Quantum geometric tensor from real-space twists of chiral chains

The quantum geometric tensor (QGT) quantifies the distances and phases encoded in the wave function, thereby revealing the topological nature of quantum matter. Despite recent strides in researching QGT within various symmetry-broken environments, its meaning and origin remain obscure. Here, we show a cause of quantum geometry by revealing how real-space twists uniquely induce QGT in a chiral chain. From the real-space metric tensor of helical geometry, an effective gauge field appears as a generator of the screw rotation, intertwining the chain-directional and the chain-perpendicular motion of electrons. Consequently, a universal form of the interband QGT emerges with equivalent in-plane components of the quantum metric tensor and Berry curvature. This applies to any quantum entities residing in the chiral chain and gives rise to diverse nonlinear Hall transports. On top of offering an intuitive insight into quantum geometry, our paper introduces a control knob of QGT through real-space geometry.