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

Sheng-Hao Li,Murray T Batchelor,Qian-Qian Shi,Huan-Qiang Zhou

doi:10.1088/1367-2630/aa8bce

Abstract

The fully anisotropic two-leg spin- 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 XY1 and XY2.

Highlights

Spin ladder systems have attracted considerable attention from both experimentalists and theoreticians alike [1, 2]
Apart from order parameters, which we make use of, the groundstate fidelity per lattice site is used as an important tool to detect quantum phase transitions
For two different groundstates ∣y (x)ñ and ∣y (x¢)ñ in a quantum system corresponding to different values x and x¢ of a control parameter, the fidelity F (x, x¢) = ∣áy (x)∣y (x¢)ñ∣ is defined as a measure of the overlap between the two states

Summary

Introduction

Spin ladder systems have attracted considerable attention from both experimentalists and theoreticians alike [1, 2]. Spin ladder systems in general represent a interesting class of quantum critical phenomena, exhibiting a rich variety of quantum phases [4,5,6,7,8]. Apart from a few cases [2], spin ladder systems are not exactly solvable, it is necessary to develop various techniques, both analytical and numerical, to investigate their physical properties [9,10,11,12,13,14,15,16,17,18,19]. An efficient tensor network (TN) algorithm has been developed which is tailored to translationally invariant infinite-size spin ladder systems [20]. The algorithm is seen to be efficient compared to the density matrix renormalization group [12] and time evolving block decimation [23], at least as far as the memory cost is concerned

Objectives

Results

Conclusion