Doublon-holon binding as origin of Mott transition and fractionalized spin liquid -- Asymptotic solution of the Hubbard model in the limit of large coordination
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number ($z$) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-$z$ limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the $2^N$-fold degeneracy of the local moments in the insulating phase. We show that the spinons are coupled to doublons/holons by a dissipative compact U(1) gauge field that is in the deconfined phase, stabilizing the spin-charge separated gapless spin liquid Mott insulator.
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number (z) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-z limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the 2N-fold degeneracy of the local moments in the insulating phase. We show that the spinons are coupled to doublons/holons by a dissipative compact U(1) gauge field that is in the deconfined phase, stabilizing the spin-charge separated gapless spin liquid Mott insulator.
The Mott metal-insulator transition in the Hubbard model is studied by constructing a dynamical slave-boson mean-field theory in the limit of large lattice coordination number z that incorporates the binding between doubly occupied (doublon) and empty (holon) sites. On the Mott insulating side where all doublons and holons bond in real space into excitonic pairs leading to the charge gap, the theory simplifies considerably to leading order in 1/z and becomes exact on the infinite-z Bethe lattice. An asymptotic solution is obtained for a continuous Mott transition associated with the closing of the charge gap at a critical value of the Hubbard Uc and the corresponding doublon density ndc, hopping ${\ensuremath{\chi}}_{d}^{c}$ and doublon-holon pairing ${\mathrm{\ensuremath{\Delta}}}_{d}^{c}$ amplitudes. We find ${U}_{c}={U}_{\mathrm{BR}}[1\ensuremath{-}2{n}_{d}^{c}\ensuremath{-}\sqrt{z}({\ensuremath{\chi}}_{d}^{c}+{\mathrm{\ensuremath{\Delta}}}_{d}^{c})]\ensuremath{\simeq}0.8{U}_{\mathrm{BR}}$, where UBR is the critical value for the Brinkman-Rice transition in the Gutzwiller approximation captured in the static mean-field solution of the slave-boson formulation of Kotliar and Ruckenstein. Thus, the Mott transition can be viewed as the quantum correction to the Brinkman-Rice transition due to doublon-holon binding. Quantitative comparisons are made to the results of the dynamical mean-field theory, showing good agreement. In the absence of magnetic order, the Mott insulator is a U(1) quantum spin liquid with nonzero intersite spinon hopping that survives the large-z limit and lifts the 2N-fold degeneracy of the local moments. We show that the spinons are coupled to the doublons/holons by a dissipative compact U(1) gauge field in the deconfined phase, realizing the spin-charge separated gapless spin liquid Mott insulator.
We argue that the binding between doubly occupied (doublon) and empty (holon) sites governs incoherent excitations and plays a key role in the Mott transition in strongly correlated Mott-Hubbard systems. We construct a new saddle-point solution with doublon-holon binding in the Kotliar-Ruckenstein slave-boson functional integral formulation of the Hubbard model. On a half-filled honeycomb lattice and square lattice, the ground state is found to exhibit a continuous transition from a paramagnetic semimetal/metal to an antiferromagnetic-ordered Slater insulator with coherent quasiparticles at Uc1, followed by a Mott transition into an electron-fractionalized AF∗ phase without coherent excitations at Uc2. Such a phase structure appears to be generic for bipartite lattices without frustration. We show that doublon-holon binding unites the three important ideas of strong correlation: coherent quasiparticles, incoherent Hubbard bands, and deconfined Mott insulator.
To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length ξdh and the minimum D-D exclusion length ξdd. Generally, a Mott transition occurs when ξdh becomes comparable to ξdd. In the conductive (superfluid) state, domains of D-H pairs overlap with each other (ξdh>ξdd); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.
We study the binding of a holon to a doublon in a half-filled Hubbard model as the mechanism of the zero-temperature metal-insulator transition. In a spin polarized system a single holon-doublon (HD) pair exhibits a binding transition on a 3D lattice, or a sharp crossover on a 2D lattice, corresponding well to the standard Mott transition in unpolarized systems. We extend the HD-pair study towards nonpolarized systems by considering more general spin background and by treating the finite HD density within a BCS-type approximation. Both approaches lead to a discontinuous transition away from the fully polarized system and give density correlations consistent with numerical results on a triangular lattice.
In the ionic Hubbard model, the on-site repulsion U, which drives a Mott insulator, and the ionic potential V, which drives a band insulator, compete with each other to open up a window of charge fluctuations when $U\ensuremath{\sim}V$. We study this model on square and cubic lattices in the limit of large U and V, with $V\ensuremath{\sim}U$. Using an effective Hamiltonian and a slave-boson approach with both doublons and holons, we find that the system undergoes a phase transition as a function of V from an antiferromagnetic Mott insulator to a paramagnetic insulator with strong singlet correlations, which is driven by a condensate of ``neutral'' doublon-holon pairs. On further increasing V, the system undergoes another phase transition to a superconducting phase driven by condensate of ``charged'' doublons and holons. The superfluid phase, characterized by the presence of a coherent (but gapped) fermionic quasiparticle and hc/e flux quantization, has a high ${T}_{c}\ensuremath{\sim}t$, which shows a dome-shaped behavior as a function of V. The paramagnetic insulator phase has a deconfined U(1) gauge field and associated gapless photon excitations. We also discuss how these phases can be detected in the ultracold-atom context.
Dynamics in a triangular-lattice Hubbard model is studied at half filling on the basis of the cluster dynamical mean field theory. Numerical calculations use a solver of the continuous-time quantum Monte Carlo method based on the strong-coupling expansion. We examine the change in the nearest-neighbor dynamical correlations of doublon and holon in the time domain with varying the Coulomb repulsion near the Mott transition. We demonstrate that the nearest-neighbor doublon-holon pair shows a strong attractive correlation, particularly in the insulating phase, while the nearest-neighbor doublon-doublon pair shows a repulsive correlation. Useful information is provided by the trajectories in the complex plane of the dynamical correlation functions. The short-time dynamics of the nearest-neighbor doublon and holon in the metallic phase indicates larger fluctuations than in the insulating phase. Their trajectories in the complex plane show that the short-time dynamics of the doublon-holon pair has an opposite behavior to that of the doublon-doublon pair. We find that their time scale of dynamics can be characterized by the period in which the phase rotates π around the long-time limit in both phases. In the long-time region, fluctuations persist up to a very long time in the metallic phase, while they quickly vanish in the insulating phase.