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

Magnetic vortex crystals in frustrated Mott insulator

Quantum fluctuations become particularly relevant in highly frustrated quantum magnets and can lead to new states of matter. We provide a simple and robust scenario for inducing magnetic vortex crystals in frustrated Mott insulators. By considering a quantum paramagnet that has a gapped spectrum with six-fold degenerate low energy modes, we study the magnetic field induced condensation of these modes. We use a dilute gas approximation to demonstrate that a plethora of multi-$\mathbf{Q}$ condensates are stabilized for different combinations of exchange interactions. This rich quantum phase diagram includes magnetic vortex crystals, which are further stabilized by symmetric exchange anisotropies. Because magnetic skyrmion and domain wall crystals have already been predicted and experimentally observed, this novel vortex phase completes the picture of emergent crystals of topologically nontrivial spin configurations.Comment: 12 pages, 12 figures; published in Phys. Rev.

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