Large Deviations in Quantum Lattice Systems: One-Phase Region

Marco Lenci, Luc Rey-Bellet

Aydin Deger, Fredrik Brange, Christian Flindt

The authors determine the Lee-Yang zeros of an Ising spin lattice in one, two, and three dimensions from the thermodynamic fluctuations that are inherent to critical regions. They can thereby predict the critical behavior of the lattice from remarkably small system sizes and, furthermore, express the large-deviation statistics of the magnetization in terms of the Lee-Yang zeros. The method used by the authors can be applied to a wide range of critical systems both in theory and experiment.

Karel Netočný, Frank Redig

Reinhard F. Werner

A. L. Chernyshev

We demonstrate the versatility, simplicity, and power of the minimally augmented spin-wave theory in studying phase diagrams of the quantum spin models in which unexpected magnetically ordered phases occur or the existing ones expand beyond their classical stability regions. We use this method to obtain approximate phase diagrams of the two paradigmatic spin-$\frac{1}{2}$ models on the honeycomb lattice: the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ ferro-antiferromagnetic and ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic $XXZ$ models. For the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ case, various combinations of the $XXZ$ anisotropies are analyzed. In a dramatic deviation from their classical phase diagrams, which host significant regions of the noncollinear spiral phases, quantum fluctuations stabilize several unconventional collinear phases and significantly extend conventional ones to completely supersede spiral states. These results are in close agreement with the available density-matrix renormalization group calculations. The applicability of this approach to the other models and its potential extension to different types of orders are discussed.

D. Goderis, André F. Verbeure, P. Vets