Classification and realization of topological phases in strongly correlated systems: a tensor network approach – TNTOP
It was long believed that Landau symmetry-breaking theory describes all possible orders and all possible (continuous) phase transitions in materials. However, Nature is always full of surprises. In last three decades, it has become more and more clear that Landau symmetry-breaking theory fails to describe all possible orders in strongly correlated systems. One famous example is the fractional quantum Hall (FQH) effect. It turns out that FQH states are topological phases of quantum mater and contain a new class of order – topological order.
Topological order is believed to exist in general strongly correlated systems and will make great impact on future industry, e.g, the realization of topological quantum computation. Unfortunately, a unified analytical and numerical framework to study topological phenomena in strongly correlated systems has not been developed so far due to the lack of principle analogous to symmetry breaking and mathematical approach analogous to mean field theory. Recent years, it has been realized that topological phases of quantum matter can be systematically characterized by long-range entanglement, which can be efficiently encoded by the so-called tensor network states. Therefore, the analytic and numerical study of tensor network state will become a very powerful tool to understand topological phases of quantum matter.
However, great challenges still need to be overcome for implementing tensor network states to systematically study topological phenomena in strongly correlated systems. Analytically, it is still unclear if tensor network states can faithfully represent all topologically ordered states or not. Numerically, it turns out that it can be exponentially hard to calculate physical quantities (ground state energy, correlation functions, etc.) exactly for general tensor network states.
This joint project will form a strong-strong union of an theoretical team in France and Hong Kong to solve the key difficulties in tensor network approach to topological phases of quantum matter in strongly correlated systems. We will team up to classify and realize topological phases of quantum matter in strongly correlated systems using tensor network states approach. We will use tensor network states to systematically classify topological phases of quantum matter in strongly correlated systems. Then we will construct physically motivated tensor network variational wavefunctions to study topological phase transitions. Finally, we will develop new algorithm and implement tensor network states with large bond dimension to study realistic topological materials, such as frustrated magnets and doped Mott-insulator.
Monsieur Zhengcheng Gu (The Chinese University of Hong kong)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
CNRS - LPT Centre national de la recherche scientifique - LABORATOIRE DE PHYSIQUE THEORIQUE
CUHK The Chinese University of Hong kong
Help of the ANR 561,224 euros
Beginning and duration of the scientific project: December 2018 - 48 Months