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The study of phase transitions in strongly correlated systems remains a central problem of modern condensed matter physics. Of particular interest is the metal-insulator transition in strongly correlated fermion systems whereas the physical behavior of many body systems drastically different from that of free fermions. In this sense the exact solvable (1+1)D lattice models, such as the Hubbard and extended Hubbard models, are perspective ones for understanding of correlation effects at the phase transitions in quantum low dimensional systems. In practice, the usual Hamiltonians of the considered (1+1)D models are invariant under the particle-hole symmetry operation and the scenario of the metal-insulator phase transition in this case is well known in the literature [1]. Namely, there is one point at the phase diagram (at half-filling), where a dielectric phase exists and the corresponding charge excitations are gapped. Similar picture of the metal-insulator phase transition is realized in the XXZ spin-1/2 Heisenberg model or the model of spinless fermions with the density-density interaction between fermions on the nearest-neighbor lattice sites [2]. Any other scenario of the phase transition does not realize in exact solvable (1+1)D quantum models of strongly correlated fermions as soon as the particle-hole symmetry of the model Hamiltonian is conserved. At the same time, phase transitions with different ground states can be realized in (2+1)D model of strongly correlated fermions, where the ground state for itinerant electrons can be frustrated also. 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 model Hamiltonian includes one-particle hopping of an electron on the empty and the occupied lattice sites, and the latter process creates an electron pair. The annihilation of the electron pairs arises due to two-particle correlated hopping of electrons on the nearest-neighbor lattice sites. The particle-hole asymmetry in this many-body system causes a metal-insulator transition with a phase separation. The exact solution of the (1+1)D model obtained here, indicate that there is a novel kind of a metal-insulator phase transition in a quantum model of strongly correlated electrons. On the one hand we obtain a metal-insulator phase transition at half-filling, on other hand the point of the phase transition indicates the phase transition into a mixed phases state. This mixed phases state consists of the Luttinger liquid state of itinerant electrons or frozen spinless fermions and localized electron pairs and their ratio is determined by the coupling constants. Thus, the point of the metal-insulator transition is the point of the phase transition in the separated phases state. The new interface boundary between phases is formed by pairs localized at high density v. Due to separation of itinerant electrons phases onto two phase states (itinerant electrons and localized electron pairs), the itinerant electrons do not interact with the boundary which yields the phase transition on the surface of the system in the point of phase transition. 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] defines the ground state of a fermion chain. 1. LIEB H.E. and WU F.Y., Phys.Rev.Lett., 20 (1968) 1445. 2.TAHAKASHI M., Thermodynamics of One-dimensional Solvable Problems (Cambridge: Cambridge University Press, 1999). |
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