A resonant valence bond spin liquid in the dilute limit of doped frustrated Mott insulators

TL;DR

The paper tackles the long-standing question of realizing a resonating valence bond (RVB) spin liquid with spin-charge separation in a realistic Hubbard setting. By analyzing a large-$U$ Hubbard model on lattices of corner-sharing tetrahedra with frustrated hopping, the authors derive an exact single-hole RVB ground state and prove a lower energy bound $E_g=-4t$ at $J=0$, supported by numerical ED and DMRG data for finite systems. They also show a robust RVB phase persists at finite exchange, with a two-hole sector achieving $E_g=-8t$ and clear spinon-holon correlations, while the stoichiometric limit remains singular and the phase relies on hole doping and kinetic energy frustration. The work establishes kinetic energy frustration as a viable route to topologically ordered spin liquids in real materials and outlines potential experimental platforms, notably pyrochlore lattices, for probing these predictions.

Abstract

Ideas about resonant valence bond liquids and spin-charge separation have led to key concepts in physics such as quantum spin liquids, emergent gauge symmetries, topological order, and fractionalisation. Despite extensive efforts to demonstrate the existence of a resonant valence bond phase in the Hubbard model that originally motivated the concept, a definitive realisation has yet to be achieved. Here we present a solution to this long-standing problem by uncovering a resonant valence bond phase exhibiting spin-charge separation in realistic Hamiltonians. We show analytically that this ground state emerges in the dilute-doping limit of a half-filled Mott insulator on corner-sharing tetrahedral lattices with frustrated hopping, in the absence of exchange interactions. We confirm numerically that the results extend to finite exchange interactions, finite-sized systems and finite dopant density. Although much attention has been devoted to the emergence of unconventional states from geometrically frustrated interactions, our work demonstrates that kinetic energy frustration in doped Mott insulators may be essential for stabilising robust, topologically ordered states in real materials.

Figures (11)

• Figure 1: Pictorial illustration of one of the dimer-singlet states. These states participate in the superposition forming the RVB liquid ground state of the $t$-$J$ model, Eq. \ref{['eq:ham']}, on a lattice of corner-sharing tetrahedra. Singlets are indicated by dark thin ellipsoids, and a holon at a given location by a light sphere. The $\pi$-fluxes depict the phase induced by the singlet coverings (relative to a ferromagnetic background) when the holon moves around the corresponding triangular plaquette. The inset shows an Y$_2$Ir$_2$O$_7$ pyrochlore crystal grown by D. Prabhakaran in Oxford.
• Figure 2: Correlations and spin structure factor in the RVB state. Top, blue dots show the holon density $\langle \hat{O}\rangle = \langle 1-\hat{n}_i\rangle$ ($\hat{n}_i$ being the electron density operator) for a 16-site and a 32-site pyrochlore system doped with a single hole as a function of distance from the pinned spin, $\vert \bm{r}_i - \bm{r}_0 \vert$, for system sizes $N = 16, \, 32$. It indicates that the spinon and holon separate (the two different values at distance $\sim 0.7$ are due to the two inequivalent third-nearest-neighbour sites on the pyrochlore lattice). Crosses show the holon-holon correlations when there are two holes present in the system. They are numerically identical to the holon-spinon correlations. Bottom, spin structure factor in the $(hhk)$ and $(hk0)$ reciprocal lattice planes for the 32-site pyrochlore system with one hole (top half) and two holes (bottom half), for $t = 1$ and $J=0$. Accessible momenta are marked by grey pluses.
• Figure 3: Spin structure factor. Dependence of the ground state spin structure factor $S(\bm{Q})$ (for all individual reciprocal lattice points $\bm{Q}$) on $J/t$ ($t > 0$) for a 16-site system. Left, the system is doped with one hole. The region where the correlations are antiferromagnetic, despite the ferromagnetic $J$, is shaded. Right, the system is doped with one electron, for comparison.
• Figure S1: 16-site pyrochlore system. This is constructed from a single cubic unit cell with lattice vectors ${\bm a}_1 = (1,0,0)$, ${\bm a}_2 = (0,1,0)$ and ${\bm a}_3 = (0,0,1)$.
• Figure S2: 32-site pyrochlore system. This is constructed from a $2\times 2\times 2$ lattice of the ffc unit cell with lattice vectors ${\bm a}_1=(0,1/2,1/2)$, ${\bm a}_2=(1/2,0,1/2)$ and ${\bm a}_3=(1/2,1/2,0)$. Each unit cell has four sites (a single tetrahedron).