The spectral gap of quantum many-body Hamiltonians is an important but difficult concept in condensed matter. Its identification is complicated and, quite often, controversial because the gap, together with the ground-state degeneracy is a thermdynamic limit notion rather than any finite-size energy splitting.
In this talk, we will discuss a gaplessness indicator. Specifically, we prove that the ground state(s) of an SO(3)-symmetric gapped spin chain must be spin singlet(s), and the expectation value of a twisting operator asymptotically approaches unity in the thermodynamic limit, where finite-size corrections are inversely proportional to the system size. This theorem provides (i) supporting evidence for various conjectured gapped phases, and, contrapositively, (ii) a sufficient criterion for identifying gapless spin chains. We test the efficiency of our theorem by numerical simulations for a variety of spin models and show that it indeed offers a novel efficient way to identify gapless phases in spin chains with spin-rotation symmetry.
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