The spectral gap for some spin chains with discrete symmetry breaking

摘要: We prove that for any finite set of generalized valence bond solid (GVBS) states a quantum spin chain there exists translation invariant finite-range Hamiltonian which this is the ground states. This result implies are GVBS models with arbitrary broken discrete symmetries described as combinations lattice translations, reflections, and local unitary or anti-unitary transformations. also show all satisfy some natural conditions have spectral gap. The existence gap obtained by applying simple quite general strategy proving lower bounds on generator classical dynamics. scheme interesting in its own right threfore, although basic idea not new, we present it system-independent setting. results illustrated number examples.