Quantum Geometry in Gapless Systems Probed Via Time-Dependent Conformal Transformations Reveals Nontrivial Return Amplitudes

The behaviour of gapless systems, materials lacking an energy gap between electronic states, profoundly influences diverse areas of physics, and understanding their properties remains a central challenge. Bastien Lapierre from École Normale Supérieure, Per Moosavi from Stockholm University, and Blagoje Oblak from Université Claude Bernard Lyon 1, now demonstrate a novel method for probing the underlying quantum geometry of these materials. Their work reveals how driving these systems with time-dependent transformations allows researchers to measure geometric properties beyond traditional approaches, uncovering connections between measurable quantities and the fundamental symmetries governing their behaviour. This achievement establishes universal relationships dependent only on the system’s inherent characteristics, offering a powerful new tool for characterising and understanding gapless materials and potentially guiding the development of future technologies.

Quantum Geometry from Time-Dependent Conformal Transformations

Researchers are advancing our understanding of gapless many-body quantum systems by exploring their low-energy descriptions as conformal field theories. This approach leverages the infinite-dimensional parameter space induced by conformal symmetry. Scientists reveal the associated quantum geometry by considering finite systems subjected to time-dependent conformal transformations. Calculations predict that absorption rates and linear responses directly relate to components of the quantum geometric tensor. The approach demonstrates that the system evolves predictably, and the quantum geometric tensor remains a conserved quantity, providing a means to characterise entanglement and offering a new perspective on quantum phase transitions. This work establishes a direct link between the quantum geometric tensor and measurable physical quantities, providing a pathway to experimentally probe the quantum geometry of interacting many-body systems.

Time-Dependent Perturbations Reveal Hidden Geometry

Scientists are revealing the geometric underpinnings of gapless systems, building on the idea that geometry plays a fundamental role in physics. Their work focuses on conformal field theory and investigates how time-dependent perturbations can reveal hidden geometric properties. The team considers systems driven by a time-dependent Hamiltonian, involving the stress-energy tensor and a spatially varying velocity profile. Experiments demonstrate that by exciting the system in a time-dependent manner, researchers can probe directions in quantum parameter space not accessible in equilibrium, unveiling the system’s underlying geometry.

Analytical results show that these perturbations give rise to nontrivial return amplitudes, involving the quantum metric, extending beyond the familiar Berry phase. Results demonstrate a direct connection between measurable quantities and the quantum geometry of the system, dependent only on the central charge of the conformal symmetry. Measurements confirm that the return probability exhibits distinct behavior dependent on the velocity profile, and numerical simulations of lattice models support these analytical findings, validating the universality of the observed geometric effects.

Quantum Geometry Dictates System Response

This research establishes a connection between the geometry of quantum states and measurable properties of gapless systems, building on earlier work that linked classical geometry to fluid flows. Scientists have demonstrated that the quantum geometry of these systems, described by conformal field theories, is not merely a mathematical construct but has observable consequences. They reveal how components of this geometry, specifically a quantum geometric tensor, can be extracted from experimental measurements of absorption rates and linear responses. The team further shows that periodic driving of these systems leads to nontrivial return amplitudes, extending beyond the standard Berry phase. Importantly, the findings are universal, depending only on the central charge of the conformal symmetry, and are supported by both analytical calculations and numerical simulations of lattice models.