Quantum Renormalization Group for Ground-State Fidelity

Abstract

Ground-state fidelity (GSF) and quantum renormalization group theory (QRG) have proven useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method to calculate GSF through QRG, obviating the need for calculating or approximating ground states. This method thus enhances characterization of quantum criticality as well as scaling analysis of relevant properties with system size. We illustrate the formalism in the one-dimensional Ising model in a transverse field and the anisotropic spin-1/2 Heisenberg model.

5 pages and 5 figures (revised)

References in corpus (18)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Quantum Phase Transitions and Bipartite Entanglement
• Ground state fidelity from tensor network representations
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Quantum fidelity and quantum phase transitions in matrix product states
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• Quantum Adiabatic Brachistochrone
• Ground-state fidelity in one-dimensional gapless model
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Quantum fidelity in the thermodynamic limit
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Fidelity approach to the disordered quantum XY model
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Operator fidelity susceptibility, decoherence and quantum criticality
• Reduced fidelity in topological quantum phase transitions
• Scaling of the fidelity susceptibility in a disordered quantum spin chain

Cited by in corpus (18)

• Fidelity and criticality of quantum Ising chain with long-range interactions
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Driving enhanced quantum sensing in partially accessible many-body systems
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
• Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field
• Generalized fidelity susceptibility at phase transitions
• Fidelity Susceptibility in the Quantum Rabi Model
• Ground-state fidelity of the spin-1 Heisenberg chain with single ion anisotropy: quantum renormalization group and exact diagonalization approaches
• Fidelity as a probe for a deconfined quantum critical point
• Quantum renormalization group approach to geometric phases in spin chains
• Quantum critical phase diagram of bond alternating Ising model with Dzyaloshinskii-Moriya interaction: signature of ground state fidelity
• Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature
• Real space renormalization of Majorana fermions in quantum nano-wire superconductors
• On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain
• Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube