Ground state fidelity from tensor network representations

TL;DR

This paper introduces a method to compute ground state fidelity for D-dimensional quantum lattice systems using tensor network algorithms, linking it to classical statistical models to analyze phase diagrams.

Contribution

It presents a novel approach to calculate ground state fidelity via tensor networks, enabling phase diagram characterization in quantum many-body systems.

Findings

Fidelity per site effectively characterizes phase transitions.

Method applied successfully to 2D quantum Ising model.

Provides a computational framework linking quantum and classical models.

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.