arXiv:cond-mat/0405380 · Physical Review B

Phase diagram of the two-leg Kondo ladder

J. C. Xavier, E. Miranda, Elbio R. Dagotto

Published Nov 23, 2004• 6 citations

Abstract

The phase diagram of the two-leg Kondo ladder is investigated using computational techniques. Ferromagnetism is present, but only at small conduction electron densities and robust Kondo coupling $J$. For densities $n\ensuremath{\gtrsim}0.4$ and any Kondo coupling, a paramagnetic phase is found. We also observed spin dimerization at densities $n=1∕4$ and $n=1∕2$. The spin-structure factor at small $J$ peaks at $\stackrel{P\vec}{q}=(2n,0)\ensuremath{\pi}$ for $n\ensuremath{\lesssim}0.5$, and at $\stackrel{P\vec}{q}=(n,1)\ensuremath{\pi}$ for $n\ensuremath{\gtrsim}0.5$. The charge structure factor suggests that electrons behave as free particles with spin $\ensuremath{-}1∕2$ (spin-0) for small (large) $J$.

DOI: 10.1103/physrevb.70.172415

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Phase diagram of coupled ladders

T. F. A. Müller, Thomas Maurice Rice

arXiv:cond-mat/9802297Physical review. B, Condensed matterAug 1, 199818 citations

Low-energy properties of spin-1/2 two-leg antiferromagnetic Heisenberg ladders with ferromagnetic diagonal coupling

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arXiv:cond-mat/0405380 · Physical Review B

Phase diagram of the two-leg Kondo ladder

J. C. Xavier, E. Miranda, Elbio R. Dagotto

Published Nov 23, 2004• 6 citations

arXiv HTML PDF

Abstract

The phase diagram of the two-leg Kondo ladder is investigated using computational techniques. Ferromagnetism is present, but only at small conduction electron densities and robust Kondo coupling

J

. For densities

n\ensuremath{\gtrsim}0.4

and any Kondo coupling, a paramagnetic phase is found. We also observed spin dimerization at densities

n=1∕4

and

n=1∕2

. The spin-structure factor at small

J

peaks at

\stackrel{P\vec}{q}=(2n,0)\ensuremath{\pi}

for

n\ensuremath{\lesssim}0.5

, and at

\stackrel{P\vec}{q}=(n,1)\ensuremath{\pi}

for

n\ensuremath{\gtrsim}0.5

. The charge structure factor suggests that electrons behave as free particles with spin

\ensuremath{-}1∕2

(spin-0) for small (large)

J

DOI: 10.1103/physrevb.70.172415

Related papers

Phase diagram of coupled ladders

T. F. A. Müller, Thomas Maurice Rice

The two-leg $t\ensuremath{-}J$ ladder forms a spin liquid at half filling that evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e., rungs and legs equal) as a function of electron density n and the ratio $J/t.$ Two known limiting cases are $n<\frac{1}{2},$ which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for $1>n>\frac{1}{2}.$ We find evidences for gapless behavior in both spin and charge channels for $J/t<0.3,$ consistent with Luttinger liquids in both bonding and antibonding bands (i.e., $C2S2).$ This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger $J/t$ shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For $J/t<0.3$ this is very weak, indicating a lack of pairing between these channels.The two-leg $t\ensuremath{-}J$ ladder forms a spin liquid at half filling that evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e., rungs and legs equal) as a function of electron density n and the ratio $J/t.$ Two known limiting cases are $n<\frac{1}{2},$ which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for $1>n>\frac{1}{2}.$ We find evidences for gapless behavior in both spin and charge channels for $J/t<0.3,$ consistent with Luttinger liquids in both bonding and antibonding bands (i.e., $C2S2).$ This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger $J/t$ shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For $J/t<0.3$ this is very weak, indicating a lack of pairing between these channels.

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Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.Using the density matrix renormalization group method, we have obtained the ground-state phase diagram of a spin-1/2 two-leg antiferromagnetic Heisenberg ladder with a ferromagnetic diagonal interaction ${J}_{\ifmmode\times\else\texttimes\fi{}}.$ The boundary between the two phases found in the system, the Haldane phase and the singlet phase, lies in the frustrated area of the parameter space, i.e., both the rung coupling ${J}_{\ensuremath{\perp}}$ and the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ are ferromagnetic. The spin gap is found to be insensitive to the change of the ferromagnetic diagonal coupling strength when the ratio of the rung coupling constant ${J}_{\ensuremath{\perp}}$ to the leg coupling constant ${J}_{\ensuremath{\Vert}}$ is 0.5, in agreement with the analysis of recent experimental spin susceptibility data.

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In this work, we study N-leg Kondo ladders at half-filling through the density matrix renormalization group. We found nonzero spin and charge gaps for any finite number of legs and Kondo coupling $J>0.$ We also show evidence of the existence of a quantum critical point in the two-dimensional Kondo lattice model, in agreement with previous works. Based on the binding energy of two holes, we did not find evidence of superconductivity in the two-dimensional Kondo lattice model close to half filling.In this work, we study N-leg Kondo ladders at half-filling through the density matrix renormalization group. We found nonzero spin and charge gaps for any finite number of legs and Kondo coupling $J>0.$ We also show evidence of the existence of a quantum critical point in the two-dimensional Kondo lattice model, in agreement with previous works. Based on the binding energy of two holes, we did not find evidence of superconductivity in the two-dimensional Kondo lattice model close to half filling.

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Ground-state phase diagram of a spin- 12 frustrated three-leg antiferromagnetic Heisenberg ladder

Xiaoqun Wang, Ningsheng Zhu, Changfeng Chen

Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge $c=2.$ The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.Using the density matrix renormalization group method we have studied the ground-state phase diagram of a spin-1/2 frustrated three-leg antiferromagnetic Heisenberg ladder, and identified two phases corresponding to the spin-3/2 chain and the standard spin ladder. Varying the diagonal coupling ${J}_{\ifmmode\times\else\texttimes\fi{}}$ leads to a quantum phase transition from one ground state to the other, but does not alter the gapless nature of the excitation spectra. On the phase boundary, the degenerate ground states form a chiral spin liquid with a central charge $c=2.$ The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.

Physical review. B, Condensed matterNov 15, 200211 citations

The phase diagram of the two-leg Kondo ladder is investigated using computational techniques. Ferromagnetism is present, but only at small conduction electron densities and robust Kondo coupling

J

. For densities

n\ensuremath{\gtrsim}0.4

and any Kondo coupling, a paramagnetic phase is found. We also observed spin dimerization at densities

n=1∕4

and

n=1∕2

. The spin-structure factor at small

J

peaks at

\stackrel{P\vec}{q}=(2n,0)\ensuremath{\pi}

for

n\ensuremath{\lesssim}0.5

, and at

\stackrel{P\vec}{q}=(n,1)\ensuremath{\pi}

for

n\ensuremath{\gtrsim}0.5

. The charge structure factor suggests that electrons behave as free particles with spin

\ensuremath{-}1∕2

(spin-0) for small (large)

J

J/t.

Two known limiting cases are

n<\frac{1}{2},

which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for

1>n>\frac{1}{2}.

We find evidences for gapless behavior in both spin and charge channels for

J/t<0.3,

consistent with Luttinger liquids in both bonding and antibonding bands (i.e.,

C2S2).

This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger

J/t

shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For

J/t<0.3

this is very weak, indicating a lack of pairing between these channels.

In this work, we study N-leg Kondo ladders at half-filling through the density matrix renormalization group. We found nonzero spin and charge gaps for any finite number of legs and Kondo coupling

J>0.

We also show evidence of the existence of a quantum critical point in the two-dimensional Kondo lattice model, in agreement with previous works. Based on the binding energy of two holes, we did not find evidence of superconductivity in the two-dimensional Kondo lattice model close to half filling.

We present the phase diagram of the

S=1/2

Heisenberg model on the two leg ladder with cyclic four-spin exchange, determined by a combination of exact diagonalization and density-matrix renormalization group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality, or collinear spin correlations. We localize the phase transitions and investigate their nature.

c=2.

The critical value of ${J}_{\ifmmode\times\else\texttimes\fi{}}$ is insensitive to the number of legs in the ladder, suggesting that a quantum phase transition may occur at ${J}_{\ifmmode\times\else\texttimes\fi{}}=0.6$ for the isotropic spin-1/2 antiferromagnetic Heisenberg model on the square lattice.