Symmetric states charge conservation

Consider a linear chain of N sites composed of four blocks, labelled i = 1,..., 4. At present we consider symmetric systems with open boundary conditions so that blocks 1 and 4, and blocks 2 and 3 are equivalent. This is illustrated in Fig. H.l. A general state of the block i is denoted by TOj) where m is a shorthand label for the quantum numbers of the block (e.g. the conserved quantum numbers, spin and charge, and any other state index). Block i has Ni sites and its Hilbert space is spanned by Mi states. 

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