Valence-bond Ground States Research Articles

Ergodic Archimedean dimers

We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.

Bond ordering and molecular spin-orbital fluctuations in the cluster Mott insulator GaTa4Se8

For materials where spin-orbit coupling is competitive with electronic correlations, the spatially anisotropic spin-orbital wave functions can stabilize degenerate states that lead to many and diverse quantum phases of matter. Here we find evidence for a dynamical spin-orbital state preceding a ${T}^{*}$ = 50 K order-disorder spin-orbital ordering transition in the $j=3/2$ lacunar spinel ${\mathrm{GaTa}}_{4}{\mathrm{Se}}_{8}$. Above ${T}^{*}, {\mathrm{GaTa}}_{4}{\mathrm{Se}}_{8}$ has an average cubic crystal structure, but total scattering measurements indicate local noncubic distortions of ${\mathrm{Ta}}_{4}$ tetrahedral clusters for all measured temperatures $2<T<300$ K. Inelastic neutron-scattering measurements reveal the dynamic nature of these local distortions through symmetry forbidden optical phonon modes that modulate $j=3/2$ molecular orbital occupation as well as intercluster Ta-Se bonds. Spin-orbital ordering at ${T}^{*}$ cannot be attributed to a classic Jahn-Teller mechanism and, based on our findings, we propose that intercluster interactions acting on the scale of ${T}^{*}$ act to break global symmetry. The resulting staggered intercluster dimerization pattern doubles the unit cell, reflecting a spin-orbital valence bond ground state.

YbMgGaO4: A Triangular‐Lattice Quantum Spin Liquid Candidate

AbstractResonating valence bond ground state, the prototype of a quantum spin liquid (QSL), had been first proposed by P. W. Anderson back in 1973 on the triangular lattice. In such a 2D QSL, spinons created as unpaired spins can propagate by locally rearranging the uncorrelated valence bonds. However, the corresponding candidate materials are still rare to date. YbMgGaO4, first proposed in 2015 may fill this gap: the magnetic rare‐earth Yb3+ ions arrange on the triangular lattice with the perfect R‐3m symmetries and with a large interlayer distance. No conventional spin freezing is observed down to 40 mK without residual magnetic entropy, despite the significant antiferromagnetic coupling of ≈2 K. This report reviews and classifies the relevant experimental and theoretical progress on some (effective) spin‐1/2 triangular antiferromagnets, especially on YbMgGaO4, followed by discussion and outlook on some of the pending issues.

Spectra of correlated many-electron systems: From a one- to a two-particle description

State-of-the-art spectroscopic techniques allow for a comprehensive understanding of one-electron excitations in various physically interesting and/or technologically relevant materials. While for weakly-correlated systems the corresponding one-particle spectral function A(ω, k) contains essentially all information about their physical properties the situation is much more complicated in the presence of strong electronic correlations. In fact, in the latter case different theoretical treatments often lead to very different explanations of the origin of specific features in the spectrum. A typical example is the pseudogap in the cuprates, i.e., the momentum-selective suppression of spectral weight at the Fermi level, which has been related to spin, charge or (d-wave) pairing fluctuations by different authors. This ambiguity about the underlying physical mechanism at work can be overcome by considering two-particle correlation functions as they are able to describe the collective modes of the system and can be also related to certain ground state properties. In this work, we will present different theoretical approaches for analyzing the spectrum of correlated systems by exploiting the information contained in these two-particle correlation functions. For the specific case of the pseudogap these procedures have allowed us (1) to identify antiferromagnetic spin fluctuations as microscopic origin of this spectral feature which (2) can be related to the formation of a resonating valence bond ground state in the system.

End states in a one-dimensional topological Kondo insulator in large-Nlimit

To gain further insight into the properties of interacting topological insulators, we study a one-dimensional model of topological Kondo insulators which can be regarded as the strongly interacting limit of the Tamm-Shockley model. Treating the model in a large-$N$ expansion, we find a number of competing ground-state solutions, including topological insulating and valence bond ground states. One of the effects to emerge in our treatment is a reconstruction of the Kondo screening process near the boundary of the material (``Kondo band-bending''). Near the boundary for localization into a valence bond state, we find that the conduction character of the edge state grows substantially, leading to states that extend deeply into the bulk. We speculate that such states are the one-dimensional analog of the light $f$-electron surface states which appear to develop in the putative topological Kondo insulator, ${\mathrm{SmB}}_{6}$.

Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8

The emergence of complex electronic behaviour from simple ingredients has resulted in the discovery of numerous states of matter. Many examples are found in systems exhibiting geometric magnetic frustration, which prevents simultaneous satisfaction of all magnetic interactions. This frustration gives rise to complex magnetic properties such as chiral spin structures orbitally-driven magnetism, spin-ice behavior exhibiting Dirac strings with magnetic monopoles, valence bond solids, and spin liquids. Here we report the synthesis and characterization of LiZn2Mo3O8, a geometrically frustrated antiferromagnet in which the magnetic moments are localized on small transition metal clusters rather than individual ions. By doing so, first order Jahn-Teller instabilities and orbital ordering are prevented, allowing the strongly interacting magnetic clusters in LiZn2Mo3O8 to probably give rise to an exotic condensed valence-bond ground state reminiscent of the proposed resonating valence bond state. Our results also link magnetism on clusters to geometric magnetic frustration in extended solids, demonstrating a new approach for unparalleled chemical control and tunability in the search for collective, emergent electronic states of matter.

Supersolid Phases of a Doped Valence-Bond Quantum Antiferromagnet: Evidence for a Coexisting Superconducting Order Parameter

Motivated by numerical evidence of the valence-bond ground state 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-Tc cuprates as well as possible relevance to frustrated noncuprate superconductors such as spinels and pyrochlores is discussed.

Two-dimensional spin-1 frustrated Heisenberg model with valence-bond ground states

In this paper, we propose a method to understand the nature of the quantum disorder phase of the two-dimensional (2D) high-spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose ground state can be found exactly. By analogy to the pseudopotential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valence-bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used reveals the connection between the fractional quantum Hall effect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system and can be verified by a numerical method.

Resonating Valence-Bond Ground State in a Phenalenyl-Based Neutral Radical Conductor

An organic material composed of neutral free radicals based on the spirobiphenalenyl system exhibits a room temperature conductivity of 0.3 siemens per centimeter and a high-symmetry crystal structure. It displays the temperature-independent Pauli paramagnetism characteristic of a metal with a magnetic susceptibility that implies a density of states at the Fermi level of 15.5 states per electron volt per mole. Extended Hückel calculations indicate that the solid is a three-dimensional organic metal with a band width of approximately 0.5 electron volts. However, the compound shows activated conductivity (activation energy, 0.054 electron volts) and an optical energy gap of 0.34 electron volts. We argue that these apparently contradictory properties are best resolved in terms of the resonating valence-bond ground state originally suggested by Pauling, but with the modifications introduced by Anderson.

Identification of topologically different valence bond states in spin ladders

We discuss relation between three different methods to identify topologically distinct short-range valence-bond ground states in spin-$\frac12$ two-leg ladders: the string order parameters, the level-crossing method, and the ground-state expectation value of the twist operator. For this purpose we reexamine a phase transition in the frustrated spin ladder. We propose a proper bosonization of the string order parameters. Then, these three methods are shown to be equivalent reflecting the $Z_2\times Z_2$ symmetry breaking of the order and the disorder fields of the two-dimensional Ising model.

Kekulé‐based Valence Bond Model. I. The Ground‐state Properties of Conjugated 7ü‐Systems

AbstractThe Kekulé‐based valence bond (VB) method, in which the VB model is solved using covalent Kekulé structures as basis functions, is justified in the present work. This method is demonstrated to provide satisfactory descriptions for resonance energies and bond lengths of benzenoid hydrocarbons, being in good agreement with SCF‐MO and experimental results. In addition, an alternative way of discussing characters of localized substructures within a polycyclic benzenoid system is suggested based upon such simplified VB calculations. Finally, the symmetries of VB ground states for nonalternant conjugated systems are also illustrated to be obtainable through these calculations, presenting very useful information for understanding the chemical behaviors of some nonalternant conjugated molecules.

Phase transitions between topologically distinct gapped phases in isotropic spin ladders

We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide into two topologically distinct classes, and as a consequence, there exist two topologically distinct types of string order. Therefore, not all gapped phases belong to the same universality class. We show that phase transitions occur when we interpolate between models belonging to different topological classes, and we study the nature of these transitions.

Valence bond ground states in quantum antiferromagnets and quadratic algebras

The wave functions corresponding to the zero energy eigenvalue of a one-dimensional quantum chain Hamiltonian can be written in a simple way using quadratic algebras. Hamiltonians describing stochastic processes have stationary states given by such wave functions and various quadratic algebras were found and applied to several diffusions processes. We show that similar methods can also be applied for equilibrium processes. As an example, for a class of q-deformed O(N) symmetric antiferromagnetic quantum chains, we give the zero energy wave functions for periodic boundary conditions corresponding to momenta zero and $\pi$. We also consider free and various non-diagonal boundary conditions and give the corresponding wave functions. All correlation lengths are derived.

Models of impurities in valence-bond spin chains and ladders

We present the class of models of a nonmagnetic impurity in an S = 1/2 generalized ladder with an Affleck-Kennedy-Lieb-Tasaki-type (AKLT-type) valence-bond ground state, and of an S = 1/2 impurity in the S = 1 AKLT chain. The ground state in the presence of impurity can be found exactly. The recently studied phenomenon of local enhancement of antiferromagnetic correlations around the impurity is absent for this family of models.

Variational states for the spin-Peierls system

We introduce a family of Jastrow pair product states for quasi one-dimensional spin systems. Depending on a parameter they interpolate between the resonating valence bond ground state of the Haldane-Shastry model describing a spin liquid and the (dimerized) valence bond solid ground states of the Majumdar-Ghosh spin chain. These states are found to form an excellent basis for variational studies of Heisenberg chains with next nearest neighbour interaction and bond alternation as realized in the spin-Peierls system CuGeO_3.

Quantum Melting of Magnetic Order due to Orbital Fluctuations

We have studied the phase diagram and excitations of the spin-orbital model derived for a three dimensional perovskite lattice, as in KCuF_3. The results demonstrate that the orbital degeneracy drastically increases quantum fluctuations and suppresses the classical long-range order near the multicritical point in the mean-field phase diagram. This generates a qualitatively new spin liquid, providing the first example of a valence bond ground state in three dimensions.

Potential energy surfaces of pseudoaromatic molecules: An MMVB and CASSCF study of pentalene

The S0 and S1 potential energy surfaces of pentalene were studied using MMVB—a hybrid force-field/parametrized valence bond (VB) method designed to simulate CASSCF calculations for ground and covalent excited states. The results were calibrated against full CASSCF calculations. Four distinct critical points were optimized: on S0, a C2h minimum (with alternating single and double bonds) and a D2h transition structure; and on S1, a D2h minimum and an adjacent S1/S0 conical intersection. A VB exchange density matrix (which is independent of the choice of the spin-coupled basis) was used to rationalize the S0 and S1 surface topologies. Craig defined pseudoaromatic molecules to be those with nontotally symmetric electronic ground states. For pentalene, this is true for both CASSCF and MMVB calculations: the CASSCF S0 transition structure is an open-shell B1x singlet, and the VB ground state is dominated by a spin-coupling which transforms as B1g. A C2v minimum and a D2h transition structure were located on the CASSCF S2 potential energy surface. This state cannot be represented by MMVB because of the importance of ionic configurations. The characters of the S1 S2 states of pentalene are shown to be reverse of the S1 and S2 states of benzene. © 1996 John Wiley & Sons, Inc.

Temperley-Lieb words as valence-bond ground states

Based on the Temperley--Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two point correlation functions can be computed employing the Temperley--Lieb relations. Choosing a spin-1/2 representation of the algebra we obtain a generalization of the (q-deformed) Majumdar--Ghosh model. The ground states become valence-bond states.

Q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE-BOND GROUND STATES

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighboring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-½ Majumdar-Ghosh model.

Propagator descriptions of ionisation and excitation phenomena using valence bond reference functions

The H 2 molecule in a minimal basis is used to explore the possibility of using a valence bond ground state reference function for propagator calculations of ionisation energies, electron affinities and excitation energies.