Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension
| dc.creator | Stafford, C. A. | |
| dc.creator | Millis, A. J. | |
| dc.date | 1993-01-27 | |
| dc.date.accessioned | 2026-07-07T06:33:02Z | |
| dc.date.available | 2026-07-07T06:33:02Z | |
| dc.description | We use the Bethe ansatz equations to calculate the charge stiffness $D_{\rm c} = (L/2) d^2 E_0/dΦ_{\rm c}^2|_{Φ_{\rm c}=0}$ of the one-dimensional repulsive-interaction Hubbard model for electron densities close to the Mott insulating value of one electron per site ($n=1$), where $E_0$ is the ground state energy, $L$ is the circumference of the system (assumed to have periodic boundary conditions), and $(\hbar c/e)Φ_{\rm c}$ is the magnetic flux enclosed. We obtain an exact result for the asymptotic form of $D_{\rm c}(L)$ as $L\to \infty$ at $n=1$, which defines and yields an analytic expression for the correlation length $ξ$ in the Mott insulating phase of the model as a function of the on-site repulsion $U$. In the vicinity of the zero temperature critical point U=0, $n=1$, we show that the charge stiffness has the hyperscaling form $D_{\rm c}(n,L,U)=Y_+(ξδ, ξ/L)$, where $δ=|1-n|$ and $Y_+$ is a universal scaling function which we calculate. The physical significance of $ξ$ in the metallic phase of the model is that it defines the characteristic size of the charge-carrying solitons, or {\em holons}. We construct an explicit mapping for arbitrary $U$ and $ξδ\ll 1$ of the holons onto weakly interacting spinless fermions, and use this mapping to obtain an asymptotically exact expression for the low temperature thermopower near the metal-insulator transition, which is a generalization to arbitrary $U$ of a result previously obtained using a weak- coupling approximation, and implies hole-like transport for $0<1-n\llξ^{-1}$. | |
| dc.description | 34 pages, REVTEX (5 figures by request) | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9301036 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9301036 | |
| dc.identifier | Phys.Rev. B48 (1993) 1409 | |
| dc.identifier | doi:10.1103/PhysRevB.48.1409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99059 | |
| dc.subject | Condensed Matter | |
| dc.title | Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension | |
| dc.type | text |