Band to Mott Insulator Transition in the Ionic Hubbard Model
We investigate the ground state phase diagram of the one-dimensional “ionic” Hubbard model with an alternating periodic potential at half filling by numerical diagonalization of finite systems with the Lanczos and DMRG methods. In addition, we present res
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Introduction
The so-called "ionic" Hubbard model was originally proposed about 20 years ago in the context of organic charge transfer crystals consisting of a sequence of alternating donor (D) and acceptor (A) molecules ( ... D+PA-PD+PA-P) [1,2]. These stacks form quasi one-dimensional (lD) insulating or semiconducting chains, and are classified into two categories depending on the amount of charge transfer p: quasi-neutral for p < 0.5, and quasi-ionic for p > 0.5. Torrance et al. [1] found that several of these systems undergo a reversible neutral-to-ionic phase transition (NIT), i.e. a discontinuous jump in the ionicity p upon changing temperature or pressure. In a different context, the ionic Hubbard model has also been used recently to describe the ferroelectric transition in perovskite materials such as BaTi0 3 [4]. Explicitely, the 1D ionic Hubbard model is defined by the Hamiltonian " (1 H -_-t"L.."
(t
+ (-1) i 8) cia ci+1a + h.c.
)
t,a
(1) where cra creates an electron on site i with spin (J', n ia = claCia, U the onsite Hubbard interaction, .:1 an on-site potential; in (1) we have included an additional Peierls modulation 8 of the hopping matrix element t. The limit L\ = 0 and 8 > 0 is called the Peierls-Hubbard model. The NIT at finite temperatures has been intensively studied theoretically in a series of articles by Nagaosa et al. [2] using quantum Monte Carlo (QMC) simulations. NIT has been investigated. The 1D ionic Hubbard model (1) with Ll > 0 and 8 = 0 at half filling has served as an appropriate model for E. Krause et al. (eds.), High Performance Computing in Science and Engineering '01 © Springer-Verlag Berlin Heidelberg 2002
168
P. Brune and A.P. Kampf
a D-A chain. The model parameters U and Ll in (1) are used for an effective description of the microscopic parameters, like e.g. the electron affinity of the acceptor molecules, the ionization potential of the donors, and the Madelung energy of ionized D+ A-pairs. Within this picture, Ll could be interpreted as the energy necessary to move an electron from the donor to the acceptor. For an understanding of the existence of a phase transition in the 1D ionic Hubbard model with b = the best starting point is the atomic limit [8]. For t = 0, it is immediately seen that for half filling and U < Ll the ground state of (1) has two electrons on the B (i odd), and no electrons on the A sites (i even) ("neutral" phase). This corresponds to a charge density wave (CDW) ordering with maximum amplitude. On the other hand, for U > Ll each site is occupied by one electron ("ionic" phase). Obviously, for t = a transition occurs at a critical value Ue = Ll. This transition is expected to persist for t > 0, where the alternating potential still defines two sublattices A and B, opening up a band gap Ll for U = at k = ±7r /2. For t > the critical coupling shifts to Uc(t) > Ll, with Ue monotonically increasing with increasing Ll. For U, Ll » t the system is close to atomic limit, and Ue approaches Ll from above. For U = the ground state at half-filling is
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