Nonequilibrium and semiclassical dynamics in topological phases of quantum matter

Haoran Qian, Ming Gong, Jia-Hui Zhang +35 more

Topological phases of matter are of both fundamental and practical interest. In this study, we implemented both equilibrium and nonequilibrium higher-order topological phases using a two-dimensional programmable superconducting quantum processor. Quantum programming of nonequilibrium higher-order topological phases was achieved by constructing quantum circuits comprising >50 cycles of Floquet operators on a six-by-six qubit array. Additionally, we introduce a universal approach based on measuring the dynamics of chiral density to identify distinct nonequilibrium higher-order topological features, including Floquet corner topological invariants and π-energy topological corner modes. Our work may enable the use of programmable quantum processors to explore exotic higher-order nonequilibrium topological phases of matter.

Wei-Feng Tsai, Hsin Lin, Arun Bansil

F. D. M. Haldane

Giandomenico Palumbo

It has long been established that certain higher-dimensional topological phases of matter support extended objects like quasistrings and quasimembranes in their bulk states. In this study, we investigate the physics of these topological systems using a phase-space approach in the semiclassical regime, incorporating tensorial coordinates related to the extended objects. Specifically, we explore the semiclassical currents associated to open quasistrings in topological phases in three spatial dimensions, considering the presence of both coordinate-space Kalb-Ramond fields and momentum-space tensor Berry connections. Our results show that the currents associated to the endpoints of open quasistrings on the system’s boundary exhibit a quantum Hall response. This formalism accurately reproduces the boundary response as predicted by an Abelian BF theory proving a novel way to study extended objects in topological matter.

Nannan Ma, Jiangbin Gong

Nonequilibrium topological matter has been a fruitful topic of both theoretical and experimental interest. A great variety of exotic topological phases unavailable in static systems may emerge under nonequilibrium situations. How to locate the borders between different nonequilibrium topological phases is an important issue to facilitate topological characterization and further understand phase transition behaviors. In this paper, we develop an unsupervised machine-learning protocol to distinguish between different Floquet (periodically driven) topological phases possessed by theoretical models, by incorporating the system's dynamics within one driving period, adiabatic deformation in the time dimension, plus the system's symmetry all into our machine-learning algorithm. Results from two rich case studies indicate that machine learning is able to reliably reveal intricate topological phase boundaries and can hence be a powerful tool to analyze and discover previously unknown topological phases afforded by the time dimension. As inspired by previous elegant methods in analyzing Floquet topological phases, one essential ingredient in our machine-learning approach is to directly investigate the system's evolution operators parametrized by time.

D. J. Thouless