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arXiv:cond-mat/9612006 · Physical Review Letters

Two Interacting Quasiparticles Above the Fermi Sea

Philippe Jacquod, Dima L. Shepelyansky

Published Jun 30, 1997• 31 citations
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Abstract

We study numerically the interaction and disorder effects for two quasiparticles in two and three dimensions. The dependence of the interaction-induced Breit-Wigner width $\ensuremath{\gamma}$ on the excitation energy above the Fermi level $(\ensuremath{\epsilon})$, the disorder strength, and the system size are determined. A regime is found where $\ensuremath{\gamma}$ is practically independent of $\ensuremath{\epsilon}$. The results allow us to estimate the two quasiparticle mobility edge.

DOI
10.1103/physrevlett.78.4986

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We study numerically the interaction and disorder effects for two quasiparticles in two and three dimensions. The dependence of the interaction-induced Breit-Wigner width \ensuremathγ\ensuremath{\gamma}\ensuremathγ on the excitation energy above the Fermi level (\ensuremathϵ)(\ensuremath{\epsilon})(\ensuremathϵ), the disorder strength, and the system size are determined. A regime is found where \ensuremathγ\ensuremath{\gamma}\ensuremathγ is practically independent of \ensuremathϵ\ensuremath{\epsilon}\ensuremathϵ. The results allow us to estimate the two quasiparticle mobility edge.
The localization properties of quasiparticle pairs above a frozen Fermi sea in the two- and three-dimensional Anderson model with Hubbard interaction are investigated. The dependence of the width Γ of the local spectral density on the pair excitation energy ε2, the disorder W, the interaction strength U and the linear system size L is determined. The obtained results allow to emphasize an interaction-induced pair delocalization effect even when the quasiparticles remain individually localized. The corresponding mobility edge is further estimated and the disorder versus interaction phase diagram is determined. Further investigations focusing on the spectral properties of the system and the transition from Poisson to Wigner-Dyson statistics corroborate these conclusions. The relevance of this effect with respect to the one-quasiparticle lifetime is finally discussed.
For many-body Fermi systems we determine the dependence of the Breit-Wigner width $\ensuremath{\gamma}$ and inverse participation ratio $\ensuremath{\xi}$ on interaction strength $U\ensuremath{\ge}{U}_{c}$ and energy excitation $\ensuremath{\delta}E\ensuremath{\ge}\ensuremath{\delta}{E}_{\mathrm{ch}}$ when a crossover from Poisson to Wigner-Dyson P(s)P(s)P(s) statistics takes place. At $U\ensuremath{\ge}{U}_{c}$ the eigenstates are composed of a large number of noninteracting states and even for U<UcU<{U}_{c}U<Uc​ there is a regime where P(s)P(s)P(s) is close to the Poisson distribution but $\ensuremath{\xi}\ensuremath{\gg}1$.
Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions. An important outstanding problem is the fate of the Anderson transition in the presence of additional Hubbard interactions of strength UUU between particles. Based on large-scale numerics, we compute the position of the mobility edge for a system of two identical bosons or two fermions with opposite spin component. The resulting phase diagram in the interaction-energy-disorder space possesses a remarkably rich and counterintuitive structure, with multiple metallic and insulating phases. We show that this phenomenon originates from the molecular or scattering-like nature of the pair states available at given energy and disorder strength. The behavior of the disorder-averaged density of states of the effective model for the pair is also discussed.
Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions.An important outstanding problem is the fate of the Anderson transition in the presence of additional Hubbard interactions of strength U between particles.Based on large-scale numerics, we compute the position of the mobility edge for a system of two identical bosons or two fermions with opposite spin components.The resulting phase diagram in the interaction-energy-disorder space possesses a remarkably rich and counterintuitive structure, with multiple metallic and insulating phases.We show that this phenomenon originates from the molecular or scatteringlike nature of the pair states available at given energy E and disorder strength W .The disorder-averaged density of states of the effective model for the pair is also investigated.Finally, we discuss the implications of our results for ongoing research on many-body localization.
We analyze the disorder-driven localization of the two-dimensional Bose-Hubbard model by evaluating the full low-energy quasiparticle spectrum via a recently developed fluctuation operator expansion method.For any strength of the local interaction we find a mobility edge that displays an approximately exponential decay with increasing disorder strength.We determine the finite-size scaling collapse and exponents at this critical line finding that the localization of excitations is characterized by weak multifractality and a thermal-like critical gap ratio.A direct comparison to a recent experiment yields an excellent match of the predicted finite-size transition point and scaling of single particle correlations.
It has recently been established that a short-range interaction can strongly delocalize a pair of particles moving in a disordered potential. We investigate whether an analogous effect exists also for pairs of quasiparticles in the Anderson insulator by employing an approximate numerical evaluation of the two-particle Green function of the many-body system. At the Fermi energy, the quasiparticle pair is localized on the scale of the single-particle localization length. The delocalization effect is recovered when the excitation energy of the pair is comparable to the bandwidth.