This series consists of talks in the area of Condensed Matter.
In this talk we propose a Hamiltonian approach to 2+1D gapped topological phases on an open surface with boundary. The bulk part is
(Levin-Wen) string-net models arising from a unitary fusion category (can be viewed as Hamiltonian approach to extended Turaev-Viro TQFT), while the boundary Hamiltonian is constructed using any Frobenius algebra in the input category. The combined Hamiltonian is exactly solvable and gives rise to a gapped energy spectrum which is topologically protected.
Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions.
Topological states of matter are of of fundamental interest in contemporate condensed matter physics. Today, the fractional Quantum Hall effect remains the only known experimental system expected to exhibit intrinsic topological order. The question remains whether also different systems might stabilize this kind of ordering. Chiral spin liquids are an analogue of Fractional Quantum Hall Effect wave functions for spin systems.
Since its first discovery in 1986, high-Tc superconductors have been attracting constant interests and meticulous efforts from both theorists and experimentalists, not merely due to its large transition temperature, but also because it offers a well characterized laboratory for the study of exotic phenomena such as quantum criticality, non-Fermi liquid behavior, and intertwined orders. One pressing question in the field is the role played by disorder:
Motivated by the question about reconstructing a Conformal field theory from the data of a subfactor of finite index, Jones studied the continuous limit of the periodic quantum spin chain which Thompson group acts on. Based on planar algebras, the topological axiomatization of subfactors, we will illustrate the idea of the correspondence between the skein theory of planar algebras and presentation of Thompson groups.
Bosonic symmetric protected topological (BSPT) phases are bosonic anagolue of electron topological insulators and superconductors. Despite the theoretical progresses of classifying these states, little attention has been paid to experimental realization of BSPT states in dimensions higher than 1. We propose bilayer graphene system in a out-of-plane magnetic field with Coulomb interaction is a natural platform for BSPT states with $U(1)\times U(1)$ symmetry.
The matrix product state (MPS) ansatz makes possible computationally-efficient representations of weakly entangled many-body quantum systems with gapped Hamiltonians near their ground states, notably including massive, relativistic quantum fields on the lattice. No Wick rotation is required to apply the time evolution operator, enabling study of time-dependent Hamiltonians. Using free massive scalar field theory on the 1+1 Robertson-Walker metric as a toy example, I present early efforts to exploit this fact to model quantum fields in curved spacetime.
Unlike entanglement entropy and mutual information which may mix both classical and quantum correlations, entanglement negativity received extensive interest recently, for its merit of measuring the pure quantum entanglement in the system. In this talk, I will introduce the entanglement negativity in 2+1 dimensional topologically ordered phases. For a bipartitioned or tripartitioned spatial manifold, we show how the universal part of entanglement negativity depends on the presence of quasiparticles and the choice of ground states.