One dimensional staggered bosons, clock models, and their noninvertible symmetries

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mi>N</a:mi></a:msub></a:math> symmetry predict that these are critical points with a <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>U</d:mi><d:mo stretchy="false">(</d:mo><d:mn>1</d:mn><d:mo stretchy="false">)</d:mo></d:math> current algebra at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>c</h:mi><h:mo>=</h:mo><h:mn>1</h:mn></h:math> and radius <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msqrt><j:mrow><j:mn>2</j:mn><j:mi>N</j:mi></j:mrow></j:msqrt></j:math> whenever <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>N</l:mi><l:mo>&gt;</l:mo><l:mn>4</l:mn></l:math>. We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024