Spin-liquid and spin-glass behavior in quantum spin models with all-to-all p-spin interactions

TL;DR

This paper investigates the transition between spin-liquid and spin-glass phases in quantum spin models with all-to-all p-spin interactions, revealing how anisotropy and system size influence phase behavior and providing a unified phase diagram.

Contribution

It introduces a comprehensive analysis of phase transitions in p-spin models, unifying phase diagrams through a scaling law and exploring the effects of anisotropy and external fields.

Findings

Transition point depends on system size and p.

Anisotropy suppresses the spin-liquid phase.

Unified phase diagram via N/p^2 scaling.

Abstract

Spin-liquid and spin-glass states represent two distinct phases of disordered quantum spin systems. These states are, in principle, distinguished by quantum-entangled fluctuations and spin freezing, but identifying each state and characterizing the transition between them remains challenging. Here, we systematically explore the relationship between the spin-liquid and spin-glass states using a model with all-to-all random interactions among p spins, which interpolates between the Ising-like one-component, XY-like two-component, and isotropic three-component cases. By analyzing the system-size N dependence of the Edwards-Anderson order parameter and the density of states, we identify the transition from the spin liquid to the spin glass for various values of p. We show that the phase diagrams for different p can be unified through a scaling with N/p2, revealing that increasing anisotropy in the interactions systematically suppresses the spin-liquid phase and extends the spin-glass regime. Furthermore, we examine the competition between multiple-spin interactions and anisotropy under an external magnetic field in the isotropic case, and find that the spin-liquid phase transitions into the spin-glass phase before entering a quantum paramagnetic phase. Our findings provide insights into quantum disordered phases and the transitions between them.