We present a set of models which realize interacting topological phases. The models are constructed in 2 dimensions for a system with U(1)xU(1) symmetry. We demonstrate that the models are topological by measuring their Hall conductivity, and demonstrating that they have gapless edge modes. We have also studied the models numerically.
In this talk, I will present recent work aimed at tackling two cornerstone problems in the field of strongly correlated electrons---(1) conducting non-Fermi liquid electronic fluids and (2) the continuous Mott metal-insulator transition---via controlled numerical and analytical studies of concrete electronic models in quasi-one-dimension. The former is motivated strongly by the enigmatic "strange metal" central to the cuprates, while the latter is pertinent to, e.g., the spin-liquid candidate 2D triangular
When a large number of quantum mechanical particles are put together and allowed to interact, various condensed matter phases emerge with macroscopic quantum properties. While conventional quantum phases like superfluids or quantum magnets can be understood as a simple collection of
The decomposition of the magnetic moments in spin ice into freely moving magnetic monopoles has added a new dimension to the concept of fractionalization, showing that geometrical frustration, even in the absence of quantum fluctuations, can lead to the apparent reduction of fundamental objects into quasi particles of reduced dimension . The resulting quasi-particles map onto a Coulomb gas in the grand canonical ensemble . By varying the chemical potential one can drive the ground state from a vacuum to a monopole crystal with the Zinc blend structure .
Many of the topological insulators, in their naturally available form are not insulating in the bulk. It has been shown that some of these metallic compounds, become superconductor at low enough temperature and the nature of their superconducting phase is still widely debated. In this talk I show that even the s-wave superconducting phase of doped topological insulators, at low doping, is different from ordinary s-wave superconductors and goes through a topological phase transition to an ordinary s-wave state by increasing the
The existence of three generations of neutrinos and their mass mixing is a deep mystery of our universe. Majorana's elegant work on the real solution of Dirac equation predicted the existence of Majorana particles in our nature, unfortunately, these Majorana particles have never been observed. In this talk, I will begin with a simple 1D condensed matter model which realizes a T^2=-1time reversal symmetry protected superconductors and then discuss the physical property of its boundary Majorana zero modes.
The symmetric Kugel-Khomskii can be seen as a minimal model describing the interactions between spin and orbital degrees of freedom in certain transition-metal oxides with orbital degeneracy, and it is equivalent to the SU(4) Heisenberg model of four-color fermionic atoms. We present simulation results for this model on various two-dimensional lattices obtained with infinite projected-entangled pair states (iPEPS), an efficient variational tensor-network ansatz for two dimensional wave functions in the thermodynamic limit.
Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin is an important property of a topological quasi-particle, which is the Berry phase obtained in the adiabatic self-rotation of the quasi-particle by . For chiral topological states with robust chiral edge states, another fundamental topological property is the edge state chiral central charge .