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We consider the simplest example of lattice frustration in the 1/4-filledband, a one-dimensional chain with next-nearest neighbor interactions. For thiszigzag ladder with electron-electron as well as electron-phonon interactions wepresent numerical results for ground state as well as thermodynamic properties.In this system the ground state bond distortion pattern is independent ofelectron-electron interaction strength. The spin gap in the ground state of thezigzag ladder increases with the degree of frustration. Unlike inone-dimension, where the spin-gap and charge ordering transitions can bedistinct, we show that in the ladder they occur simultaneously. We discuss spingap and charge ordering transitions in 1/4-filled materials with one, two, orthree dimensional crystal structures. We show empirically that regardless ofdimensionality the occurrence of simultaneous or distinct charge and magnetictransitions can be correlated with the ground state bond distortion pattern.

Ground state and finite temperature behavior of 1/4-filled band zigzag ladders