We show that a new glassy phase can emerge in presence of strong magnetic frustration and quantum fluctuations. It is a Valence Bond Glass. We study its properties solving the Hubbard-Heisenberg model on a Bethe lattice within the large $N$ limit introduced by Affleck and Marston. We work out the phase diagram that contains Fermi liquid, dimer and valence bond glass phases. This new glassy phase has no electronic or spin gap (although a pseudo-gap is observed), it is characterized by long-range critical valence bond correlations and is not related to any magnetic ordering. As a consequence it is quite different from both valence bond crystals and spin glasses.
We present a large-N variational approach to describe the magnetism of insulating doped semiconductors based on a disorder-generalization of the resonating-valence-bond theory for quantum antiferromagnets. This method captures all the qualitative and even quantitative predictions of the strong-disorder renormalization group approach over the entire experimentally relevant temperature range. Finally, by mapping the problem on a hard-sphere fluid, we could provide an essentially exact analytic solution without any adjustable parameters.
The hardcore extended Bose Hubbard model on a bilayer square lattice with attractive (repulsive) interplane (intraplane) interactions has been investigated numerically. Focusing on the strong interplane hopping parameter regime, triplet valence bonds of dimers are stabilized to form valence bond checkerboard solid at quarter filling. Increasing the particle number we confirm, for the first time, the presence of the exotic valence bond supersolid phase, where the valence bond solid ordering and the boson superfluidity coexist. Rising further the particle number will lead to a checkerboard solid…
Doped IrTe$_2$ is considered a platform for topological superconductivity and therefore receives currently a lot of interest. In addition, the superconductivity in these materials exists in close vicinity of electronic valence bond crystals, which we explore here by means of high-pressure single crystal x-ray diffraction in combination with density functional theory. Our crystallographic refinements provide unprecedented information about the structural evolution as a function of applied pressure up to 42 GPa. Using this structural information for density functional theory calculations, we sho…
The phase diagram of Kane-Mele-Heisenberg (KMH) model in classical limit~\cite{zare}, contains disordered regions in the coupling space, as the result of to competition among different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phase in the quantum limit, for a $S=1/2$. Employing exact diagonalization (ED) in $S_z$ and nearest neighbor valence bond (NNVB) bases, bond and plaquette valence bond mean field theories, We show that the disordered regions are divided into ordered quantum states in the form of plaquet…
We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagome and the pyrochlore lattice. Focussing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry breaking instability towards a twofold degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.
We introduce for SU(2) quantum spin systems the Valence Bond Entanglement Entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with Quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a Valence Bond Solid state and multiplicative logarithmic corrections for the Neel phase.
We present a theory for site dilution in the Valence Bond Crystal Phase of the Kagome Lattice Heisenberg Model. The presence of an empty site leads to strong singlet bond across the impurity. It also creates a free spin, which delocalizes inside the unit cell. Finite concentration of quenched impurities leads to a Valence Bond Glass phase. This phase has short-range Valence Bond order, no spin-gap, large spin susceptibilities, linear specific heat due to two-level systems, as well as singlet and triplet excitations that decompose into kink-antikink pairs delocalized over a few lattice constant…
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$_2$.
We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte C…
We propose a set of maximized string order parameters to describe the hidden topological order in the valence bond solid states of quantum integer spin-S chains. These optimized string order parameters involve spin-twist angles corresponding to $Z_{S+1}$ rotations around $z$ or $x$-axes, suggesting a hidden $Z_{S+1}\times Z_{S+1}$ symmetry. Our results also suggest that a local triplet excitation in the valence bond solid states carries a $Z_{S+1}$ topological charge measured by these maximized string order parameters.
The pressure-dependent relation between Eu valence and lattice structure in model compound EuO is studied with synchrotron-based x-ray spectroscopic and diffraction techniques. Contrary to expectation, a 7% volume collapse at $\approx$ 45 GPa is accompanied by a reentrant Eu valence transition into a $\emph{lower}$ valence state. In addition to highlighting the need for probing both structure and electronic states directly when valence information is sought in mixed-valent systems, the results also show that widely used bond-valence methods fail to quantitatively describe the complex electroni…
The honeycomb lattice material Li2RuO3 undergoes a dimerization of Ru4+ cations on cooling below 270C, where the magnetic susceptibility vanishes. We use density functional theory calculations to show that this reflects the formation of a 'valence bond crystal', with a strong bond disproportionation. On warming, x-ray diffraction shows that discrete three-fold symmetry is regained on average, and the dimerization apparently disappears. In contrast, local structural measurements using high-energy x-rays, show that disordered dimers survive at the nanoscale up to at least 650C. The high temperat…
We present the class of models of a nonmagnetic impurity in S=1/2 generalized ladder with an AKLT-type valence bond ground state, and of a S=1/2 impurity in the S=1 AKLT chain. The ground state in presence of impurity can be found exactly. Recently studied phenomenon of local enhancement of antiferromagnetic correlations around the impurity is absent for this family of models.
Recent evidence from magnetic torque, electron spin resonance, and second harmonic generation indicate that the prototypical quantum spin liquid candidate, herbertsmithite, has a symmetry lower than its x-ray refined trigonal space group. Here, we consider known and possible distortions of this mineral class, along with related copper kagome oxides and fluorides, relate these to possible valence bond patterns, and comment on their relevance to the physics of these interesting materials.
Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.
We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.
Every singlet state of a quantum spin 1/2 system can be decomposed into a linear combination of valence bond basis states. The range of valence bonds within this linear combination as well as the correlations between them can reveal the nature of the singlet state, and are key ingredients in variational calculations. In this work, we study the bipartite valence bond distributions and their correlations within the ground state of the Heisenberg antiferromagnet on bipartite lattices. In terms of field theory, this problem can be mapped to correlation functions near a boundary. In dimension d >= …
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 introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry SP(n) and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.
We present a valence bond theory of the spin-S quantum Heisenberg model. For nonfrustracting, local exchange and dimension d > 1, it predicts a resonating ground state with bond amplitudes h(r) ~ (a^2+r^2)^(-p/2) and decay exponent p=d+1. Different values of p can be achieved by introducing frustrating (p > d+1) or nonfrustrating (p < d+1) long-range interactions. For d=2, but not d=3, there is a critical value of the decay exponent p_c above which the ground state is a spin liquid. The phase transition is analogous to quantum percolation, with fractal valence bond loops playing the role of pe…
A generalized one-dimensional $SU(2)\times SU(2)$ spin-orbital model is studied by Schwinger boson mean-field theory (SBMFT). We explore mainly the dimer phases and clarify how to capture properly the low temperature properties of such a system by SBMFT. The phase diagrams are exemplified. The three dimer phases, orbital valence bond solid (OVB) state, spin valence bond solid (SVB) state and spin-orbital valence bond solid (SOVB) state, are found to be favored in respectively proper parameter regions, and they can be characterized by the static spin and pseudospin susceptibilities calculated i…
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 Hamiltonians are provided so that the valence bond solid states are their unique ground states. For quantum integer spin-$S$ chains, we discuss two topologically distinct classes of valence bond solid states: One consists of two virtual SU(2) spin-$J$ variables in each site and another is formed by using two $SO(2S+1)$ spinors. Among them, a new spin-1 fermionic v…
We discuss ground-state projector simulations of a modified two-dimensional S=1/2 Heisenberg model in the valence bonds basis. Tuning matrix elements corresponding to the diagonal and off-diagonal terms in the quantum dimer model, we show that there is a quantum phase transition from the antiferromagnet into a columnar valence-bond-solid (VBS). There are no signs of discontinuities, suggesting a continuous or very weakly first-order transition. The Z4-symmetric VBS order parameter exhibits an emergent U(1) symmetry as the phase transition is approached. We extract the associated length-scale g…
We extend the quantum dimer model (QDM) introduced by Rokhsar and Kivelson so as to construct a concrete example of the model which exhibits the first-order phase transition between different valence-bond solids suggested recently by Batista and Trugman and look for the possibility of other exotic dimer states. We show that our model contains three exotic valence-bond phases (herringbone, checkerboard and dimer smectic) in the ground-state phase diagram and that it realizes the phase transition from the staggered valence-bond solid to the herringbone one. The checkerboard phase has four-fold r…
A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations o…
On the basis of a Berry-phase analysis, we study the ground state of the $J_1$-$J_2$ Heisenberg chain for $S=2,3,4$. We find that changes of the Berry phase occur $S$ times for spin-$S$ systems, indicating the sequential phase transitions. The sequential phase transitions are associated with the change of valence-bond configurations of the ground states. To demonstrate this numerically, we connect the $J_1$-$J_2$ Heisenberg Hamiltonian with the generalized Affleck-Kennedy-Lieb-Tasaki model, and show that the different phases are connected to the different valence-bond-solid states.
We argue that neutron spectra in a short-range ordered Valence Bond state is dominated by two-spinon states localized in small spatial regions such as a pinwheel. These excitations lead to angle averaged dynamic structure factor that is spread over a wide frequency range up to about $2.5 J$, whereas its wavevector dependence at all frequencies remains very close to that of isolated dimers. These results are in excellent agreement with recent Neutron scattering data in the Herbertsmithite materials ZnCu$_3$(OH)$_6$Cl$_2$.
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 investigate theoretically the ordering effect of quantum spin fluctuations in a Heisenberg antiferromagnet on a two-dimensional network of corner sharing tetrahedra. This network is obtained as a {111} slice of the highly frustrated pyrochlore lattice, from which it inherits the equivalence of all three pairs of opposite bonds of each tetrahedron. The lowest-order (in 1/S) quantum corrections partially lift the huge degeneracy of the classical ground state and select an ensemble of states with long-range valence-bond order.
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 …
In a system with an even number of SU(2) spins, there is an overcomplete set of states--consisting of all possible pairings of the spins into valence bonds--that spans the S=0 Hilbert subspace. Operator expectation values in this basis are related to the properties of the closed loops that are formed by the overlap of valence bond states. We construct a generating function for spin correlation functions of arbitrary order and show that all nonvanishing contributions arise from configurations that are topologically irreducible. We derive explicit formulas for the correlation functions at second…
We report on the unconventional magnetism in the cubic B-site ordered double perovskite Ba2YMoO6, using AC and DC magnetic susceptibility, heat capacity and muSR. No magnetic order is observed down to 2 K while the Weiss temperature is ~ -160 K. This is ascribed to the geometric frustration in the lattice of edge-sharing tetrahedra with orbitally degenerate Mo5+ s=1/2 spins. Our experimental results point to a gradual freezing of the spins into a disordered pattern of spin-singlets, quenching the orbital degeneracy while leaving the global cubic symmetry unaffected, and providing a rare exampl…
We have synthesized a new spinel oxide LiRh2O4 with a mixed-valent configuration of Rh3+ and Rh4+. At room temperature it is a paramagnetic metal, but on cooling, a metal-insulator transition occurs and a valence bond solid state is formed below 170 K. We argue that the formation of valence bond solid is promoted by a band Jahn-Teller transition at 230 K and the resultant confinement of t2g holes within the xy band. The band Jahn-Teller instability is also responsible for the observed enhanced thermoelectric power in the orbital disordered phase above 230 K.
We have applied the bond valence method to cerium oxides to determine the oxidation states of the Ce ion at the various site symmetries of the crystals. The crystals studied include cerium dioxide and the two sesquioxides along with some selected intermediate phases which are crystallographically well characterized. Our results indicate that cerium dioxide has a mixed-valence ground state with an f-electron population on the Ce site of 0.27 while both the A- and C-sesquioxides have a nearly pure f^1 configuration. The Ce sites in most of the intermediate oxides have non-integral valences. Furt…
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…
A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a quantum spin system where local spin singlets are formed in some regular pattern. We here study the competition between VBS order and a fully polarized ferromagnetic state as function of an external magnetic field in a one-dimensional extended Heisenberg model---the J-Q$_2$ model---using stochastic series expansion quantum Monte Carlo simulations with directed loop updates. We discuss the ground state phase diagram.
We report on a valence bond projector Monte Carlo simulation of the cubic lattice quantum Heisenberg model with additional higher-order exchange interactions in each unit cell. The model supports two different valence bond solid ground states. In one of these states, the dimer pattern is a three-dimensional analogue of the columnar pattern familiar from two dimensions. In the other, the dimers are regularly arranged along the four main diagonals in 1/8 of the unit cells. The phases are separated from one other and from a Neel phase by strongly first order boundaries. Our results strengthen the…
General conditions in which disordered, spin liquid, and valence-bond ordered phases occur in quantum Ising antiferromagnets are studied using the prototype Kagome lattice spin models. A range of quantum dynamical processes in the Ising model, with and without total Ising spin conserved, are analytically shown to yield all three characteristic quantum paramagnetic phases in the Kagome system. Special emphasis is given to the XXZ model that can be sensibly compared to the Kagome lattice Heisenberg antiferromagnet. It is explicitly demonstrated that the total-spin-conserving dynamics can yield a…
Recently, neutron scattering data on powder samples of Zn-paratacamite, Zn$_x$Cu$_{4-x}$(OH)$_6$Cl$_{2}$, with small Zn concentration has been interpreted as evidence for valence bond solid and Néel ordering [1]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn-paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and X-ray scattering…
We present variational results for the ground state of the antiferromagnetic quantum Heisenberg model with frustrating next-nearest-neighbour interactions. The trial wave functions employed are of resonating-valence-bond type, elaborated to account for various geometric motifs of adjacent bond pairs. The calculation is specialized to a square-lattice cluster consisting of just sixteen sites, large enough that the system can accommodate nontrivial singlet dimer correlations but small enough that exhaustive enumeration of states in the total spin zero sector is still feasible. A symbolic computa…
Motivated by recent experiments on SrCu$_2$(BO$_3$)$_2$, we investigate the ground states of the doped Mott insulator on the Shastry-Sutherland lattice. To provide a unified theoretical framework for both the valence-bond solid state found in undoped SrCu$_2$(BO$_3$)$_2$ and the doped counterpart being pursued in on-going experiments, we analyze the t-J-$V$ model via the bond operator formulation. It is found that novel superconducting states emerge upon doping with their properties crucially depending on the underlying valence bond order. Implications to future experiments are discussed.
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 \approx 0.23$. C…
The $\EtMeP$ and $\EtMeSb$ nearly triangular organic salts are distinguished from most other Pd[(dmit)$_2$] based salts, as they display valence bond and no long range order, respectively. Under pressure, a superconducting phase is revealed in EtMe$_3$P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperatu…
Motivated by a recent experiment on Rb2Cu3SnF12, where spin-1/2 Cu2+ moments reside on the layers of Kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed Kagome lattices. The deformation is characterized by a weaker exchange coupling (alpha*J) on certain lattice links appropriate for Rb2Cu3SnF12 with alpha=1 corresponding to the ideal Kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operato…
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 propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the configuration of the valence bonds. This allows us to determine the phase transition point in between different VBS states accurately. We demonstrate this theory in the bond-alternating Heisenberg chain and in the frustrated spin ladder.
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 stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.
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.
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…
Using the density matrix renormalization group, we investigate the $S=1/2$ Heisenberg model on the honeycomb lattice with first- ($J_1$) and second-neighbor ($J_2$) interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For $J_2/J_1$ near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for $J_2\lesssim 0.26$ and by a valence bond crystal for $J_2\gtrsim 0.36$. The longest correlation length that we find in this intermediate phase is for plaquette valence bond (PVB) order. This correlation length grows strongly with cy…
Using both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-di…
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 study a variational wave function for the ground state of the two-dimensional S=1/2 Heisenberg antiferromagnet in the valence bond basis. The expansion coefficients are products of amplitudes h(x,y) for valence bonds connecting spins separated by (x,y) lattice spacings. In contrast to previous studies, in which a functional form for h(x,y) was assumed, we here optimize all the amplitudes for lattices with up to 32*32 spins. We use two different schemes for optimizing the amplitudes; a Newton/conjugate-gradient method and a stochastic method which requires only the signs of the first derivat…
In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states, and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function for the SVBS states can describe resonating valence bond states (RVB). The SVBS states for the spin mo…
Motivated by numerical evidence of the valence bond groundstate of the two-dimensional Heisenberg pyrochlore lattice, we argue using a $t$-$J$ model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-$T_c$ cuprates as well as possible relevance to frustrated noncuprate superconductors such as …
Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence Bond Crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid/metallic phases under increasing hopping is investigated at T=0K. More specifically, we identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negati…
A molecular Mott insulator $κ$-(ET)$_2$B(CN)$_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits a quantum disordered state with gapped spin excitation in the ground state. $^{13}$C nuclear magnetic resonance, magnetization, and magnetic torque measurements reveal that magnetic field suppresses valence bond order and induces long-range magnetic order above a critical field $\sim 8$ T. The nuclear spin-lattice relaxation rate $1/T_1$ shows persistent evolution of antiferromagnetic correlation above the transition temperature, highlighting a quantum spin…
