Frustration and disorder in quantum spin chains and ladders
In quantum spins systems, frustration and low-dimensionality generate quantum fluctuations and give rise to exotic quantum phases. This thesis studies a spin ladder model with frustrating couplings along the legs, motivated by experiments on cuprate BiCu2PO6.
First, we present an original variational method to describe the low-energy excitations of a single frustrated chain. Then, the phase diagram of two coupled chains is computed with numerical methods. The model exhibits a quantum phase transition between a dimerized phase and resonating valence bound (RVB) phase. The physics of the RVB phase is studied numerically and by a mean-field treatment. In particular, the onset of incommensurability in the dispersion relation, structure factor and correlation functions is discussed in details.
Then, we study the effects of non-magnetic impurities on the magnetization curve and the Curie law at low temperature. A low-energy effective model is derived within the linear response theory and is used to explain the behaviors of the magnetization and Curie constant.
Eventually, we study the effect of bonds disorder, on a single frustrated chain. The variational method, introduced in the non-disordered case, gives a low disorder picture of the dimerized phase instability, which consists in the formation of Imry-Ma domains delimited by localized spinons.