Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2411.03771 · Physical review. B./Physical review. B

Evidence for valence-bond pairing in a one-dimensional two-orbital system

M. Mierzejewski, Elbio R. Dagotto, J. Herbrych

Published Jun 24, 2025• 0 citations
arXivHTMLPDF

Abstract

Valence bond (VB) states as the formation mechanism of Cooper pairs, eventually leading to high-temperature superconductivity, remain a controversial topic. Although various VB-like states find variational relevance in the description of specific spin models and quantum spin liquids, in the realm of many-body fermionic Hamiltonians, the evidence for such states as ground states wave functions remains elusive, challenging the valence-bond pairing mechanism. Here, we present evidence of a VB ground state with pairing tendencies, particularly at finite doping. We achieved this for the generic two-orbital Hubbard model in low dimension, where the VB states can be associated with the presence of the topological order manifested by edge states.

DOI
10.1103/qyqw-yy3j

Related papers

Emergence of superconductivity in doped multiorbital Hubbard chains

Niravkumar D. Patel, Nitin Kaushal, Alberto Nocera +2 more

Abstract We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.

arXiv:2001.00589•npj Quantum Materials•May 8, 2020•20 citations

d-Symmetry superconductivity as a consequence of valence-bond type correlations

Alexander A. Ovchinnikov, M. Ya. Ovchinnikova, Evgeny A. Plekhanov

It is shown that d x 2−y 2 symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to T c are of the order of 2Δ≃0.1t and 2Δ/kT c≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed.

Journal of Experimental and Theoretical Physics Letters•Mar 1, 1998•3 citations

Plaquette valence bond theory of high-temperature superconductivity

Malte Harland, Mikhail I. Katsnelson, Alexander I. Lichtenstein

We present a strong-coupling approach to the theory of high-temperature superconductivity based on the observation of a quantum critical point in the plaquette within the $t,{t}^{\ensuremath{'}}$ Hubbard model. The crossing of ground-state energies in the $N=2--4$ sectors occurs for parameters close to the optimal doping. The theory predicts the maximum of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave order parameter at the border between localized and itinerant electron behaviors and gives a natural explanation for the pseudogap formation via the soft-fermion mode related to local singlet states of the plaquette in the environment. Our approach follows the general line of resonating valence-bond theory stressing a crucial role of singlets in the physics of high-${T}_{c}$ superconductors but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.

arXiv:1604.01808•Physical review. B./Physical review. B•Sep 19, 2016•32 citations

d-symmetry superconductivity due to valence bond correlations

Alexander A. Ovchinnikov, M. Ya. Ovchinnikova, Evgeny A. Plekhanov

It is shown that d -symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d -channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T c are 2Δ≃0.1 t and 2Δ/ kT c ≃4.5−4 for U/t ≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T c on the doping δ =| n −1| and the Fermi surface shape are highly sensitive to the weak interaction t ′ leading to diagonal hoppings. In the case of t ′>0 and p -doping, the peak on the curve of T c ( δ ) occurs at the doping δ opt , when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k ∼( π ,0). In underdoped samples with δ < δ opt , the anisotropic pseudogap in the normal state corresponds to the energy difference | E ( π ,0)− μ | between this part of the spectrum and the Fermi level.

Journal of Experimental and Theoretical Physics•Sep 1, 1998•2 citations

Supersymmetric valence bond solid states

Daniel P. Arovas, Kazuki Hasebe, Xiao-Liang Qi +1 more

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. The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state.

arXiv:0901.1498•Physical Review B•Jun 2, 2009•34 citations

A generalized valence bond basis for the half-filled Hubbard model

Christopher Graves

I present a non-orthogonal and overcomplete set of states that spans the S_tot=0 Hilbert subspace for a fermionic system with four possible spin configurations per site, on a half-filled lattice with an even number of sites. This set consists of possible pairing of the spins into three bond types: singlet bonds and positive and negative charge bonds. Although I present the specific case for the half-filled Hubbard model in one-dimension, these sets of states can be trivially extended to higher dimensions. The overlap of these generalized valence bond states form closed loops with properties that are related to operator expectation values in this basis. I verify the correctness of this basis by solving the model via exact diagonalization and comparing with known results. There is evidence of structure in the ground state that may be useful to simulations using variational wave functions.

•Jan 1, 2011•0 citations
Valence bond (VB) states as the formation mechanism of Cooper pairs, eventually leading to high-temperature superconductivity, remain a controversial topic. Although various VB-like states find variational relevance in the description of specific spin models and quantum spin liquids, in the realm of many-body fermionic Hamiltonians, the evidence for such states as ground states wave functions remains elusive, challenging the valence-bond pairing mechanism. Here, we present evidence of a VB ground state with pairing tendencies, particularly at finite doping. We achieved this for the generic two-orbital Hubbard model in low dimension, where the VB states can be associated with the presence of the topological order manifested by edge states.
Abstract We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
It is shown that d x 2−y 2 symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to T c are of the order of 2Δ≃0.1t and 2Δ/kT c≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed.
We present a strong-coupling approach to the theory of high-temperature superconductivity based on the observation of a quantum critical point in the plaquette within the $t,{t}^{\ensuremath{'}}$ Hubbard model. The crossing of ground-state energies in the N=2−−4N=2--4N=2−−4 sectors occurs for parameters close to the optimal doping. The theory predicts the maximum of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave order parameter at the border between localized and itinerant electron behaviors and gives a natural explanation for the pseudogap formation via the soft-fermion mode related to local singlet states of the plaquette in the environment. Our approach follows the general line of resonating valence-bond theory stressing a crucial role of singlets in the physics of high-Tc{T}_{c}Tc​ superconductors but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.
It is shown that d -symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d -channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T c are 2Δ≃0.1 t and 2Δ/ kT c ≃4.5−4 for U/t ≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T c on the doping δ =| n −1| and the Fermi surface shape are highly sensitive to the weak interaction t ′ leading to diagonal hoppings. In the case of t ′>0 and p -doping, the peak on the curve of T c ( δ ) occurs at the doping δ opt , when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k ∼( π ,0). In underdoped samples with δ < δ opt , the anisotropic pseudogap in the normal state corresponds to the energy difference | E ( π ,0)− μ | between this part of the spectrum and the Fermi level.
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. The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state.
I present a non-orthogonal and overcomplete set of states that spans the S_tot=0 Hilbert subspace for a fermionic system with four possible spin configurations per site, on a half-filled lattice with an even number of sites. This set consists of possible pairing of the spins into three bond types: singlet bonds and positive and negative charge bonds. Although I present the specific case for the half-filled Hubbard model in one-dimension, these sets of states can be trivially extended to higher dimensions. The overlap of these generalized valence bond states form closed loops with properties that are related to operator expectation values in this basis. I verify the correctness of this basis by solving the model via exact diagonalization and comparing with known results. There is evidence of structure in the ground state that may be useful to simulations using variational wave functions.