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This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of electronic wavefunctions, encoded in the quantum metric and Berry curvature. Whereas Berry curvature-mediated transport…
We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the…
Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories…
Quantum geometry plays a pivotal role in the second-order response of $\cal PT$-symmetric antiferromagnets. Here we study the nonlinear response of 2D altermagnets protected by $C_n\cal T$ symmetry and show that their leading nonlinear…
Our previous understanding of transport in disordered system depends on the assumption that there is a well-defined Fermi velocity. The Fermi velocity determines important length scales in the system such as the diffusion length and…
Flat bands may offer a route to high critical temperatures of superconductivity. It has been predicted that the quantum geometry of the bands as well as the ratio of the number of flat bands to the number of orbitals determine flat band…
As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian…
Understanding scattering mechanisms in semiconductor heterostructures is crucial to reducing sources of disorder and ensuring high yield and uniformity in large spin qubit arrays. Disorder of the parent two-dimensional electron or hole gas…
The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…
Quantum metrology aims to exploit many-body quantum states to achieve parameter-estimation precision beyond the standard quantum limit. For unitary parameter encoding generated by local Hamiltonians, such enhancement is characterized by…
A method is proposed for studying wave and particle transport in disordered waveguide systems of dimension higher than unity by means of exact one-dimensionalization of the dynamic equations in the mode representation. As a particular case,…
Preserving the precision of the parameter of interest in the presence of environmental decoherence is an important yet challenging task in dissipative quantum sensing. In this work, we study quantum metrology when the decoherence effect is…
The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D…
We show that the position-momentum duality offers a transparent interpretation of the band geometry at the topological band crossings. Under this duality, the band geometry with Berry connection is dual to the free-electron motion under…
We identify localizable entanglement (LE) as an order parameter for measurement-induced phase transitions (MIPT). LE exhibits universal finite-size scaling with critical exponents that match previous MIPT results and gives a nice…
We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated…
Establishing long-distance quantum entanglement, i.e., entanglement transmission, in quantum networks (QN) is a key and timely challenge for developing efficient quantum communication. Traditional comprehension based on classical…
We consider estimating a small transverse displacement of an optical beam over a line-of-sight propagation path: a problem that has numerous important applications ranging from establishing a lasercom link, single-molecule tracking, guided…