Related papers: Quantum geometry of non-Hermitian systems

We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field…

We present a comprehensive analytical study that extends the conventional formulation of Berry curvature, highlighting its derivation in the context of problematic domains of definition of the operators. Our analysis reveals that handling…

Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…

In two-dimensional layered quantum materials, the stacking order of the layers determines both the crystalline symmetry and electronic properties such as the Berry curvature, topology and electron correlation. Electrical stimuli can…

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with…

We study the quantum evolution of a non-Hermitian qubit realized as a submanifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters to encircle an exceptional point results in non-reciprocal…

The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical…

We investigate two kinds of topological structures (sphere and torus) spanned by the controlled parameters of a driven two-level system's Hamiltonian, and consider the connection between the structures and the system's dynamics. We discuss…

A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…

We study and present the results of Berry connection for the topological states in quantum matter. The Berry connection plays a central role in the geometric phase and topological phenomenon in quantum many-body system. We present the…

We expect black hole microstates to differ in their chaotic properties from states associated with other geometries. For supersymmetric black holes, ordinary level statistics cannot diagnose this distinction, since their energy levels are…

Non-Hermitian topological systems show quite different properties as their Hermitian counterparts. An important, puzzled issue on non-Hermitian topological systems is the existence of defective edge states beyond usual bulk-boundary…

The most peculiar, specifically quantum, features of quantum mechanics --- quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement --- are explained on a logical-geometrical…

We consider the ground state of an electron gas embedded in a quantum gyrotropic cavity. We show that the light-matter interaction leads to a nontrivial topology of the many-body electron-photon wave function characterized by a nonzero…

Atomic self-ordering to a crystalline phase in optical resonators is a consequence of the intriguing non-linear dynamics of strongly coupled atom motion and photons. Generally the resulting phase diagrams and atomic states can be largely…

Non-Hermitian systems exhibit nontrivial band topology and a strong sensitivity of the energy spectrum on the boundary conditions. Remarkably, a macroscopic number of bulk states get squeezed toward the lattice edges under open boundary…

In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this…

Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a…

Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically HBC captures the flow of local Berry curvature in a system. Here we provide a simple formula for computing the HBC…

We formulate quantum geometry for non-Hermitian systems under open boundary conditions. By defining quantum-geometric quantities in both real-space and non-Bloch representations, we establish a unified framework beyond conventional Bloch…