Fibonacci sequence and its generalizations in doped quantum spin ladders

• Published in: Journal of magnetism and magnetic materials 2019-05, Vol.478, p.100-108
• Main Authors: Singha Roy, Sudipto, Dhar, Himadri Shekhar, Sen(De), Aditi, Sen, Ujjwal
• Format: Article
• Language: English
• Subjects: Antiferromagnetism; Coverings; Dimers; Entanglement; Entropy; Fibonacci numbers; Figure of merit; Ladders; Lattices (mathematics); Numerical methods; Sequences
• ISSN: 0304-8853; 1873-4766
• DOI: 10.1016/j.jmmm.2019.01.064

•Short-range RVB states can be recursively generated from smaller configurations.•For undoped two-legs ladders such recursion follows the fabled Fibonacci sequence.•Generalized sequences for multi-legged doped and undoped spin-ladders can be obtained.•The sequences allow estimation of many relevant physical quantities. 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.