arXiv:0804.4810 · Physical Review B

Phase diagram of the t−U−J1−J2 chain at half filling

X.Y Huang, E. Szirmai, Florian Gebhard, Jenő Sólyom, R. M. Noack

Published Aug 25, 2008• 10 citations

Abstract

We investigate the Hubbard chain at half band filling with additional nearest-neighbor and next-nearest-neighbor spin exchange ${J}_{1}$ and ${J}_{2}$ using bosonization and the density-matrix renormalization group. For ${J}_{2}=0$ we find a spin-density-wave phase for all positive values of the Hubbard interaction $U$ and the Heisenberg exchange ${J}_{1}$. A frustrating spin exchange ${J}_{2}$ induces a bond-order-wave phase. For some values of ${J}_{1}$, ${J}_{2}$, and $U$, we observe a spin-gapped metallic Luther-Emery phase.

DOI: 10.1103/physrevb.78.085128

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arXiv:0804.4810 · Physical Review B

Phase diagram of the t−U−J1−J2 chain at half filling

X.Y Huang, E. Szirmai, Florian Gebhard, Jenő Sólyom, R. M. Noack

Published Aug 25, 2008• 10 citations

arXiv HTML PDF

Abstract

We investigate the Hubbard chain at half band filling with additional nearest-neighbor and next-nearest-neighbor spin exchange

{J}_{1}

and

{J}_{2}

using bosonization and the density-matrix renormalization group. For

{J}_{2}=0

we find a spin-density-wave phase for all positive values of the Hubbard interaction

U

and the Heisenberg exchange

{J}_{1}

. A frustrating spin exchange

{J}_{2}

induces a bond-order-wave phase. For some values of

{J}_{1}

{J}_{2}

, and

U

, we observe a spin-gapped metallic Luther-Emery phase.

DOI: 10.1103/physrevb.78.085128

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We investigate the Hubbard chain at half band filling with additional nearest-neighbor and next-nearest-neighbor spin exchange

{J}_{1}

and

{J}_{2}

using bosonization and the density-matrix renormalization group. For

{J}_{2}=0

we find a spin-density-wave phase for all positive values of the Hubbard interaction

U

and the Heisenberg exchange

{J}_{1}

. A frustrating spin exchange

{J}_{2}

induces a bond-order-wave phase. For some values of

{J}_{1}

{J}_{2}

, and

U

, we observe a spin-gapped metallic Luther-Emery phase.

{t}_{2}

leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.

(t)

and next-nearest-neighbor $({t}^{\ensuremath{'}})$ hopping. The study is carried out using the bosonization approach and density-matrix renormalization-group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line ${t}_{c}^{\ensuremath{'}}(U,t)$. We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.

We study the phase diagram, ground-state properties, and excitation gaps of a frustrated spin-Peierls chain, i.e., a spin-Peierls chain with both nearest-neighbor exchange

{\mathit{J}}_{1}

and next-nearest-neighbor exchange

{\mathit{J}}_{2}

. The phase diagram is calculated using a bosonization renormalization-group method. We propose a bond-operator mean-field approximation to calculate the ground-state properties and excitation gaps.

We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-

\frac{1}{2}

Luttinger liquid coupled by a Kondo exchange interaction

{J}_{K}

to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling

{J}_{1}

and a next-nearest-neighbor (frustrating) exchange interaction

{J}_{2}

. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling

{J}_{K}

with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios

{J}_{K}/{J}_{1}

{J}_{2}/{J}_{1}

, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.