Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions

• URL: http://arxiv.org/abs/2206.14779v4
• Date: Mon, 11 Sep 2023 15:19:20 GMT
• Title: Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Authors: Ievgen I. Arkhipov, Adam Miranowicz, Franco Nori, \c{S}ahin K. \"Ozdemir, Fabrizio Minganti
• Abstract summary: An $n$-simplex represents the simplest possible polytope in $n$ dimensions. We show that $n$-simplex lattices can be constructed from the high-order field-moments space of quadratic bosonic systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Finite simplex lattice models are used in different branches of science, e.g., in condensed matter physics, when studying frustrated magnetic systems and non-Hermitian localization phenomena; or in chemistry, when describing experiments with mixtures. An $n$-simplex represents the simplest possible polytope in $n$ dimensions, e.g., a line segment, a triangle, and a tetrahedron in one, two, and three dimensions, respectively. In this work, we show that various fully solvable, in general non-Hermitian, $n$-simplex lattice models {with open boundaries} can be constructed from the high-order field-moments space of quadratic bosonic systems. Namely, we demonstrate that such $n$-simplex lattices can be formed by a dimensional reduction of highly-degenerate iterated polytope chains in $(k>n)$-dimensions, which naturally emerge in the field-moments space. Our findings indicate that the field-moments space of bosonic systems provides a versatile platform for simulating real-space $n$-simplex lattices exhibiting non-Hermitian phenomena, and yield valuable insights into the structure of many-body systems exhibiting similar complexity. Amongst a variety of practical applications, these simplex structures can offer a physical setting for implementing the discrete fractional Fourier transform, an indispensable tool for both quantum and classical signal processing.

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