This series consists of talks in the area of Condensed Matter.
We review the formalism of matrix product states and one of its recent generalisations which allows to variationally determine the dispersion relation of elementary excitations in generic one-dimensional quantum spin chains. These elementary excitations dominate the low energy effective behaviour of the system. We discuss recent work where we show how we can also describe the effective interaction between these excitations – as mediated by the strongly correlated ground state – and how we can extract the corresponding S matrix.
Electron puddles created by doping of a 2D topological insulator may violate the ideal helical edge conductance. Because of a long electron dwelling time, even a single puddle may lead to a significant inelastic backscattering. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on temperature and on the doping level. Puddles with odd electron number carry a spin and lead to a logarithmically-weak temperature dependence of the resistivity of a long edge.
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.
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.