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arXiv:1212.0736 · Physical Review B

Disorder by disorder and flat bands in the kagome transverse field Ising model

Michael Powalski, K. Coester, Roderich Moessner, Kai Phillip Schmidt

Published Feb 4, 2013• 37 citations
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Abstract

We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second-order quantum phase transition in the $3d$ $XY$ universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields $h$. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order 8 in the $1/h$ limit. This behavior can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion.

DOI
10.1103/physrevb.87.054404

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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{\mathcal{Z}}_{2}Z2​ symmetry broken phase. In contrast, we find strong evidence 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 us 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.
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