Unified phase diagram of models exhibiting a neutral-ionic transition

We have studied the neutral-ionic transition in organic mixed-stack compounds. A unified model has been derived which, in limiting cases, is equivalent to the models proposed earlier, the donor-acceptor model, and the ionic Hubbard model. Detailed numerical calculations have been performed on this unified model with the help of the density-matrix renormalization-group (DMRG) procedure calculating excitation gaps, ionicity, lattice site entropy, two-site entropy, and the dimer order parameter on long chains and the unified phase diagram has been determined.

Figure 1

Energy levels of the ionic Hubbard model in the atomic limit for $U<\Delta$ and $U>\Delta$.

Figure 2

Atomic energy levels of donor and acceptor molecules.

Figure 3

Mapping of the allowed electronic states of donor and acceptor molecules to $S=1$ spin states.

Figure 4

Phase factors in the mapping of the donor-acceptor model to a spin-1 model.

Figure 5

Mapping of the electronic states of the ionic Hubbard model to $S=1$ spin states for the even and odd sites.

Figure 6

Single-site and two-site entropies $s_{i,i+1}$ for $i=N∕2$ and $i=N∕2+1$ as well as the dimerization in the two-site entropy of the ionic Hubbard model for $t∕\Delta =0.5$ as a function of $U∕\Delta$.

Figure 7

Phase diagram of the ionic Hubbard model. The critical values at $t∕\Delta =0.05$ and 0.25 are taken from Ref. 8.

Figure 8

Same as Fig. 6 but for the effective spin-1 model at $V=0$ as a function of $\epsilon ∕t\equiv (U-\Delta )∕t$.

Figure 9

The single-site entropy $\left(s_i\right)$, two-site entropy $\left(s_{i,i+1}\right)$, and ionicity $\left({\varrho }_i\right)$ in the middle of the chains for different chain lengths at $\epsilon ∕t=-10$ as a function of $V∕t$.

Figure 10

Charge gap, spin gap, and charge-transfer gap for a small nonvanishing charge-transfer integral $(\epsilon ∕t=-10)$ using PBC.

Figure 11

Charge gap, spin gap, and charge-transfer gap for $\epsilon ∕t=-2$.

Figure 12

The single-site entropy, two-site entropy $s_{i,i+1}$ for $i=N∕2$ and $i=N∕2+1$, and the dimerization of the two-site entropy for $\epsilon ∕t=-2$.

Figure 13

Phase diagram of the unified model describing the ionic Hubbard and donor-acceptor models as a function of the parameters $\epsilon ∕t$ and $V∕t$. Dashed line indicates first-order transition, solid lines correspond to second-order or BKT transitions. The star denotes the tricritical point. The phase boundaries of the full ionic Hubbard model are also shown.