# Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder

## TL;DR

This paper uses tensor network algorithms to map out the phase diagram of a fully anisotropic two-leg spin-1/2 XXZ ladder, revealing diverse quantum phases and phase transitions.

## Contribution

It introduces an efficient tensor network method to analyze groundstates and identify phase boundaries in the anisotropic XXZ ladder model.

## Key findings

- Identified multiple quantum phases including ferromagnetic, Nèel, and Haldane.
- Mapped the comprehensive phase diagram using groundstate fidelity and order parameters.
- Detected phase transitions through fidelity per lattice site.

## Abstract

The fully anisotropic two-leg spin-1/2 $XXZ$ ladder model is studied in terms of an algorithm based on the tensor network representation of quantum many-body states as an adaptation of projected entangled pair states to the geometry of translationally invariant infinite-size quantum spin ladders. The tensor network algorithm provides an effective method to generate the groundstate wave function, which allows computation of the groundstate fidelity per lattice site, a universal marker to detect phase transitions in quantum many-body systems. The groundstate fidelity is used in conjunction with local order and string order parameters to systematically map out the groundstate phase diagram of the ladder model. The phase diagram exhibits a rich diversity of quantum phases. These are the ferromagnetic, stripe ferromagnetic, rung singlet, rung triplet, N$\rm \acute{e}$el, stripe N$\rm \acute{e}$el and Haldane phases, along with the two $XY$ phases $XY1$ and $XY2$.