Related papers: Direct probing the quantum geometric tensor for bo…
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…
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…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
Several moir\'e systems created by various twisted bilayers have manifested magnetism under flatband conditions leading to enhanced interaction effects. We theoretically study stability of moir\'e flatband ferromagnetism against collective…
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…
Starting with the partition functions for quantum group invariant systems we calculate the metric in the two-dimensional space defined by the parameters $\beta$ and $\gamma=-\beta\mu$ and the corresponding scalar curvature for these systems…
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…
Nodal planes, two-dimensional symmetry-enforced band crossings, can carry a topological charge, similar to Weyl points. While the transport properties of Weyl points are well understood, those of nodal planes remain largely unexplored.…
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…
In the framework of the method of constraint system quantization, a quantum gravitational system (QGS) with the maximally symmetric geometry is studied. The state vector of the QGS satisfies the set of wave equations which describes the…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
Quantum simulations of lattice gauge theories (LGTs) with both dynamical matter and gauge fields provide a promising approach to studying strongly coupled problems beyond classical computational reach. Yet, implementing gauge-invariant…
The quantum dynamics of the intrinsic metric profoundly influence the neutral excitations in the fractional quantum Hall system, as established by Haldane in 2011 \cite{Haldane2011}, and further evidenced by a recent two-photon experiment…
The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…
A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction…
This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction.…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Single-particle states in electronic Bloch bands form a Riemannian manifold whose geometric properties are described by two gauge invariant tensors, one being symmetric the other being antisymmetric, that can be combined into the so-called…
We report on an effective gauge theory of double-layer quantum Hall systems, that is constructed via bosonization from the response of incompressible states without referring to composite bosons and fermions. It is pointed out that…