the Holstein bipolaron.

At even stronger EPI, $V_{c}<1.16E_{p}$, $NNN$ bipolarons become stable. More importantly, holes can now form 3- and 4-particle clusters. The dominance of the potential energy over kinetic in the transformed Hamiltonian enables us to readily investigate these many-polaron cases. Three holes placed within one oxygen square have four degenerate states with the energy $2(V_{c}-1.23E_{p})+V_{c}/\sqrt{2}-0.80E_{p}$. The first-order polaron hopping processes mix the states resulting in a ground state linear combination with the energy $E_{3}=2.71V_{c}-3.26E_{p}-\sqrt{%
4t^{2}+t^{\prime }{}^{2}}$. It is essential that between the squares such triads could move only in higher orders of polaron hopping. In the first order, they are immobile. A cluster of four holes has only one state within a square of oxygen atoms. Its energy is $E_{4}=4(V_{c}-1.23E_{p})+2(V_{c}/%
\sqrt{2}-0.80E_{p})=5.41V_{c}-6.52E_{p}$. This cluster, as well as all bigger ones, are also immobile in the first order of polaron hopping. We would like to stress that at distances much larger than the lattice constant the polaron-polaron interaction is always repulsive, and the formation of infinite clusters, stripes or strings is prohibited. We conclude that at $V_{c}<1.16E_{p}$ the system quickly becomes a charge segregated insulator.

The fact that within the window, $1.16E_{p}<V_{c}<1.23E_{p}$, there are no three or more polaron bound 