Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases

TL;DR

This paper investigates the phase transition between paramagnetic and spin-glass many-body localized phases in a disordered quantum Ising model on a Cayley tree, revealing critical exponents and the structure of spin-glass clusters.

Contribution

It introduces a real-space renormalization approach analyzing eigenstates and phase transitions in a disordered quantum spin model on a Cayley tree, highlighting the nature of the spin-glass phase.

Findings

Phase transition characterized by exponents $ u=1$ and $eta=1$.

Spin-glass clusters are sparse and grow logarithmically at criticality.

The spin-glass phase exhibits a sub-extensive, variable cluster size with exponent $0< heta<1$.

Abstract

The quantum Ising model with random couplings and random transverse fields on the Cayley tree is studied by Real-Space-Renormalization in order to construct the whole set of eigenstates. The renormalization rules are analyzed via large deviations. The phase transition between the paramagnetic and the spin-glass Many-Body-Localized phases involves the activated exponent $\psi=1$ and the correlation length exponent $\nu=1$. The spin-glass-ordered cluster containing $N_{SG}$ spins is found to be extremely sparse with respect to the total number $N$ of spins : its size grows only logarithmically at the critical point $N_{SG}^{criti} \propto \ln N$, and it is sub-extensive $N_{SG} \propto N^{\theta}$ in the finite region of the spin-glass phase where the continuously varying exponent $\theta$ remains in the interval $0<\theta<1$.