The quantum geometric tensor characterizes the complete properties of states, with symmetric part being metric and antisymmetric Berry curvature. We propose a generic Hamiltonian globally degenerate ground states give general relation between corresponding non-Abelian unit Bloch vector. This enables us to construct or Euler To be concrete, we present study two topological semimetal models bands under $CP$ ${C}_{2}T$ symmetries. invariants these semimetals are Chern number class,...

We propose a feasible scheme to realize four-band Stiefel-Whitney insultor (SWI) with spin-orbit coupled ultracold atoms in an optical Raman lattice. Four selected spin states are by carefully designed lasers, generate the desired interactions spacetime inversion symmetry. map out phase diagram respect experimental parameters, where large topological region exists. further present two distinct detection methods resolve non-abelian band topology, both equilibrium and dynamical ways. The...

The complete geometry of quantum states in parameter space is characterized by the geometric tensor, which contains metric and Berry curvature as real imaginary parts, respectively. When are degenerate, take non-Abelian forms. (Abelian) Abelian have been experimentally measured. However, an feasible scheme to extract all components tensor still lacking. Here we propose a generic protocol directly arbitrary degenerate any dimensional based on measuring transition probabilities after quenches....

We propose an ultracold-atom setting where a fermionic superfluidity with attractive $s$-wave interaction is uploaded in non-Hermitian Lieb optical lattice. The existence of real-energy flat band solution revealed. show that the interplay between skin effect and flat-band localization leads to exotic properties. develop multiband mean-field description this system use both order parameters superfluid weight describe phase transition. A relation quantum metric states manifold built. find...

The concepts of topology and geometry are critical importance in exploring exotic phases quantum matter. Although they have been investigated on various experimental platforms, to date a direct probe the topological geometric properties universal computer even for minimum model is still vain. In this work, we first show that density matrix form tensor (QGT) can be explicitly reconstructed from Pauli operator measurements circuit. We then propose two algorithms suitable IBM computers directly...

We propose that a kind of four-dimensional (4D) Hamiltonians, which host tensor monopoles related to the quantum metric in even dimensions, can be simulated by ultracold atoms optical lattices. The topological properties and bulk-boundary correspondence are investigated detail. By fixing momentum along one it reduced an effective three-dimensional model manifesting with nontrivial chiral insulator phase. Using semiclassical Boltzmann equation, we calculate longitudinal resistance against...

Quantum Fisher information bounds the ultimate precision limit in parameter estimation and has important applications quantum metrology. In recent years, theoretical experimental studies of non-Hermitian Hamiltonians realized systems have attracted wide attention. Here, based on eigenstates is investigated, corresponding Cramér-Rao bound for single-parameter two-parameter estimations are given. particular, about estimating intrinsic momentum external parameters non-reciprocal gain-and-loss...

The concepts of topology and geometry are critical importance in exploring exotic phases quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe topological geometric properties universal computer even for minimum model is still vain. In this work, we first show that density matrix form the tensor (QGT) can be explicitly re-constructed from Pauli operator measurements circuit. We then propose two algorithms, suitable IBM computers,...

The geometric properties of quantum states is fully encoded by the tensor. real and imaginary parts tensor are metric Berry curvature, which characterize distance phase difference between two nearby in Hilbert space, respectively. For conventional Hermitian systems, corresponds to fidelity susceptibility has already been used specify transitions from perspective. In this work, we extend wisdom non-Hermitian systems for revealing critical points. To be concrete, employing numerical exact...

The geometric properties of quantum states are fully encoded by the tensor. real and imaginary parts tensor metric Berry curvature, which characterize distance phase difference between two nearby in Hilbert space, respectively. For conventional Hermitian systems, corresponds to fidelity susceptibility has already been used specify transitions from perspective. In this paper, we extend wisdom non-Hermitian systems for revealing critical points. To be concrete, employing numerical exact...

In this paper, we present a novel experimental approach for simulating and detecting topological invariants using ultracold fermions confined in two-dimensional hexagonal optical lattices. We propose achieving two-fold degenerate four-band models with non-trivial topologies both the AII A classes by introducing additional inertial forces, Raman processes, or periodic driving. By implementing various quench sequences observing evolution of time-of-flight pattern, can gather comprehensive...

The Stiefel-Whitney insultor is a two-dimensional topological insulator protected by parity-time ($\mathcal{PT}$) symmetry. With vanishing Chern number, the topology in this system characterized second class. We propose feasible scheme to realize four-band with spin-orbit coupled ultracold atoms an optical Raman lattice. Four selected spin states are carefully designed lasers generate desired interactions spacetime inversion map out phase diagram respect experimental parameters, where large...

In this paper, we present an experimental approach for simulating and detecting topological invariants using ultracold fermions confined in two-dimensional hexagonal optical lattices. We propose achieving degenerate four-band models with nontrivial topologies both the AII A classes by introducing additional inertial forces, Raman processes, or periodic driving. By implementing various quench sequences observing evolution of time-of-flight pattern, can gather comprehensive information about...

The quantum geometric tensor (QGT) characterizes the complete properties of states, with symmetric part being metric, and antisymmetric Berry curvature. We propose a generic Hamiltonian global degenerate ground give general relation between corresponding non-Abelian metric unit Bloch vector. This enables us to construct or Euler To be concrete, we present study two topological semimetal models bands under CP $C_2T$ symmetries, respectively. invariants these semimetals are Chern number class,...