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Journal of Physics A Mathematical and Theoretical

Particle–hole asymmetry as a source of phase separation at the metal–insulator transition

Igor N. Karnaukhov, Ilya Eremin

Published Sep 6, 2011• 0 citations
Publisher

Abstract

We propose a strongly correlated (1+1)D electron model with particle–hole asymmetry which is exactly solvable by means of the nested Bethe ansatz. The particle–hole asymmetry in this many-body system causes a metal–insulator transition with a phase separation. Here, we give a detailed analysis of the zero-temperature phase diagram of the model and demonstrate how this unusual behavior of the metal–insulator transition with phase separation arises. In particular, we show that a homogeneous phase of itinerant electrons and a mixed phase of itinerant electrons and localized electron pairs (for which two different species reside in spatially separated regions) define the ground state of a fermion chain. We also find that the metal–insulator phase transition induces phase transition on the surface with simultaneous generation of the interphase boundary.

DOI
10.1088/1751-8113/44/39/395002

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We propose a strongly correlated (1+1)D electron model with particle–hole asymmetry which is exactly solvable by means of the nested Bethe ansatz. The particle–hole asymmetry in this many-body system causes a metal–insulator transition with a phase separation. Here, we give a detailed analysis of the zero-temperature phase diagram of the model and demonstrate how this unusual behavior of the metal–insulator transition with phase separation arises. In particular, we show that a homogeneous phase of itinerant electrons and a mixed phase of itinerant electrons and localized electron pairs (for which two different species reside in spatially separated regions) define the ground state of a fermion chain. We also find that the metal–insulator phase transition induces phase transition on the surface with simultaneous generation of the interphase boundary.
We determine the ground-state phase diagram of a Hubbard Hamiltonian with correlated hopping, which is asymmetric under particle–hole transform. By lowering the repulsive Coulomb interaction U at appropriate filling and interaction parameters, the ground state separates into hole and electron conducting phases: two different wavevectors characterize the system and charge–charge correlations become incommensurate. By further decreasing U another transition occurs at which the hole conducting region becomes insulating, and conventional phase separation takes place. Finally, for negative U the whole system eventually becomes a paired insulator. It is speculated that such behavior could be at the origin of the incommensurate superconducting phase recently discovered in the 1D Hirsch model. The exact phase boundaries are calculated in one dimension.
A two parametric family of the models of two coupled nondegenerate fermion chains is proposed and solved by the means of the Bethe ansatz. We give a detailed analysis of the exact zero-temperature phase diagram at half filling for different parameters of the interactions. It is shown that insulator and ``interchain ferromagnetic'' phase states are separated by ``intermediate metallic'' state, these phase states coexist in a tricritical point. The critical fluctuations are described by a conformal field theory with the central charge c=1c=1c=1. In the tricritical point the fermion state is described as a Luttinger liquid state with one gapless mode that is characterized by abnormal large density-density correlations and correlations of the momentum distribution function.
The Mott-Hubbard metal-insulator transition is one of the most important problems in correlated-electron systems. In the past decade, much progress has been made in examining a particle-hole symmetric form of the transition in the Hubbard model with dynamical mean field theory, where it was found that the electronic self-energy develops a pole at the transition. We examine the particle-hole asymmetric metal-insulator transition in the Falicov-Kimball model and find that a number of features change when the noninteracting density of states has a finite bandwidth.
Using the Fermi-liquid approach with vertex corrections, the effects of exchange and correlation are considered in a layered two-dimensional electron gas. It is shown that the interaction in the particle–hole channel can induce the metal–insulator phase transition when the Fermi momentum is comparable with the inverse interlayer spacing, pF ≈︂ /1c. The possibility of superconductivity in the region between the insulator and normal metal phases, taking into account the particle–hole excitations, is discussed. A smooth crossover from weak to strong coupling superconductivity with the decrease of the 2D carrier density is obtained. The results suggest a new way in the explanation of the phase diagram of layered high-Tc superconductors.
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.
The effects of mass imbalance in a three-component Hubbard model are studied by the dynamical mean-field theory combined with exact diagonalization. The model describes a fermion-fermion mixture of two different particle species with a mass imbalance. One species is two-component fermion particles, and the other is single-component ones. The local interaction between particle species is considered isotropically. It is found that the mass imbalance can drive the mixture from insulator to metal. The insulator-metal transition is a species-selective-like transition of lighter mass particles and occurs only at commensurate particle densities and moderate local interactions. For weak and strong local interactions the mass imbalance does not change the ground state of the mixture.