Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-½ XXZ ladder

Abstract

The fully anisotropic two-leg spin- $\tfrac{1}{2}$ XXZ ladder model is studied in terms of an algorithm based on the tensor network (TN) 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 TN 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, Néel, stripe Néel and Haldane phases, along with the two XY phases XY 1 and XY 2.

Keywords

• quantum spin ladder
• quantum phase transition
• quantum fidelity
• tensor networks
• 74.20.-z
• 02.70.-c