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The cluster glass state in the two-dimensional extended t-J model

The recent observation of an electronic cluster glass state composed of random domains with unidirectional modulation of charge density and/or spin density on Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} reinvigorates the debate of existence of competing interactions and their importance in high temperature superconductivity. By using a variational approach, here we show that the presence of the cluster glass state is actually an inherent nature of the model based on the antiferromagnetic interaction (J) only, i.e. the well known t-J model. There is no need yet to introduce a competing interaction to understand the existence of the cluster glass state. The long-range pairing correlation is not much influenced by the disorder in the glass state which also has nodes and linear density of states. In the antinodal region, the spectral weight is almost completely suppressed. The modulation also produces subgap structures inside the "coherent" peaks of the local density of states.