Emergence of superconductivity in doped multiorbital Hubbard chains

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.

Block orbital-selective Mott insulators: a spin excitation analysis

“…12(c)] can be easily explained by the large Hund coupling that aligns ferromagnetically spins on different orbitals and favors the S = 1 state at each site. These results are in agreement with the recent proposal [66] of a generalized AffleckKennedyLiebTasaki-like state (that provides a qualitative understanding of the S = 1 Heisenberg chain [67,68]) as a ground-state of the two-orbital Hubbard model at half-filling.…”

Estimation of biquadratic and bicubic Heisenberg effective couplings from multiorbital Hubbard models

“…For the exact-diagonalization calculations, we work with the multi-orbital Hubbard model mentioned in [6,7] and described as follows:…”

“…The study of the one-dimensional spin-one (S = 1) Heisenberg chain by Haldane [1], with only nearest-neighbor spin-spin interactions (called here 'bilinear' interactions), and the prediction, and subsequent confirmation, of a spin liquid gapped ground state with protected edge states, was seminal for the start of the field of topological materials. The Haldane chain has been physically realized in several materials, such as CsNiCl 3 [2], AgVP 2 S 6 [3], NENP [4], and Y 2 BaNiO 5 [5], and recently theory predicted that doping of the fermionic two-orbital Hubbard version of the idealized Haldane chain may lead to hole pairing and eventual superconductivity [6,7]. Earlier related work employing t − J model approximations also predicted superconductivity with doping although strongly competing with ferromagnetism [8].…”

“…Our conclusion is that it is indeed possible to reach the AKLT point by suitably selecting the values of U and J H . On the other hand, for the Bethe-ansatz solvable case we conclude that it would be difficult to reach β = 1 using the fermionic system defined in [6]. Our efforts were extended to the three-orbital per site Hubbard models as well, allowing us to estimate crude upper bounds for the biquadratic and bicubic Heisenberg couplings emerging at large Hubbard U and low energy.…”

“…Our primary goal is to crudely estimate whether the recently introduced more realistic electronic two-orbital Hubbard model realization of the Haldane chain [6] can, at large and/or intermediate Hubbard U and Hund J H couplings, reach the biquadratic/bilinear ratio β = 1/3 when fermionic versus pure spin Hamiltonian models are compared at low energies. Specifically, here we solve exactly the two-site problem of the fermionic model and represent the lowest energy states using the generalized Heisenberg bilinear-biquadratic model in a vast region of parameter space, including varying the elements of the hopping matrix.…”