# Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations

### Y. Y. Atas 1 E. Bogomolny 1

#### Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2014, 47, pp.335201

Spectral density of quantum Ising model in two fields for large but finite number of spins $N$, is discussed in detail. When all coupling constants are of the same order, spectral densities in the bulk are well approximated by a Gaussian function which is typical behaviour for many-body models with short-range interactions. The main part of the paper is devoted to the investigation of a different characteristic case when spectral densities have peaks related with strong degeneracies of unperturbed states in certain limits of coupling constants. In the strict limit $N\to\infty$, peaks overlap and disappear but for values of $N$ accessible in numerical calculations they often strongly influence spectral densities and other quantities as well. A simple method is developed which permits to find general approximation formulae for multi-peak structure of spectral density in good agreement with numerics.

• 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques