arXiv:1704.05484 · New Journal of Physics

Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-$\tfrac{1}{2}$XXZladder

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

Published Sep 12, 2017• 5 citations

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 XY 1 and XY 2.

DOI: 10.1088/1367-2630/aa8bce

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arXiv:1704.05484 · New Journal of Physics

Groundstate fidelity phase diagram of the fully anisotropic two-leg spin- $\tfrac{1}{2}$ XXZladderGroundstate fidelity phase diagram of the fully anisotropic two-leg spin-$\tfrac{1}{2}$XXZladder

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

Published Sep 12, 2017• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1367-2630/aa8bce

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

\tfrac{1}{2}

XXZladder

We explore the ground-state phase diagram of the

S=1/2

two-leg ladder with different leg interactions. The

xy

and

z

components of the leg interactions between nearest-neighbor spins in the

a

(

b

) leg are respectively denoted by

J_{{\rm l},a}

and

Δ_{\rm l} J_{{\rm l},a}

(

J_{{\rm l},b}

and

Δ_{\rm l} J_{{\rm l},b}

). On the other hand, the

xy

and

z

components of the uniform rung interactions are respectively denoted by

Γ_{\rm r} J_{\rm r}

and

J_{\rm r}

. In the above,

Δ_{\rm l}

and

Γ_{\rm r}

are the

XXZ

-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when

J_{{\rm l},a} J_{{\rm l},b}<0

irrespective of the sign of

J_{\rm r}

. The phase diagram on the

Δ_{\rm l}

(

|Δ_{\rm l}| \leq 1.0

) versus

J_{{\rm l},b}

(

-2.0\leq J_{{\rm l},b}\leq 3.0

) plane in the case where

J_{{\rm l},a}=0.2

J_{\rm r}=-1.0

, and

Γ_{\rm r} = 0.5

is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and

XY1

phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.