Seminar by Zi Yang Meng
Condensed Matter Seminar Series
Zi Yang Meng
Hong Kong University
Hearing the Shape of Quantum Drums via Qiu Ku
Abstract: To hear the shape of a quantum drum is in principle not a mission impossible, where the shape means the conformal field theory (CFT) description of certain quantum phases and phase transitions in a (2+1)d manifold and the drum beat means characteristic measurements of the quantum system whose structure reveals the CFT information. In realistic quantum many-body lattice models, however, measurements such as the finite size scaling of the entanglement entropy with reliable data to extract the CFT characteristics, are rare due to numerical difficulties. To overcome such problem, we design a generic computation protocol to obtain the Rényi entanglement entropy of quantum many-body systems with efficiency and precision. Our method, dubbed ``Qiu Ku'' algorithm, is based on the massively parallelization of the nonequilibrium increment processes in quantum Monte Carlo simulations. To demonstrate its power, we show the results on few important yet difficult (2+1)d quantum lattice models, ranging from Heisenberg quantum antiferromagnet, quantum critical point with O(3) CFT, deconfined quantum critical point to the toric code Z2 topological ordered state and the Kagome Z2 quantum spin liquid model.