Quantum magnetism on small-world networks

TL;DR

This paper explores quantum magnetism on small-world networks, revealing unique critical behaviors and the impact of network topology on quantum spin systems through theoretical and simulation methods.

Contribution

It introduces a study of quantum spins on small-world networks, highlighting the interplay between network structure and quantum critical phenomena, which is less understood compared to classical systems.

Findings

Finite-temperature magnetic ordering with mean-field criticality.

Two distinct power-law behaviors for critical temperature versus coupling strength.

Competition between graph length scale and thermal correlation length affects quantum criticality.

Abstract

While classical spin systems in random networks have been intensively studied, much less is known about quantum magnets in random graphs. Here, we investigate interacting quantum spins on small-world networks, building on mean-field theory and extensive quantum Monte Carlo simulations. Starting from one-dimensional (1D) rings, we consider two situations: all-to-all interacting and long-range interactions randomly added. The effective infinite dimension of the lattice leads to a magnetic ordering at finite temperature $T_\mathrm{c}$ with mean-field criticality. Nevertheless, in contrast to the classical case, we find two distinct power-law behaviors for $T_\mathrm{c}$ versus the average strength of the extra couplings. This is controlled by a competition between a characteristic length scale of the random graph and the thermal correlation length of the underlying 1D system, thus challenging mean-field theories. We also investigate the fate of a gapped 1D spin chain against the small-world effect.