arXiv:1101.3217 · Physical Review B

Phase diagram of hard-core bosons on a zigzag ladder

Davide Rossini, Valeria Lante, Alberto Parola, Federico Becca

Published Apr 7, 2011• 5 citations

Abstract

We study hard-core bosons with unfrustrated nearest-neighbor hopping $t$ and repulsive interaction $V$ on a zigzag ladder. As a function of the boson density $\ensuremath{\rho}$ and $V/t$, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for $\ensuremath{\rho}<1/3$ (and $\ensuremath{\rho}>2/3$) at any value of $V/t$. At commensurate densities $\ensuremath{\rho}=1/3$, $1/2$, and $2/3$ insulating (crystalline) phases are stabilized for a sufficiently large interaction $V$. For intermediate densities $1/3<\ensuremath{\rho}<2/3$ and large $V/t$, the ground state shows a clear evidence of a bound state of two bosons, implying gapped single-particle excitations but gapless excitations of boson pairs. These properties can be understood by the fact that the antisymmetric sector acquires a gap and a single gapless mode survives. Finally, for the same range of boson densities and weak interactions, the system is again a one-component Tomonaga-Luttinger liquid with no evidence of any breaking of discrete symmetries, in contrast to the frustrated case, where a ${\mathcal{Z}}_{2}$ symmetry breaking has been predicted.

DOI: 10.1103/physrevb.83.155106

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Phase diagram of hard-core bosons on clean and disordered two-leg ladders: Mott insulator–Luttinger liquid–Bose glass

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arXiv:1101.3217 · Physical Review B

Phase diagram of hard-core bosons on a zigzag ladder

Davide Rossini, Valeria Lante, Alberto Parola, Federico Becca

Published Apr 7, 2011• 5 citations

arXiv HTML PDF

Abstract

We study hard-core bosons with unfrustrated nearest-neighbor hopping

t

and repulsive interaction

V

on a zigzag ladder. As a function of the boson density

\ensuremath{\rho}

and

V/t

, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for

\ensuremath{\rho}<1/3

(and

\ensuremath{\rho}>2/3

) at any value of

V/t

. At commensurate densities

\ensuremath{\rho}=1/3

1/2

, and

2/3

insulating (crystalline) phases are stabilized for a sufficiently large interaction

V

. For intermediate densities

1/3<\ensuremath{\rho}<2/3

and large

V/t

, the ground state shows a clear evidence of a bound state of two bosons, implying gapped single-particle excitations but gapless excitations of boson pairs. These properties can be understood by the fact that the antisymmetric sector acquires a gap and a single gapless mode survives. Finally, for the same range of boson densities and weak interactions, the system is again a one-component Tomonaga-Luttinger liquid with no evidence of any breaking of discrete symmetries, in contrast to the frustrated case, where a

{\mathcal{Z}}_{2}

symmetry breaking has been predicted.

DOI: 10.1103/physrevb.83.155106

Related papers

Phase diagram of hard-core bosons on clean and disordered two-leg ladders: Mott insulator–Luttinger liquid–Bose glass

François Crépin, Nicolas Laflorencie, Guillaume Roux +1 more

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Takashi Tonegawa, Toshiya Hikihara, Kiyomi Okamoto +2 more

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.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.

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

Phase diagram of one-dimensional bosons with Rydberg-dressed soft-core interactions

Shengjie Yu, Laurent Sanchez-Palencia

Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter $K>1$ to hard-rod-like behavior with $K<1$ , with a quasi-supersolid phase emerging for $K < 1/2$ . For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter $K>1$ to hard-rod-like behavior with $K<1$, with a quasi-supersolid phase emerging for $K < 1/2$. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.

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Phase diagram of the Kondo model on the zigzag ladder

Matthias Peschke, Lena-Marie Woelk, Michael Potthoff

The effect of next-nearest-neighbor hopping ${t}_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite ${t}_{2}$ , i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that ${t}_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$ , we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$ , a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak $J$ , with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.The effect of next-nearest-neighbor hopping ${t}_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite ${t}_{2}$, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that ${t}_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker $J$, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak $J$, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.

arXiv:1901.01236Physical review. B./Physical review. BFeb 27, 20194 citations

Hard-core bosons in a zig-zag optical superlattice

Arya Dhar, Tapan Mishra, Ramesh V. Pai +2 more

We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest- and next-nearest-neighbor sites. We obtain the ground-state phase diagram as a function of microscopic parameters using the finite-size density-matrix renormalization-group method. Depending on the sign of the next-nearest-neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI), and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the unfrustratedase), the system undergoes a transition from the SF to the SLMI at a nonzero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the frustrated case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next-nearest-neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond-order parameter. The transition from BO to SLMI appears to be first order.We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest- and next-nearest-neighbor sites. We obtain the ground-state phase diagram as a function of microscopic parameters using the finite-size density-matrix renormalization-group method. Depending on the sign of the next-nearest-neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI), and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the unfrustratedase), the system undergoes a transition from the SF to the SLMI at a nonzero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the frustrated case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next-nearest-neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond-order parameter. The transition from BO to SLMI appears to be first order.

arXiv:1307.4053Physical Review ANov 21, 201320 citations

We study hard-core bosons with unfrustrated nearest-neighbor hopping

t

and repulsive interaction

V

on a zigzag ladder. As a function of the boson density

\ensuremath{\rho}

and

V/t

, the ground state displays different quantum phases. A standard one-component Tomonaga-Luttinger liquid is stable for

\ensuremath{\rho}<1/3

(and

\ensuremath{\rho}>2/3

) at any value of

V/t

. At commensurate densities

\ensuremath{\rho}=1/3

1/2

, and

2/3

insulating (crystalline) phases are stabilized for a sufficiently large interaction

V

. For intermediate densities

1/3<\ensuremath{\rho}<2/3

and large

V/t

{\mathcal{Z}}_{2}

symmetry breaking has been predicted.

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.

K>1

to hard-rod-like behavior with

K<1

, with a quasi-supersolid phase emerging for

K < 1/2

. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.

The effect of next-nearest-neighbor hopping

{t}_{2}

on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite

{t}_{2}

, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that

{t}_{2}

at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong

J

, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker

J

, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak

J

, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.