationnally invariant, Projected Entangled Pair States (PEPS), we compute its non-equilibrium dynamics upon turning on inter-site Heisenberg interactions. We show tha…
Mott insulator superconductor transition, via pressure and no external doping, is studied in orbitally non degenerate spin-\half systems. It is presented as another RVB route to high \tc superconductivity. We propose a `strong coupling' hypothesis which helps to view first order Mott transition as a self doping process that also preserves superexchange on metal side . We present a generalized t-J model where a conserved $N_0$ doubly occupied ($e^-$) sites and $N_0$ empty sites ($e^+$) hop in the background of $N - 2 N_0$ singly singly occupied (neutral) sites in a lattice of N sites. An equiva…
Effects of inhomogeneous doping on the high-$T_c$ cuprate superconductors are studied within the framework of the t-J model. Especially, the boundary between two non-superconducting regions with doping rates much higher and lower than the optimal one is examined. It is found that, although there is no superconductivity in the bulk, a superconducting region appears at the boundary because singlet resonating valence bond order and holon condensation occur simultaneously in this region. The critical temperature of the induced superconductivity can be higher than that of the optimally doped sample…
Coexistence of antiferromagnetism and d-wave superconductivity within a CuO_2 plane was recently observed in a wide doping region for multilayer high-temperature cuprate superconductors. We find that the experimental phase diagram is well reproduced in the slave-boson mean-field scheme of the two-dimensional t-J model by including antiferromagnetic order. We argue that weak three dimensionality coming from a multilayer structure is sufficient to stabilize antiferromagnetic order and its coexistence with superconductivity.
We study the ground-state phase diagram of the spin-1/2 J1-J2 Heisenberg model on the square lattice with an accurate Bosonic resonating valence-bond (RVB) wave function. In contrast to the RVB ansatz based on Schwinger Fermions, the representation based on Schwinger Bosons, supplemented by a variational Monte Carlo technique enforcing the exact projection onto the physical subspace, is able to describe a fully gapped spin liquid in the strongly frustrated regime. In particular, a fully symmetric Z2 spin liquid is stable between two antiferromagnetic phases; a continuous transition at J2=0.4J1…
We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte-Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et. al. [Physical Review B {\bf 85}, 235151 (2012)]. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a 't Hoo…
Although mean field theories have been very successful to predict a wide range of properties for solids, the discovery of high temperature superconductivity in cuprates supported the idea that strongly correlated materials cannot be qualitatively described by a mean field approach. After the original proposal by Anderson, there is now a large amount of numerical evidence that the simple but general resonating valence bond (RVB) wave function contains just those ingredients missing in uncorrelated theories, so that the main features of electron correlation can be captured by the variational RVB…
Resonating valence bond (RVB) theory of high Tc superconductivity, an electron correlation based mechanism, began as an insightful response by Anderson, to Bednorz and Muller's discovery of high Tc superconductivity in cuprates in late 1986. Shortly a theoretical framework for quantum spin liquids and superconductivity was developed. This theory adresses a formidable strong coupling quantum manybody problem, in modern times. It is built on certain key experimental facts: i) survival of a dynamical Mott localization in a metallic state, ii) proliferation of bond singlets and iii) absence of fer…
A one-parameter family of long-range resonating valence bond (RVB) state on the square lattice was previously proposed to describe a critical spin liquid (SL) phase of the spin-$1/2$ frustrated Heisenberg model. We provide evidence that this RVB state in fact also realises a topological (long-range entangled) $\mathbb{Z}_2$ SL, limited by two transitions to critical SL phases. The topological phase is naturally connected to the $\mathbb{Z}_2$ gauge symmetry of the local tensor. This work shows that, on one hand, spin-$1/2$ topological SL with $C_{4v}$ point group symmetry and $SU(2)$ spin rota…
A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong onsite Hund's interactions develop intra-atomic tRVBs between the t$_{2g}$ orbitals. On doping, the presence of two iron atoms per unit cell allows thes…
We show that the liquid-to-crystal quantum phase transition in the Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortex-like excitations called ``visons''. This conclusion is drawn from the numerical studies of the vison spectrum in the liquid phase by using the Green's function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement …
The unconventional low-lying spin excitations, recently observed in neutron scattering experiments on ${\rm Cs_2 Cu Cl_4}$, are explained with a spin liquid wave function. The dispersion relation as well as the wave vector of the incommensurate spin correlations are well reproduced within a projected BCS wave function with gapless and fractionalized spin-1/2 excitations around the nodes of the BCS gap function. The proposed wave function is shown to be very accurate for one-dimensional spin-1/2 systems, and remains similarly accurate in the two-dimensional model corresponding to ${\rm Cs_2 Cu …
Gutzwiller-projected (GP) wave functions have been widely used for describing spin-liquid physics in frustrated magnets and in high-temperature superconductors. Such wave functions are known to represent states of the resonating-valence-bond (RVB) type. In the present work I discuss the RVB structure of a GP singlet superconducting state with nodes in the spectrum. The resulting state for the undoped spin system may be described in terms of the "path integral" over loop coverings of the lattice, thus extending the known construction for RVB states. The problem of the topological order in GP st…
The frustrated Heisenberg $J_{1}-J_{2}$ model on a square lattice is numerically investigated by variational Monte Carlo simulations. We propose a antiferromagnetic fermion resonating-valence-bond (AF-fRVB) state that has ability to examine the entire phase diagram in the $J_{1}-J_{2}$ model. Two phase transition points, the second order around $J_{2}/J_{1}=0.45$ and the first order around $J_{2}/J_{1}=0.6$, can be extracted more clearly than the conventional bosonic RVB state. At the maximally frustrated point ($J_{2}/J_{1}=0.5$), the AF-fRVB state shows the variational ground-state energy in…
We give an account of the short-range RVB liquid phase on the triangular lattice, starting from an elementary introduction to quantum dimer models including details of the overlap expansion used to generate them. The fate of the topological degeneracy of the state under duality is discussed, as well as recent developments including its possible relevance for quantum computing.
We propose a theory of the spin dynamics of frustrated quantum antiferromagnets, which is based on an effective action for a plaquette embedded in a self-consistent bath. This approach, supplemented by a low-energy projection, is applied to the kagome antiferromagnet. We find that a spin-liquid regime extends to very low energy, in which local correlation functions have a slow decay in time, well described by a power law behaviour and $ω/T$ scaling of the response function: $χ''(ω)\propto ω^{-α}F(ω/T)$.
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 SU(2) singlet RVB state on the kagome lattice: We prove the equivalence of toric code and dimer state, and devise an interpolation between the dimer state and the RVB state. This interpolation corresponds to a continuous path in Hamiltonian space, proving that the RVB state is the four-fold degenerate ground state of a local Hamiltonian on the (finite) kagome l…
We investigate the ground state of the $d^1$ spin-orbital model for triply degenerate $t_{2g}$ orbitals on a triangular lattice which unifies intrinsic frustration of spin and orbital interactions with geometrical frustration. Using full or Lanczos exact diagonalization of finite clusters we establish that the ground state of the spin-orbital model which interpolates between the superexchange and direct exchange interactions on the bonds is characterized by valence-bond correlations. In the absence of Hund's exchange the model describes a competition between various possible valence-bond state…
The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order paramet…
We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at t…
It is well known that in quantum spin liquids and other magnetically disordered systems, the tunneling amplitudes between different nearest-neighbor valence bond (NNVB) configurations drop exponentially in the length L of the tunneling loops. Here we show that virtual excursions outside the NNVB basis can alter completely this fundamental quantum-mechanical notion even in extreme cases where the minimal NNVB truncation appears very robust. This paradigm shift is demonstrated for the quantum spin-1/2 square-kagome, where strong geometric frustration, similar to the two-dimensional kagome, preve…
Gapped $Z_{2}$ spin liquid as the simplest spin liquid has been proved to be the most difficult to realize in realistic models. Here we show that the frustration from a third-neighbor exchange $J_{3}$ on the spin-$\frac{1}{2}$ $J_{1}-J_{2}$ model on the square lattice may serve to stabilize such a long-sought state. We argue that a Bosonic RVB description is more appropriate than a Fermonic RVB description for such a gapped spin liquid phase. We show that while the mean field ansatz of the proposed state has a $U(1)$ gauge symmetry, the gauge fluctuation spectrum on it is actually gapped and t…
We construct energy-optimized resonating valence bond wavefunctions as a means to sketch out the zero-temperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest- (J1) and next-nearest-neighbour (J2) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J2/J1 ~ 1/2 and whose exact nature is still controversial) but on exploring whether and how the Marshall sign structure breaks down in the vicinity of the phase boundaries. Numerical evaluation of two- an…
We relate properties of nearest-neighbour resonating valence bond (nnRVB) wavefunctions for $SU(g)$ spin systems on two dimensional bipartite lattices to those of fully-packed classical dimer models with potential energy $V$ on the same lattice. We define a cluster expansion of $V$ in terms of $n$-body potentials $V_n$, which are recursively determined from the nnRVB wavefunction on {\em finite subgraphs} of the original lattice. The magnitude of the $n$-body interaction $V_n$ ($n>1$) is of order ${\mathcal O}(g^{-(n-1)})$ for small $g^{-1}$, while $V_1$ reduces to a constant due to the fully-…
We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the Rényi entropy for splitting a torus into two cylinders, We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not iden…
We study bond and spin correlations of the nearest-neighbour resonating valence bond (RVB) wavefunction for a SU($2$) symmetric $S=1/2$ antiferromagnet on the honeycomb lattice. We find that spin correlations in this wavefunction are short-ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\vec{r}) \sim \cos({\mathbf Q}\cdot {\vec{r}}) /|{\vec{r}}|^{η_w(2)}$, where ${\mathbf Q} = (2π/3, -2π/3)$ is the wavevector corresponding to "columnar" valence-bond solid order on the honeycomb lattice, and $η_w(2) \approx 1.49(3)$. We use a recently introduced larg…
