Quantum disorder and local modes of the fully-frustrated transverse field Ising model on a diamond chain

TL;DR

This paper studies the fully-frustrated transverse field Ising model on a diamond chain, revealing a disorder by disorder phenomenon and identifying local modes and effective low-energy descriptions that characterize its quantum disordered phase.

Contribution

It provides the first detailed analysis of the fully-frustrated model, demonstrating the persistent disordered phase and local modes using series expansions and exact diagonalizations.

Findings

Unfrustrated case exhibits a 2d Ising quantum critical point.

Fully-frustrated case shows disorder by disorder with a quantum disordered ground state.

Identification of local modes and an effective low-energy description.

Abstract

We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2 symmetry broken phase. In contrast, we find strong evidences for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e. except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The low-energy excitations in this polarized phase are understood in terms of exact local modes of the model. Furthermore, an effective low-energy description for an infinitesimal transverse field allows to pinpoint the quantum disordered nature of the ground state via mapping to an effective transverse field Ising chain and to determine the induced gap to the elementary effective domain wall excitation very accurately.