From Band Insulator to Mott Insulator in One Dimension

Abstract

We derive the phase diagram for the one-dimensional model of a ferroelectric perovskite recently introduced by Egami, Ishihara and Tachiki [Science, 261, 1307[Science, 261, (1993]. We show that the interplay between covalency, ionicity and strong correlations results in a spontaneously dimerized phase which separates the weak-coupling band insulator from the strongcoupling Mott insulator. The transition from the band insulator to the dimerized phase is identified as an Ising critical point. The charge gap vanishes at this single point with the optical conductivity diverging as σ(ω) ∼ ω −3/4 . The spin excitations are gapless above the second transition to the Mott insulator phase. 71.30.+h, 71.10.Pm

Ising model description of the SU(2)1 quantum critical point in a dimerized two-leg spin-1/2 ladder

“…On the other hand, up to irrelevant corrections, H AT in (19) transforms to the marginal interaction terms in (2) with g = 8Ka 0 . The correspondence between theh-terms in (11) and (9) is self-evident. Thus, we have shown that, in the weak-coupling limit (20), the 1D quantum model (11) can be regarded as a symmetry preserving lattice counterpart of the continuum theory (9).…”

“…The correspondence between theh-terms in (11) and (9) is self-evident. Thus, we have shown that, in the weak-coupling limit (20), the 1D quantum model (11) can be regarded as a symmetry preserving lattice counterpart of the continuum theory (9). General universality considerations allow us to expect that, if the field-theoretical model (9) displays a certain quantum critical behavior, this should also be a property of the quantum lattice model (11) even when its parameters are not restricted by the condition (20).…”

“…by σ z 1 , asymptotically decouple and can be tuned to criticality. Universality then implies that such separation between the fast and slow modes is valid close to the transition at arbitrary h. This approach made it possible to study the Ising criticality in a number of applications of the DSG model to physical systems [10,11].…”

“…Such a scheme has been recently proposed in Ref. [10] to tackle the Ising transition in the DSG model. The approach was based on the mapping onto a model of two quantum Ising (QI) chains coupled by an Ashkin-Teller (AT) interaction and also by a magnetic-field type coupling hσ z 1 σ z 2 .…”

“…General universality considerations allow us to expect that, if the field-theoretical model (9) displays a certain quantum critical behavior, this should also be a property of the quantum lattice model (11) even when its parameters are not restricted by the condition (20). It is then legitimate to consider the model (11) in the strong-coupling, large-h, limit where the description of the SU(2) 1 criticality greatly simplifies.…”