Ground state fidelity from tensor network representations

Abstract

For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well-defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.

4 pages, 2 figures. Published version in Physical Review Letters

References in corpus (5)

• DMRG and periodic boundary conditions: a quantum information perspective
• Quantum critical scaling of the geometric tensors
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Ground-state fidelity in one-dimensional gapless model
• Scaling Properties of Fidelity in Spin-one Anisotropic Model

Cited by in corpus (5)

• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Fidelity analysis of topological quantum phase transitions
• Universal geometric entanglement close to quantum phase transitions
• Fidelity approach to Gaussian transitions
• Ground-state fidelity of Luttinger liquids: A wave functional approach