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Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
The covariantly constant spacetime torsion is one of the fields which may break Lorentz and CPT symmetry. We review the previous works on the dynamical torsion in the framework of effective quantum field theory (QFT). It turns out that the…
Investigating the geometric effects resulting from the detailed behaviors of the confining potential, we consider square and circular confinements to constrain a particle to a space curve. We find a torsion-induced geometric potential and a…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
In our previous work, we have explored quantum gravity induced entanglement of mass (QGEM) in curved spacetime, observing entanglement formation between particles moving along geodesics in a Schwarzschild spacetime background. We find that…
We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum…
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
The aim of this article is to provide an introduction to the use of quantum information methods for investigating the interface between quantum theory and gravity. To this end, we discuss the basic principles of two current research streams…
15 years ago Dmitry Diakonov wrote the paper "Towards lattice-regularized Quantum Gravity", arXiv:1109.0091. In his approach, gravity with metric and tetrads arise from pre-geometric quantum fields leading to unusual dimensions of physical…
We investigate up to which extend the kinematic setting of loop quantum gravity can be fit into a diffeomorphism invariant setting of algebraic QFT generalizing the Haag-Kastler setting of Wightman type QFT. The net of local (Weyl-)algebras…
We study a group field theory (GFT) for quantum gravity coupled to four massless scalar fields, using these matter fields to define a (relational) coordinate system. We exploit symmetries of the GFT action, in particular under shifts in the…
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin…
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,…
Bosonic Bogoliubov de Gennes (BBdG) Hamiltonians describe the excitations of weakly interacting Bose condensates as well as photonic systems under parametric driving. Their topological features have been studied mainly by utilizing a…
We employ the quantum Boltzmann equation to analyze the gravitationally generated entanglement between two remote qubits by considering two explicit microscopic models. A graviton propagator is employed as the mediator of the interactions,…
The quantum geometric tensor (QGT) embodies the geometry of the eigenstates of a system's Hamiltonian, and its full characterization across diverse quantum systems is essential. However, it is challenging to characterize the QGT of…
We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The…
Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static)…
Presented is a quantum gravity theory that is a quantum mechanical generalization of Einstein's vierbein field-based approach, where the classical metric tensor field is promoted to a quantum mechanical metric tensor field operator. The…