This series consists of talks in the area of Condensed Matter.
In the first part of the seminar, I will describe a general approach to write down a large family of model SU(N) anti-ferromagnets that do not suffer from the sign problem. In the second half I will show how such Hamiltonians are useful for the study of deconfined quantum critical points and possibly other exotic physics.
Quantum Monte Carlo is a versatile tool for studying strongly interacting theories in condensed matter physics from first principles. A prominent example is the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. I will present numerical results for different properties of the homogeneous, spin-balanced unitary Fermi gas across the superfluid transition, such as the critical temperature, the equation of state and the temperature dependence of the contact density. Our values show good agreement with recent experimental data.
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this talk, I consider a simple bilayer fractional quantum Hall (FQH) system with the 1/3 Laughlin state in each layer, in the presence of interlayer tunneling.
Superselection rules in quantum theory assert the impossibility of preparing coherent superpositions of certain conserved quantities. For instance, it is commonly presumed that there is a superselection rule for charge and for baryon number, as well as a "univalence superselection rule" forbidding a coherent superposition of a fermion and a boson. I will show how many superselection rules can be effectively lifted using a reference frame for the variable that is conjugate to the conserved quantity.
Holographic duality is a duality between quantum many-body systems (boundary) and gravity systems with one additional spatial dimension (bulk). In this talk, I will describe a new approach to holographic duality for lattice systems, called the exact holographic mapping. The key idea of this approach can be summarized by two points: 1) The bulk theory is nothing but the boundary theory viewed in a different basis. 2) Space-time geometry is determined by the structure of correlations and quantum entanglement in a quantum state.
A topological phase is a phase of matter which cannot be characterized by a local order parameter. We first introduce non-local order parameters that can detect symmetry protected topological (SPT) phases in 1D systems and then show how to generalize the idea to detect symmetry enriched topological (SET) phases in 2D. SET phases are new structures that occur in topologically ordered systems in the presence of symmetries. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions.
The talk is divided into two parts: in the first, I will talk about dynamics of far-from equilibrium initial states in different lattice models. I will present results of quench dynamics of the XXZ-Heisenberg magnet, where interesting physics emerges after quenching the system. Then I will present results for scattering of solitonic objects in different integrable and non-integrable lattice models. In the second part, I will talk about dynamics of impurity systems.
The quantum spin liquid is an emergent new state of matter, which has attracted a lot of recent attention. In particular, the time reversal symmetry broken spin liquid (Kalmeyer et. al. and Wen et. al.), characterized by the chiral ordering and fractionalized quasi-particle as a realization of the fractional quantum Hall state had been proposed for more than 20 years, but never identified as the true ground state in any more generic (e.g. Heisenberg spin exchange) models with time reversal symmetry.