Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model

Abstract

For an extended Harper model, the fidelity for two lowest band edge states corresponding to different model parameters, the fidelity susceptibility and the von Neumann entropy of the lowest band edge states, and the spectrum-averaged von Neumann entropy are studied numerically, respectively. The fidelity is near one when parameters are in the same phase or same phase boundary; otherwise it is close to zero. There are drastic changes in fidelity when one parameter is at phase boundaries. For fidelity susceptibility the finite scaling analysis performed, the critical exponents $\alpha$, $\beta$, and $\nu$ depend on system sizes for the metal-metal phase transition, while not for the metal-insulator phase transition. For both phase transitions $\nu /\alpha \approx 2$. The von Neumann entropy is near one for the metallic phase, while small for the insulating phase. There are sharp changes in von Neumann entropy at phase boundaries. According to the variation of the fidelity, fidelity susceptibility, and von Neumann entropy with model parameters, the phase diagram, which including two metallic phases and one insulating phase separated by three critical lines with one bicritical point, can be completely characterized, respectively. These numerical results indicate that the three quantities are suited for revealing all the critical phenomena in the model.

9 pages, 12 figures

References in corpus (17)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Mixed-state fidelity and quantum criticality at finite temperature
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Single-Site Entanglement of Fermions at a Quantum Phase Transition
• The fidelity approach to the Hubbard model
• Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems
• Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase
• Von Neumann entropy and localization-delocalization transition of electron states in quantum small-world networks
• Mode entanglement of an electron in one-dimensional determined and random potentials
• von Neumann entropy and localization properties of two interacting particles in one-dimensional nonuniform systems

Cited by in corpus (16)

• Dynamic framework for criticality-enhanced quantum sensing
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers
• Driving enhanced quantum sensing in partially accessible many-body systems
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Free-Fermionic Topological Quantum Sensors
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Interplay of disorder and interactions in a flat-band supporting diamond chain
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Flat-band-based multifractality in the all-band-flat diamond chain
• Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots
• Quantum metrology in the noisy intermediate-scale quantum era
• Density-functional fidelity approach to quantum phase transitions
• Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
• Effects of local decoherence on quantum critical metrology
• Reduced fidelity approach for quantum phase transitions in spin-1/2 dimerized Heisenberg chains
• Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains