Collective excitations and marginal stability of quantum Ising spin glasses

TL;DR

This paper analyzes the quantum glass phase of the SK model in a transverse field, revealing it is critical everywhere with gapless excitations, interpreted as disordered spin waves acting as weakly coupled oscillators.

Contribution

It provides an exact solution for the quantum SK model in a transverse field and characterizes the collective excitations and marginal stability of the glass phase.

Findings

The glass phase is critical with gapless Ohmic spectral function.

Disordered spin waves behave as weakly coupled harmonic oscillators.

Low frequency spectrum approaches a universal limit at small transverse fields.

Abstract

We solve the Sherrington-Kirkpatrick (SK) model in a transverse field \Gamma deep in its quantum glass phase at zero temperature. We show that the glass phase is critical everywhere, exhibiting collective excitations with a gapless Ohmic spectral function. Using an effective potential approach, we interpret the latter as being due to disordered spin waves which behave as weakly coupled, underdamped harmonic oscillators. In the limit of small transverse field the low frequency tail of the spectrum tends to a universal, \Gamma-independent limit.