arXiv:2311.06733 · Physics Letters A

Ground-state phase diagram of two-component interacting bosons on a two-leg ladder

Po Chen, Chenrong Liu

Published Apr 5, 2024• 1 citation

arXiv HTML PDF

DOI: 10.1016/j.physleta.2024.129485

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arXiv:2311.06733 · Physics Letters A

Ground-state phase diagram of two-component interacting bosons on a two-leg ladder

Po Chen, Chenrong Liu

Published Apr 5, 2024• 1 citation

arXiv HTML PDF

DOI: 10.1016/j.physleta.2024.129485

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FrustratedS= 1/2 Two-Leg Ladder with Different Leg Interactions

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We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J 1, a and J 1, b between nearest neighbor spins in the legs a and b , respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by J r and Δ J r , respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J 1, a J 1, b < 0 irrespective of the sign of J r . The phase diagrams on the Δ (0≤Δ<1) versus J 1, b plane in the cases of J 1, a = − 0.2 and J 1, a = 0.2 with J r = −1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state , when J 1, a + J 1, b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J 1, a and J 1, b between nearest neighbor spins in the legs a and b , respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by J r and Δ J r , respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J 1, a J 1, b < 0 irrespective of the sign of J r . The phase diagrams on the Δ (0≤Δ<1) versus J 1, b plane in the cases of J 1, a = − 0.2 and J 1, a = 0.2 with J r = −1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state , when J 1, a + J 1, b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.

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arXiv:1808.01090Journal of the Physical Society of JapanSep 12, 20188 citations

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.