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The interplay among differential geometry, statistical physics, and quantum information science has been increasingly gaining theoretical interest in recent years. In this paper, we present an explicit analysis of the Bures and Sjoqvist…
We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…
We consider the superfluid weight, speed of sound and excitation fraction of a flat band Bose-Einstein condensate (BEC) within multiband Bogoliubov theory. The superfluid weight is calculated by introducing a phase winding and minimizing…
We use the quantum metric to understand the properties of quasicrystals, represented by the one-dimensional (1D) Fibonacci chain. We show that the quantum metric can relate the localization properties of the eigenstates to the…
Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable…
Quantum geometry of Bloch wavefunctions has gained considerable interest with the discovery of moir\'e materials that exhibit bands flattened by quantum interference. The quantum metric, the symmetric part of the quantum geometric tensor,…
Bloch electrons in multiorbital systems carry quantum geometric information characteristic of their wavevector-dependent interorbital mixing. The geometric nature impacts electromagnetic responses, and this effect carries over to the…
We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalised tensor networks. This class specifically includes spin networks, the kinematic…
Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The…
Quantum metrology makes use of coherent superpositions to detect weak signals. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by…
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…
We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We…
Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting…
Strong spin-orbit coupling can have a profound effect on the electronic structure in a metal or semiconductor, particularly for low electron concentrations. We show how, for small values of the Fermi energy compared to the spin-orbit…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
Flat-band systems are of great interest due to their strong electron correlations and unique band geometry. Recent studies have linked the properties of Cooper pairs in flat-band superconductors to the quantum metric. Unlike prior studies…
We investigate strong-coupling superfluidity in a uniform gas of Fermi atoms attractively interacting via quasi-molecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy $2\nu$ of the…
Nonreciprocal critical supercurrents give rise to the superconducting diode effect (SDE) in noncentrosymmetric superconductors when time-reversal symmetry is broken. In this paper, we investigate the SDE in superconductors with vanishing…
Quantum geometry has been shown to make an important contribution to the superfluid stiffness of superconductors, especially for flat-band systems such as moir\'e materials. In this work we use mean-field theory to derive an expression for…
The surface states of 3D topological insulators possess geometric structures that imprint distinctive signatures on electronic transport. A prime example is the Berry curvature, which controls, for instance, electric frequency doubling via…