This series consists of talks in the area of Condensed Matter.
Recent studies of highly frustrated antiferromagnets (AFMs) have demonstrated the qualitative impact of virtual, longer-range singlet excitations on the effective RVB tunneling parameters of the low energy sector of the problem [1,2]. Here, I will discuss the current state of affairs on the RVB description of the spin-1/2 kagome AFM, and present new results that settle a number of issues in this problem .
 I. Rousochatzakis, Y. Wan, O. Tchernyshyov, and F. Mila, PRB 90,
We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions.
The quest for quantum spin liquids is an important enterprise in strongly correlated physics, yet candidate materials are still few and far between. Meanwhile, the classical front has had far more success, epitomized by the exceptional agreement between theory and experiment for a class of materials called spin ices. It is therefore natural to introduce quantum fluctuations into this well-established classical spin liquid model, in the hopes of obtaining a fully quantum spin liquid state.
Topological quantum computing requires phases of matter which host fractionalized excitations that are neither bosons nor fermions. I will present a new route toward realizing such fractionalized phases of matter by literally building on existing topological phases. I will first discuss how existing topological phases, when interfaced with other systems, can exhibit a “topological proximity effect” in which nontrivial topology of a different nature is induced in the neighboring system.
In this talk, I will talk about my current study and the future directions that I am interested to explore, which include: (1) topological phases in cold atom, (2) spin liquid phases in frustrated magnets, (3) strongly interacting conformal field theory, (4) no equilibrium dynamics. Specifically, I will elaborate on several topics that I plan to work on in the near future: (1) cold atom realization and detection of symmetry protected topological phases,
(2) effect of charge fluctuation in the spin liquid phases, (3) entanglement properties of 3D CFT.
A closed quantum system is ergodic and satisfies equilibrium statistical physics when it completely loses local information of its initial condition under time evolution, by 'hiding' the information in non-local properties like entanglement. In the last decade, a flurry of theoretical work has shown that ergodicity can be broken in an isolated, quantum many-body system even at high energies in the presence of disorder, a phenomena known as many-body localization (MBL).
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.