Hidden unity in the quantum description of matter

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity behind seemingly unrelated physical phenomena, thus establishing exact connections between them. This leads to the fundamental concept of {\it universality} of physical phenomena, a general concept not restricted to the domain of critical behavior. Key to our framework is the concept of {\it languages} and the construction of {\it dictionaries} relating them.Comment: 10 pages 2 psfigures. Appeared in Recent Progress in Many-Body Theorie

Field Induced Supersolid Phase in Spin-One Heisenberg Models

We use quantum Monte Carlo methods to demonstrate that the quantum phase diagram of the S=1 Heisenberg model with uniaxial anisotropy contains an extended supersolid phase. We also show that this Hamiltonian is a particular case of a more general and ubiquitous model that describes the low energy spectrum of a class of {\it isotropic} and {\it frustrated} spin systems. This crucial result provides the required guidance for finding experimental realizations of a spin supersolid state.Comment: 4 pages, 4 figure