Exactly solvable Russian-doll model: Renormalization-group cycles meet fractality

arXiv:2603.17674 · cond-mat.stat-mech, hep-th, quant-ph · Submitted 2026-03-18 · Read on arXiv

cond-mat.stat-mech, hep-th, quant-ph

Submitted: 2026-03-18

Updated: 2026-09-22

Comments: Published in Phys. Rev. B 114, L140202: https://link.aps.org/doi/10.1103/3qgd-425n

Journal ref: Phys. Rev. B 114, L140202 (2026)

License: http://creativecommons.org/licenses/by/4.0/

The gist: We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking, which exhibits a cyclic renormalization group.

Terminology

Bethe Ansatz — 8× in this paper
Russian Doll — 8× in this paper
Hilbert Space — 4× in this paper · explained in 2 episodes
Limit Cycles — 2× in this paper · explained in 2 episodes
Quantization — 2× in this paper · explained in 12 episodes
Symmetry Breaking — 2× in this paper · explained in 3 episodes
Decoupling — 1× in this paper · explained in 2 episodes
Generalization — 1× in this paper · explained in 13 episodes

Abstract

We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking, which exhibits a cyclic renormalization group. By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector, which includes localized, fractal, and delocalized phases. We show that the quantum number Q, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states. Using the action of the renormalization group on the eigenstates, we demonstrate that Q serves as an order parameter, providing a new mechanism for the formation of the fractal phase in the deterministic systems and an example of the interplay between fractality and cyclic RG.

Exactly solvable Russian-doll model: Renormalization-group cycles meet fractality

Terminology

Abstract

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