Simulation of Chiral Topological Phases in Driven Low Dimensional Systems

Gloria Platero

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.

Emmanuel V. C. Lopes

Rui Tian, Xiayao He, Tianhao Wu +3 more

Martin Rodriguez-Vega, Babak Seradjeh

We study the low-frequency dynamics of periodically driven one-dimensional systems hosting Floquet topological phases. We show, both analytically and numerically, in the low frequency limit Ω→0, the topological invariants of a chirally symmetric driven system exhibit universal fluctuations. While the topological invariants in this limit nearly vanish on average over a small range of frequencies, we find that they follow a universal Gaussian distribution with a width that scales as 1/sqrt[Ω]. We explain this scaling based on a diffusive structure of the winding numbers of the Floquet-Bloch evolution operator at low frequency. We also find that the maximum quasienergy gap remains finite and scales as Ω^{2}. Thus, we argue that the adiabatic limit of a Floquet topological insulator is highly structured, with universal fluctuations persisting down to very low frequencies.

János K. Asbóth

Discrete-time quantum walks have been shown to simulate all known topological phases in one and two dimensions. Being periodically driven quantum systems, their topological description, however, is more complex than that of closed Hamiltonian systems. We map out the topological phases of the particle-hole symmetric one-dimensional discrete-time quantum walk. We find that there is no chiral symmetry in this system: its topology arises from the particle-hole symmetry alone. We calculate the ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ topological invariant in a simple way that is consistent with a general definition for one-dimensional periodically driven quantum systems. These results allow for a transparent interpretation of the edge states on a finite lattice via the the bulk-boundary correspondence. We find that the bulk Floquet operator does not contain all the information needed for the topological invariant. As an illustration to this statement, we show that in the split-step quantum walk, the edges between two bulks with the same Floquet operator can host topologically protected edge states.