相关论文: Quantum critical scaling of the geometric tensors

Parametrically driven nonlinear resonators represent a building block for realizing fault-tolerant quantum computation and are useful for critical quantum sensing. From a fundamental viewpoint, the most intriguing feature of such a system…

We show that geometric phase of the ground state in the XY model obeys scaling behavior in the vicinity of a quantum phase transition. In particular we find that geometric phase is non-analytical and its derivative with respect to the field…

The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…

The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…

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 define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…

Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…

The fidelity susceptibility serves as a universal probe for quantum phase transitions, offering an order-parameter-free metric that captures ground-state sensitivity to Hamiltonian perturbations and exhibits critical scaling. Classical…

We address the question whether the super-Heisenberg scaling for quantum estimation is realizable. We unify the results of two approaches. In the first one, the original system is compared with its copy rotated by the parameter dependent…

We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…

Phase transitions represent a compelling tool for classical and quantum sensing applications. It has been demonstrated that quantum sensors can in principle saturate the Heisenberg scaling, the ultimate precision bound allowed by quantum…

In many-body quantum systems, the quantum Fisher information an observer can obtain is susceptible to decoherence. Consequently, quantum enhanced metrology, such as Heisenberg scaling, cannot usually be achieved. We show, via two distinct…

We study scaling behavior of the geometric tensor $\chi_{\alpha,\beta}(\lambda_1,\lambda_2)$ and the fidelity susceptibility $(\chi_{\rm F})$ in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model.…

Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the…

The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…

Using high-precision numerical analysis, we show that 3+1 dimensional gauge theories holographically dual to 4+1 dimensional Einstein-Maxwell-Chern-Simons theory undergo a quantum phase transition in the presence of a finite charge density…

Critical quantum systems are a promising resource for quantum metrology applications, due to the diverging susceptibility developed in proximity of phase transitions. Here, we assess the metrological power of parametric Kerr resonators…

We combine the finite size scaling method with the meshfree spectral method to calculate quantum critical parameters for a given Hamiltonian. The basic idea is to expand the exact wave function in a finite exponential basis set and…

In this paper, we extend the quantum geometric tensor for parameter-dependent curved spaces to higher dimensions, and introduce an equivalent definition that generalizes the Zanardi, et al, formulation of the tensor. The parameter-dependent…