The effect of a weak random potential on two-leg Hubbard ladders is investigated. The random potential is shown to induce Anderson localization except for attractive enough interactions, supressing completely d-wave superconductivity. These localization effects remain very strong even for many ladders coupled by Josephson coupling. Both dc and ac conductivities and localization lengths are obtained. Consequences for the superconducting ladder compound SrxCa14−xCu24O41+δ are discussed. The two-chain Hubbard ladder is a toy model of a metal with a spin-gap, reminiscent of the metallic phase of underdoped cuprates. Recent experiments[1] on the superconducting transition in Sr14−xCaxCu24O41 have been interpreted in the framework of this model. However, impurities are only considered as a source of holes and not a source of random potential although it is known that an infinitesimal disorder localizes all electronic states in one dimension. It is therefore important to investigate the disordered Hubbard ladder. The disordered Hubbard ladder is defined by the Hamiltonian: H = −t ‖ (c † i+1,p,σci,p,σ + c † i,p,σci+1,p,σ) − t⊥ i,p,σ i,σThe effect of a weak random potential on two-leg Hubbard ladders is investigated. The random potential is shown to induce Anderson localization except for attractive enough interactions, supressing completely d-wave superconductivity. These localization effects remain very strong even for many ladders coupled by Josephson coupling. Both dc and ac conductivities and localization lengths are obtained. Consequences for the superconducting ladder compound SrxCa14−xCu24O41+δ are discussed. The two-chain Hubbard ladder is a toy model of a metal with a spin-gap, reminiscent of the metallic phase of underdoped cuprates. Recent experiments[1] on the superconducting transition in Sr14−xCaxCu24O41 have been interpreted in the framework of this model. However, impurities are only considered as a source of holes and not a source of random potential although it is known that an infinitesimal disorder localizes all electronic states in one dimension. It is therefore important to investigate the disordered Hubbard ladder. The disordered Hubbard ladder is defined by the Hamiltonian: H = −t ‖ (c † i+1,p,σci,p,σ + c † i,p,σci+1,p,σ) − t⊥ i,p,σ i,σ

Jan 1, 19983 citations

Hole-doped Hubbard ladders

Holger Fehske, Georg Hager, Gerhard Wellein +1 more

arXiv:cond-mat/0505666Physica B Condensed MatterFeb 20, 20062 citations

Exact Localized and Ballistic Eigenstates in Disordered Chaotic Spin Ladders and the Fermi-Hubbard Model

Thomas Iadecola, Marko Žnidarič

We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations. They can exhibit Anderson localization with area-law eigenstate entanglement or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy, which we show give rise to diffusive transport as expected in a chaotic quantum system. We discuss how to observe these atypical eigenstates in cold-atom experiments realizing the Fermi-Hubbard model, and comment on the robustness of their properties.We demonstrate the existence of exact atypical many-body eigenstates in a class of disordered, interacting one-dimensional quantum systems that includes the Fermi-Hubbard model as a special case. These atypical eigenstates, which generically have finite energy density and are exponentially many in number, are populated by noninteracting excitations. They can exhibit Anderson localization with area-law eigenstate entanglement or, surprisingly, ballistic transport at any disorder strength. These properties differ strikingly from those of typical eigenstates nearby in energy, which we show give rise to diffusive transport as expected in a chaotic quantum system. We discuss how to observe these atypical eigenstates in cold-atom experiments realizing the Fermi-Hubbard model, and comment on the robustness of their properties.

arXiv:1811.07903Physical Review LettersJul 16, 201992 citations

Self-consistent study of Anderson localization in the Anderson-Hubbard model in two and three dimensions

Peter Henseler, Johann Kroha, Boris Shapiro

We consider the change in electron localization due to the presence of electron-electron repulsion in the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. We find rich nonmonotonic behavior of the localization length $\ensuremath{\xi}$ in two-dimensional systems, including an interaction-induced exponential enhancement of $\ensuremath{\xi}$ for small and intermediate disorders although $\ensuremath{\xi}$ remains finite. In three dimensions we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbard-gapped phases. For small $U$ there is re-entrant behavior from the Anderson localized phase to the metallic phase.We consider the change in electron localization due to the presence of electron-electron repulsion in the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. We find rich nonmonotonic behavior of the localization length $\ensuremath{\xi}$ in two-dimensional systems, including an interaction-induced exponential enhancement of $\ensuremath{\xi}$ for small and intermediate disorders although $\ensuremath{\xi}$ remains finite. In three dimensions we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbard-gapped phases. For small $U$ there is re-entrant behavior from the Anderson localized phase to the metallic phase.

arXiv:0808.3734Physical Review BDec 12, 200821 citations

U

there is re-entrant behavior from the Anderson localized phase to the metallic phase.