The past decades have witnessed an explosion of interest in topological materials, and a lot mathematical concepts been introduced condensed matter physics. Among them, the bulk-boundary correspondence is central topic physics, which has inspired researchers to focus on boundary Recently, phases extended non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides topology, non-Hermiti...

Non-Hermitian topological phases have gained widespread interest due to their unconventional properties, which no Hermitian counterparts. In this work, we propose use machine learning identify and predict non-Hermitian phases, based on winding number. We consider two examples---non-Hermitian Su-Schrieffer-Heeger model its generalized version in one dimension nodal line semimetal three dimension...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...