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arXiv:cond-mat/0407114 · Physical Review B

Gapped spin-liquid states in a one-dimensional Hubbard model with antiferromagnetic exchange interaction

Jianhui Dai, Xiaoyong Feng, Tao Xiang, Yue Yu

Published Aug 31, 2004• 32 citations
arXivHTMLPDF

Abstract

We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange $J$. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as $J$ increases, the spin-charge couplings become important and the critical point ${U}_{c}$ is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.

DOI
10.1103/physrevb.70.064518

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The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.
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We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the density-matrix renormalization-group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion U, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U, sufficiently large next-nearest-neighbor hopping t2{t}_{2}t2​ 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.
We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at U=Uc{U=U}_{c}U=Uc​ and U=Us{U=U}_{s}U=Us​ that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase (U<Uc)(U<{U}_{c})(U<Uc​) and drops below the band gap when U exceeds a special point Ue.{U}_{e}.Ue​. The exciton gap closes at the first critical point Uc{U}_{c}Uc​ while the charge and spin gaps persist and coincide between Uc<U<Us{U}_{c}<U<{U}_{s}Uc​<U<Us​ where the system is dimerized. Both the charge and spin gaps collapse at U=Us{U=U}_{s}U=Us​ when the transition to the MI phase occurs. In the MI phase (U>Us)(U>{U}_{s})(U>Us​) the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.
We calculate the charge compressibility and uniform spin susceptibility for the two-dimensional (2D) Hubbard model slightly away from half filling within a two-loop renormalization group scheme. We find numerically that both those quantities flow to zero as we increase the initial interaction strength from weak to intermediate couplings. This result implies gap openings in both charge and spin excitation spectra for the latter interaction regime. When this occurs, the ground state of the lightly doped 2D Hubbard model may be interpreted as an insulating spin liquid as opposed to a Mott insulating state.
Using the field theoretical bosonization and renormalization group techniques, we analytically study quantum phase diagram of a one-dimensional half-filled extended Hubbard model with on-site (U) and spin-dependent nearest-neighbor interactions (V⊥, V‖) in the weak coupling regime. In the case of easy-plane anisotropy (V⊥ > V‖) and at V‖ < U/2, the existence of bond-ordered spin-density-wave phase, corresponding to spin gapless transverse magnetization located on bonds (BSDW±) is shown.