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arXiv:1112.3847 · Europhysics Letters (EPL)

Correlated metallic two-particle bound states in quasiperiodic chains

Sergej Flach A, Mikhail Ivanchenko, Рамаз Хомерики

Published Jun 1, 2012• 31 citations
arXivHTMLPDF

Abstract

Single-particle states in a chain with quasiperiodic potential show a metal-insulator transition upon the change of the potential strength. We consider two particles with local interaction in the single-particle insulating regime. The two-particle states change from being localized to delocalized upon an increase of the interaction strength to a nonperturbative finite value. At even larger interaction strength the states become localized again. This transition of two-particle bound states into correlated metallic ones is due to a resonant mixing of the noninteracting two-particle eigenstates. In the discovered correlated metal states two particles move coherently together through the whole chain.

DOI
10.1209/0295-5075/98/66002

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Single-particle states in a chain with quasiperiodic potential show a metal-insulator transition upon the change of the potential strength. We consider two particles with local interaction in the single-particle insulating regime. The two-particle states change from being localized to delocalized upon an increase of the interaction strength to a nonperturbative finite value. At even larger interaction strength the states become localized again. This transition of two-particle bound states into correlated metallic ones is due to a resonant mixing of the noninteracting two-particle eigenstates. In the discovered correlated metal states two particles move coherently together through the whole chain.
We investigate the zero-temperature metal-insulator transition in a one-dimensional two-component Fermi gas in the presence of a quasiperiodic potential resulting from the superposition of two optical lattices of equal intensity but incommensurate periods. A mobility edge separating (low-energy) Anderson localized and (high-energy) extended single-particle states appears in this continuous-space model beyond a critical intensity of the quasiperiodic potential. To discern the metallic phase from the insulating phase in the interacting many-fermion system, we employ unbiased quantum Monte Carlo (QMC) simulations combined with the many-particle localization length familiar from the modern theory of the insulating state. In the noninteracting limit, the critical optical-lattice intensity for the metal-insulator transition predicted by the QMC simulations coincides with the Anderson localization transition of the single-particle eigenstates. We show that weak repulsive interactions induce a shift of this critical point towards larger intensities, meaning that repulsion favors metallic behavior. This shift appears to be linear in the interaction parameter, suggesting that even infinitesimal interactions can affect the position of the critical point.
We consider the quasiperiodic Aubry-Andr\'e chain in the insulating regime with localized single-particle states. Adding local interaction leads to the emergence of extended correlated two-particle bound states. We analyze the nature of these states, including their multifractality properties. We use a projected Green function method to compute numerically participation numbers of eigenstates and analyze their dependence on the energy and the system size. We then perform a scaling analysis. We observe multifractality of correlated extended two-particle bound states, which we confirm independently through exact diagonalization.
Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.
We apply the coherent potential approximation to study the three-component Falicov - Kimball model, in which single-component and two-component fermionic particles are mixed in an optical lattice. In the model, the heavy single-component fermionic particles are localized while the light two-component fermionic particles can hop in the lattice. At half-filling, two transitions from an insulator via a metallic state to a Mott insulator are found with increasing the particle correlations. By contrast, at third-filling, only one transition from the metallic state to the Mott insulating phase is observed for strong repulsive interactions. Our results are consistent with those obtained by the dynamical mean field theory as well as by the slave boson mean field approach.
We study the influence of many-particle interaction in a system which, in the single particle case, exhibits a metal-insulator transition induced by a finite amount of onsite pontential fluctuations. Thereby, we consider the problem of interacting particles in the one-dimensional quasiperiodic Aubry-Andr\'e chain. We employ the density-matrix renormalization scheme to investigate the finite particle density situation. In the case of incommensurate densities, the expected transition from the single-particle analysis is reproduced. Generally speaking, interaction does not alter the incommensurate transition. For commensurate densities, we map out the entire phase diagram and find that the transition into a metallic state occurs for attractive interactions and infinite small fluctuations --- in contrast to the case of incommensurate densities. Our results for commensurate densities also show agreement with a recent analytic renormalization group approach.
Identifying the fingerprints of the Mott-Hubbard metal-insulator transition may be quite elusive in correlated metallic systems if the analysis is limited to the single particle level. However, our dynamical mean-field calculations demonstrate that the situation changes completely if the frequency dependence of the two-particle vertex functions is considered: The first nonperturbative precursors of the Mott physics are unambiguously identified well inside the metallic regime by the divergence of the local Bethe-Salpeter equation in the charge channel. In the low-temperature limit this occurs for interaction values where incoherent high-energy features emerge in the spectral function, while at high temperatures it is traceable up to the atomic limit.