Theory of Valence-Bond Lattice on Spin Lattice

TL;DR

This paper develops a microscopic formalism for valence-bond lattices in low-dimensional quantum spin systems, analyzing their ground and excited states, with detailed focus on 1D frustrated models and discussions on 2D lattices.

Contribution

It introduces a systematic microscopic theory for valence-bond lattices that preserves rotational symmetry and applies it to various low-dimensional spin models.

Findings

Microscopic formalism guarantees rotational symmetry of VBL systems.

Detailed analysis of 1D frustrated spin-1/2 models.

Discussion of VBL systems on 2D square and kagome lattices.

Abstract

Quantum spin-lattice systems in low dimensions exhibit a variety of interesting zero-temperature phases, some of which show non-classical (i.e., non-magnetic) long-range orders, such as dimer or trimer valence-bond order. These symmetry-breaking systems with localized valence bonds are referred to as valence-bond lattices (VBL) in this article. A review of our systematic microscopic formalism based on a proper set of composite operators for the ground and excited states of the VBL systems is given. The one-dimensional (1D) spin-$1\over2$ frustrated model is investigated in detail. Several possible VBL systems on the 1D spin-1 chains, the 2D square and {\it kagom\'e} lattices are also discussed. That our microscopic theory guarantees the rotational symmetry of the VBL systems is emphasized.