Quantum Phase Transitions in Random Spin Systems

T. Senthil

Yu-Liang Xu, Panpan Zhang, Li-Zhen Hu +2 more

Olga V. Dimitrova, Marc Mézard

After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random transverse field. The quantum cavity equations describing the ferromagnetic-paramagnetic phase transition can be transformed into the well-known problem of a classical directed polymer in a random medium. The glass transition of this polymer problem translates into the existence of a 'Griffiths phase' close to the quantum phase transition of the quantum spin problem, where the physics is dominated by rare events. The physical behaviour of random transverse-field ferromagnets on the Bethe lattice is found to be very similar to that found in finite-dimensional systems, and the quantum cavity method gets back the known exact results of the one-dimensional problem.

Ristig, M L, Abu, Qasam K, DAMIAN J. J. FARNELL +1 more

Kazutaka Takahashi, Yoshiki Matsuda

We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad distributions of the energy gap. As a result, the linear, spin-glass, and nonlinear susceptibilities behave differently from each other. The power-law tail of the distribution implies a quantum Griffiths-like effect that could be observed in various random quantum systems. We also discuss the mechanisms of the phase transition in terms of the energy gap by comparing the Sherrington-Kirkpatrick model and random energy model, which demonstrate the difference between the continuous and discontinuous phase transitions.

MANFRED L. RISTIG, Khaled Abu Qasem, DAMIAN J. J. FARNELL