Valence Bond State Research Articles

Mechanistic Insights into the Reactivity and Activation Barrier Origins for CO2 Capture by Heavy Group-14 Imine Analogues.

Using M06-2X-D3/def2-TZVP, the [2 + 2] cycloaddition reactions of carbon dioxide with the heavy imine analogues G14=N-Rea (G14 = Group 14 element) were investigated. The theoretical evidence reveals that the nature of the doubly bonded G14=N moiety in heavy imine analogues, G14=N-Rea (L1L2G14=N-L3), is characterized by the electron-sharing interaction between triplet L1L2G14 and triplet N-L3 fragments. Based on our theoretical studies, except for the carbon-based imine, all four heavy imine analogues with Si=N, Ge=N, Sn=N, and Pb=N groups can easily engage in [2 + 2] cycloaddition reactions with CO2. Energy decomposition analysis-natural orbitals for chemical valence analyses and the FMO theory strongly suggest that in the CO2 capture reaction by heavy imine analogues G14=N-Rea, the primary bonding interaction is the occupied p-π orbital (G14=N-Rea) → vacant p-π* orbital (CO2) interaction, instead of the empty p-π* orbital (G14=N-Rea) ← filled p-π orbital (CO2) interaction. The activation barrier of the CO2 capture reactions by G14=N-Rea molecules is primarily determined by the deformation energy of CO2. Shaik's valence bond state correlation diagram model, used to rationalize the computed results, indicates that the singlet-triplet energy splitting of G14=N-Rea is a key factor in determining the reaction barrier for the current CO2 capture reactions.

Triplon analysis of magnetic disorder and order in maple-leaf Heisenberg magnet

The nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice formed by hexagons (couplingJh), triangles (couplingJt), and dimers (couplingJd), is investigated in a parameter regime whereJh>0andJt,Jd<0. This investigation aims to identify regions hosting exotic valence-bond solid states. Two potential magnetically disordered ground states are identified, and their stability is assessed through plaquette-triplon mean-field analyses. The resulting quantum phase diagram reveals that at large|Jt|and|Jd|, the system adopts a magnetically disordered dimerized VBS state, while for small|Jd|, it stabilizes a Néel state. A second-order phase transition from the dimerized phase to a Néel phase is observed, which, being Landau-forbidden, suggests the potential presence of exotic phenomena such as a deconfined quantum critical point or the appearance of a quantum spin liquid. This work provides insights into the phase diagram of the nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice and lays the groundwork for further investigations into its intriguing physics.

Twisted graphene superlattices: resonating valence bond states and magnetic properties

Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin–spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.

Entanglement negativity between separated regions in quantum critical systems

We study the entanglement between disjoint subregions in quantum critical systems through the lens of the logarithmic negativity. We work with systems in arbitrary dimensions, including conformal field theories and their corresponding lattice Hamiltonians, as well as resonating valence-bond states. At small separations, the logarithmic negativity is big and displays universal behavior, but we show nonperturbatively that it decays faster than any power at large separations. This can already be seen in the minimal setting of single-spin subregions. The corresponding absence of distillable entanglement at large separations generalizes the one-dimensional result, and indicates that quantum critical ground states do not possess long-range bipartite entanglement, at least for bosons. For systems with fermions, a more suitable definition of the logarithmic negativity exists that takes into account fermion parity, and we show that it decays algebraically. Along the way we obtain general results for the moments of the partially transposed density matrix. Published by the American Physical Society 2024

Anyon condensation and confinement transition in a Kitaev spin liquid bilayer

Transitions between quantum spin liquids (QSLs) are fundamental problems lying beyond the Landau paradigm and requiring a deep understanding of the entanglement structures of QSLs called topological orders. The novel concept of anyon condensation has been proposed as a theoretical mechanism, predicting various possible transitions between topological orders, but it has long been elusive to confirm the mechanism in quantum spin systems. Here, we introduce a concrete spin model that incarnates the mechanism of the anyon condensation transition. Our model harbors two topological QSLs in different parameter regions, a non-Abelian Kitaev spin liquid (KSL) bilayer state and a resonating valence bond (RVB) state. The bilayer-KSL-to-RVB transition indeed occurs by the mechanism of anyon condensation, which we identify by using parton theories and exact diagonalization studies. Moreover, we observe “anyon confinement” phenomena in our numerical results, akin to the quark confinement in high-energy physics. Namely, non-Abelian Ising anyons of the bilayer KSL are confined in the transition to the RVB state. Implications and extensions of this study are discussed in various aspects such as (i) anyon-condensed multilayer construction of Kitaev's 16-fold way of anyon theories, (ii) an additional vison condensation transition from the RVB to a valence bond solid in the Kitaev bilayer system, (iii) dynamical anyon condensation in a non-Hermitian Kitaev bilayer, (iv) generalizations of our model to other lattice geometries, and (v) experimental realizations. This work puts together the two fascinating QSLs that are extensively studied in modern condensed matter and quantum physics into a concrete spin model, offering a comprehensive picture that unifies the anyon physics of the Kitaev spin liquids and the resonating valence bonds. Published by the American Physical Society 2024

Physics-Inspired Quantum Simulation of Resonating Valence Bond States─A Prototypical Template for a Spin-Liquid Ground State.

Spin liquids─an emergent, exotic collective phase of matter─have garnered enormous attention in recent years. While experimentally many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of such phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics. In this report, we strive to use the power of the latter to study a prototypical model, a spin-1/2-unit cell of a Kagome antiferromagnet. Extended lattices of such unit cells are known to possess a magnetically disordered spin-liquid ground state. We employ robust classical numerical techniques such as the density-matrix renormalization group (DMRG) to identify the nature of the ground state through a matrix-product state (MPS) formulation. We subsequently use the gained insight to construct an auxiliary Hamiltonian with reduced measurables and also design an ansatz that is modular and gate-efficient. With robust error-mitigation strategies, we are able to demonstrate that the said ansatz is capable of accurately representing the target ground state even on a real IBMQ backend within 1% accuracy in energy. Since the protocol is linearly scaling O(n) in the number of unit cells, gate requirements, and the number of measurements, it is straightforwardly extendable to larger Kagome lattices that can pave the way for efficient construction of spin-liquid ground states on a quantum device.

Separability and entanglement of resonating valence-bond states

We investigate separability and entanglement of Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. These states play a prominent role in condensed matter physics, as they can describe quantum spin liquids and quantum critical states of matter, depending on their underlying lattices. For dimer RK states on arbitrary tileable graphs, we prove the exact separability of the reduced density matrix of kk disconnected subsystems, implying the absence of bipartite and multipartite entanglement between the subsystems. For more general RK states with local constraints, we argue separability in the thermodynamic limit, and show that any local RK state has zero logarithmic negativity, even if the density matrix is not exactly separable. In the case of adjacent subsystems, we find an exact expression for the logarithmic negativity in terms of partition functions of the underlying statistical model. For RVB states, we show separability for disconnected subsystems up to exponentially small terms in the distance dd between the subsystems, and that the logarithmic negativity is exponentially suppressed with dd. We argue that separability does hold in the scaling limit, even for arbitrarily small ratio d/Ld/L, where LL is the characteristic size of the subsystems. Our results hold for arbitrary lattices, and encompass a large class of RK and RVB states, which include certain gapped quantum spin liquids and gapless quantum critical systems.

50 years of quantum spin liquids

In 1973, Philip Anderson published a paper introducing the resonating valence bond state, which can be recognized in retrospect as a topologically ordered phase of matter — one that cannot be classified in the conventional way according to its patterns of spontaneously broken symmetry. Steven Kivelson and Shivaji Sondhi reflect on the impact of this paper over the past 50 years.

Resonating Valence Bond States in an Electron-Phonon System.

We study a simple electron-phonon model on square and triangular versions of the Lieb lattice using an asymptotically exact strong coupling analysis. At zero temperature and electron density n=1 (one electron per unit cell), for various ranges of parameters in the model, we exploit a mapping to the quantum dimer model to establish the existence of a spin-liquid phase with Z_{2} topological order (on the triangular lattice) and a multicritical line corresponding to a quantum critical spin liquid (on the square lattice). In the remaining part of the phase diagram, we find a host of charge-density-wave phases (valence-bond solids), a conventional s-wave superconducting phase, and with the addition of a small Hubbard U to tip the balance, a phonon-induced d-wave superconducting phase. Under a special condition, we find a hidden pseudospin SU(2) symmetry that implies an exact constraint on the superconducting order parameters.

Real-time dynamics of a critical resonating valence bond spin liquid

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 that projecting the time-evolution onto the PEPS manifold remains accurate at small time scales. We also find that the state evolves within a PEPS sub-manifold characterized by a U($1$) gauge symmetry, suggesting that the Coulomb phase is stable under such unitary evolution.

Optical Conductivity as a Probe of the Interaction-Driven Metal in Rhombohedral Trilayer Graphene

Study of the strongly correlated states in van der Waals heterostructures is one of the central topics in modern condensed matter physics. Among these, the rhombohedral trilayer graphene (RTG) occupies a prominent place since it hosts a variety of interaction-driven phases, with the metallic ones yielding exotic superconducting orders upon doping. Motivated by these experimental findings, we show within the framework of the low-energy Dirac theory that the optical conductivity can distinguish different candidates for a paramagnetic metallic ground state in this system. In particular, this observable shows a single peak in the fully gapped valence-bond state. On the other hand, the bond-current state features two pronounced peaks in the optical conductivity as the probing frequency increases. Finally, the rotational symmetry breaking charge-density wave exhibits a minimal conductivity with the value independent of the amplitude of the order parameter, which corresponds precisely to the splitting of the two cubic nodal points at the two valleys into two triplets of the band touching points featuring linearly dispersing quasiparticles. These features represent the smoking gun signatures of different candidate order parameters for the paramagnetic metallic ground state, which should motivate further experimental studies of the RTG.

Quantum phases of dipolar bosons in a multilayer optical lattice

We consider a minimal model to investigate the quantum phases of hardcore, polarized dipolar atoms confined in multilayer optical lattices. The model is a variant of the extended Bose-Hubbard model, which incorporates intralayer repulsion and interlayer attraction between the atoms in nearest-neighbour sites. We study the phases of this model emerging from the competition between the attractive interlayer interaction and the interlayer hopping. Our results from the analytical and cluster-Gutzwiller mean-field theories reveal that multimer formation occurs in the regime of weak intra and interlayer hopping due to the attractive interaction. In addition, intralayer isotropic repulsive interaction results in the checkerboard ordering of the multimers. This leads to an incompressible checkerboard multimer phase at half-filling. At higher interlayer hopping, the multimers are destabilized to form resonating valence-bond like states. Furthermore, we discuss the effects of thermal fluctuations on the quantum phases of the system.

The reactivity of the trapping reaction of the benzene-bridged boron/phosphorus-based frustrated Lewis pair with difluorocarbene and its group 14 analogs: A theoretical investigation.

The trapping reactions of carbene analogs G14F2 (G14=group 14 element) by the benzene-bridged B/P-Rea frustrated Lewis pair (FLPs) molecule are studied using density functional theory (B3LYP-D3(BJ)/def2-TZVP). Our theoretical investigations predict that only the CF2 intermediate rather than other heavy carbene analogs can be trapped by the B/P-Rea FLP-type molecule. Energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) analyses indicate that the bonding nature of the G14F2 catching reactions by the B/P-Rea FLP-type molecule is a donor-acceptor (singlet-singlet) interaction rather than an electron-sharing (triplet-triplet) interaction. Moreover, EDA-NOCV and frontier molecular orbital (FMO) theory findings strongly suggest that the lone pair (LP) (P) → vacant p-π-orbital (G14F2 ) interaction rather than the empty σ-orbital (B) ← sp2 -σ-orbital (G14F2 ) interaction plays a predominant role in establishing its bonding condition during the G14F2 trapping reaction with the B/P-Rea FLP-associated molecule. Our activation strain model findings reveal that the atomic radius of the G14 element of G14F2 plays a key role in determining the activation barrier of the G14F2 trapping reactions by the benzene-bridged B/P-Rea FLP. The valence bond state correlation diagram (VBSCD) model developed by Shaik is used to rationalize the calculated results. The VBSCD findings demonstrate that in the present trapping reactions, the singlet triplet splitting of G14F2 plays a significant role in influencing its reaction barrier and reaction enthalpy. Our theoretical results demonstrate that the relationship between the geometrical parameters of the transition states and the corresponding reaction free energy barriers agrees well with the findings based on the Hammond postulate.

Dynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays.

We theoretically analyze recent experiments [Semeghini etal., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.

Gutzwiller approximation approach to the SU(4) t−J model

We develop the Gutzwiller approximation method to obtain the renormalized Hamiltonian of the SU(4) $t\text{\ensuremath{-}}J$ model with the corresponding renormalization factors. Subsequently, a mean-field theory is employed on the renormalized Hamiltonian of the model on the honeycomb lattice under the scenario of a cooperative condensation of carriers moving in the resonating valence bond state of flavors. In particular, we find that the extended $s$-wave superconducting state is more favorable than the $d\ifmmode\pm\else\textpm\fi{}id$-wave superconducting state in the doping range close to quarter filling. The pairing states of the SU(4) case reveal the property that the spin-singlet pairing and the spin-triplet pairing can coexist simultaneously. Our results might provide new insights into the twisted bilayer graphene system.

Triplet resonating valence bond theory and transition metal chalcogenides

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 incorporate the effect of charge doping which stabilizes $p+ip$-wave superconductivity. Beyond the pure theoretical interest, our study may help to resolve contradictory statements on certain transition metal chalcogenides, including 1T-TaS$_2$, as a potential tRVB spin-liquid.

Dimerization in α-TiCl3 and α-TiBr3: the DFT study

A series of DFT calculations for two layered compounds with honeycomb lattice—α-TiCl3 and α-TiBr3 has been performed. It was shown that the symmetric SU(4) spin-orbital model recently proposed for d 1 systems with honeycomb lattice cannot be realized in these titanates because they dimerize in the low temperature phase. This explains experimentally observed drop in magnetic susceptibility of α-TiBr3. Our results also suggest formation of valence-bond liquid state in the high-temperature phase of α-TiCl3 and α-TiBr3.

Supersymmetry and multicriticality in a ladder of constrained fermions

Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

Coincidence inelastic neutron scattering for detection of two-spin magnetic correlations

Inelastic neutron scattering (INS) is one powerful technique to study the low-energy single-spin dynamics of magnetic materials. A variety of quantum magnets show novel magnetic correlations such as quantum spin liquids. These novel magnetic correlations are beyond the direct detection of INS. In this paper we propose a coincidence technique, coincidence inelastic neutron scattering (cINS), which can detect the two-spin magnetic correlations of the magnetic materials. In cINS there are two neutron sources and two neutron detectors with an additional coincidence detector. Two neutrons from the two neutron sources are incident on the target magnetic material, and they are scattered by the electron spins of the magnetic material. The two scattered neutrons are detected by the two neutron detectors in coincidence with the coincidence probability described by a two-spin Bethe-Salpeter wave function. Since the two-spin Bethe-Salpeter wave function defines the momentum-resolved dynamical wave function with two spins excited, cINS can explicitly detect the two-spin magnetic correlations of the magnetic material. Thus, it can be introduced to study the various spin valence bond states of the quantum magnets.

Probing resonating valence bond states in artificial quantum magnets

Designing and characterizing the many-body behaviors of quantum materials represents a prominent challenge for understanding strongly correlated physics and quantum information processing. We constructed artificial quantum magnets on a surface by using spin-1/2 atoms in a scanning tunneling microscope (STM). These coupled spins feature strong quantum fluctuations due to antiferromagnetic exchange interactions between neighboring atoms. To characterize the resulting collective magnetic states and their energy levels, we performed electron spin resonance on individual atoms within each quantum magnet. This gives atomic-scale access to properties of the exotic quantum many-body states, such as a finite-size realization of a resonating valence bond state. The tunable atomic-scale magnetic field from the STM tip allows us to further characterize and engineer the quantum states. These results open a new avenue to designing and exploring quantum magnets at the atomic scale for applications in spintronics and quantum simulations.