Local conservation laws in spin-1/2 XY chains with open boundary conditions

Maurizio Fagotti

Published 2016-01-08Version 1

We revisit the conserved quantities in the spin-1/2 XY model with open boundary conditions. We show that in the original investigations infinitely many local charges were missed and, in fact, half of the seeming conservation laws are conserved only if the number of sites is odd. In even chains the set of noninteracting charges is abelian, like in the periodic case when the number of sites is odd. In odd chains the set is doubled and becomes non-abelian, like in even periodic chains. We consider also the transverse-field Ising chain, where the situation is more ordinary. The generalization to the XY model in a transverse field is not straightforward and we propose a general framework to carry out similar calculations. We conjecture the form of the bulk part of the local charges and discuss the emergence of quasilocal conserved operators. As a by-product, we study a class of block-Toeplitz-plus-Hankel operators and identify the conditions that their symbols satisfy in order to commute with a given block-Toeplitz.