Topological lattice as open quantum system - Wang, Danqi (Nanyang Technological University, 2024)
Topological Insulators are novel materials with unique properties, such as topologically protected boundary states. However, current research is more focused on topological insulators as closed systems, and little is known about their properties as open quantum system. In this project, I aim to study the properties of a bosonic Hofstadter lattice connected to thermal baths of different temperatures at its boundaries, including intriguing features such as (1) Thermal Erasure Eﬀect, (2) Topological Thermal Currents, (3) Edge Nonequilibrium Crosscurrent. In this report, I have reviewed the beginning of topological condensed mater physics from the discovery of Quantum Hall Eﬀect, with its robust topologically protected edge states which inspired the prediction of existence of 2D Topological Insulator with similarly topologically protected robust edge states but without the need to break Time-Reversal Symmetry (TRS). I then reviewed the boundary driven open quantum system, in which an open quantum system is connected to the environment at its boundaries and allowed to equilibrate, reaching a Non-Equilibrium Steady States (NESS). This justiﬁed the use of local GLSK quantum master equation under weak coupling to the environment. [1] I then brieﬂy described our project which aimed to use QuTiP to simulate the Topological Heat Transport of bosonic topological lattices connected to thermal baths. I aimed to reproduce the results of the paper by Rivas.[2] As a warmup, I have used QuTiP to simulate the NESS of simple systems such as the Heisenberg ladders and Bosonic ladders, using Local GLSK equation. I then moved on to study topological bosonic Hofstadter lattice as Thermal Hall Insulators including observing the nonequilibrium thermal currents carried by edge states, as well as how varying driving bias as well as the strength of the gauge field can affect the magnitude of the edge currents. My results can be realized in bosonic systems such as ultracold atoms simulations as well as photonic chips. These results can be applicable to nano-engineering of topological insulators under non- equilibrium conditions to account for the thermal hall effect. Other potential uses of topological insulators as thermal hall insulators as well as rectiﬁer can be similarly explored in future studies.