Topological phases in two-dimensional systems

Antônio Sérgio Teixeira Pires

Gang-Feng Guo, Xi-Xi Bao, Lei Tan +1 more

We propose a one-dimensional optical lattice model to simulate and explore two-dimensional topological phases with ultracold atoms, considering the phases of the hopping strengths as an extra dimension. It is shown that the model exhibits nontrivial phases, and corresponding two chiral-edge states. Moreover, we demonstrate the connections between changes in the topological invariants and the Dirac points. Furthermore, the topological order detected by the particle pumping approach in cold atoms is also investigated. The results obtained here provide a feasible and flexible method of simulating and exploring high-dimensional topological phases in low-dimension systems via the controllable phase of the hopping strength.

Oscar Viyuela, ́Angel Rivas, Miguel Angel Martin-Delgado

We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the topological Uhlmann number n_{U}. With it, we study thermal topological phases in several two-dimensional models of topological insulators and superconductors, computing phase diagrams where the temperature T is on an equal footing with the coupling constants in the Hamiltonian. Moreover, we find novel thermal-topological transitions between two nontrivial phases in a model with high Chern numbers. At small temperatures we recover the standard topological phases as the Uhlmann number approaches to the Chern number.

Saurabh Basu

Li-Jun Lang, Xiaoming Cai, Shu Chen

We show that one-dimensional quasiperiodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. The butterflylike spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices.

Roderich Moessner, Joel E. Moore