Fibonacci sequence and its generalizations in doped quantum spin ladders

TL;DR

This paper generalizes Fibonacci sequences for doped quantum spin ladders, enabling recursive state generation and estimation of entanglement properties without complex numerics, revealing doping effects on entanglement in these systems.

Contribution

It introduces generalized Fibonacci sequences for multi-legged and doped quantum spin ladders, facilitating analytical estimation of quantum states and entanglement measures.

Findings

Sequences enable recursive state generation in doped ladders

Doping influences entanglement entropy, reducing differences between odd and even legs

Formalism allows estimation of physical quantities without numerical methods

Abstract

An interesting aspect of antiferromagnetic quantum spin ladders, with complete dimer coverings, is that the wave function can be recursively generated by estimating the number of coverings in the valence bond basis, which follow the fabled Fibonacci sequence. In this work, we derive generalized forms of this sequence for multi-legged and doped quantum spin ladders, which allow the corresponding dimer-covered state to be recursively generated. We show that these sequences allow for estimation of physically and information-theoretically relevant quantities in large spin lattices without resorting to complex numerical methods. We apply the formalism to calculate the valence bond entanglement entropy, which is an important figure of merit for studying cooperative phenomena in quantum spin systems with SU(2) symmetry. We show that introduction of doping may mitigate, within the quarters of entanglement entropy, the dichotomy between odd- and even- legged quantum spin ladders.