Related papers: Quantum geometric bound and ideal condition for Eu…
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…
Berry curvature fundamentally dictates the topological ground state, anomalous transport and optical properties of quantum materials. However, directly mapping its momentum-space distribution in real materials remains an outstanding…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann…
Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…
Quantum geometry, which encompasses both Berry curvature and the quantum metric, plays a key role in multi-band interacting electron systems. We study the entanglement entropy of a region of linear size $\ell$ in fermion systems with…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…
Quantized transport not only exist in gapped topological states but also in metallic states. Recently, Kane proposed a quantized nonlinear conductance in ballistic metals whose value is determined by the Euler characteristic of the Fermi…
We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A…
A version of quantum Cram\'{e}r-Rao bound dictates that the covariance of any set of operators is bounded by a product of the derivatives of expectation values and the inverse of quantum metric. We elaborate that because quantum metric…
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…
The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…