We consider two strongly correlated two-component quantum systems, consisting of quantum mobile particles and classical immobile particles. The both systems are described by Falicov-Kimball-like Hamiltonians on a square lattice, extended by direct short-range interactions between the immobile particles. In the first system the mobile particles are spinless fermions while in the second one they are hardcore bosons. We construct rigorously ground-state phase diagrams of the both systems in the strong-coupling regime and at half-filling. Two main conclusions are drawn. Firstly, short-range interactions in quantum gases are sufficient for the appearance of charge stripe-ordered phases. By varying the intensity of a direct nearest-neighbor interaction between the immobile particles, the both systems can be driven from a phase-separated state (the segregated phase) to a crystalline state (the chessboard phase) and these transitions occur necessarily via charge-stripe phases: via a diagonal striped phase in the case of fermions and via vertical (horizontal) striped phases in the case of hardcore bosons. Secondly, the phase diagrams of the two systems (mobile fermions or mobile hardcore bosons) are definitely different. However, if the strongest effective interaction in the fermionic case gets frustrated gently, then the phase diagram becomes similar to that of the bosonic case.
We present exact results for the ground-state and thermodynamic properties of the spin-1/2 XX chain with three-site interactions in a random (Lorentzian) transverse field. We discuss the influence of randomness on the quantum critical behavior known to be present in the nonrandom model. We find that at zero temperature the characteristic features of the quantum phase transition, such as kinks in the magnetization versus field curve, are smeared out by randomness. However, at low but finite temperatures signatures of the quantum critical behavior are preserved if the randomness is not too large. Even the quantum critical region may be slightly enlarged for very weak randomness. In addition to the exact results for Lorentzian randomness we present a more general discussion of an arbitrarily random transverse magnetic field based on the inspection of the moments of the density of states.PACS numbers: 75.10.Jm Keywords: quantum phase transitions, random quantum spin chains, multi-site interactions, Green functions, density of states I. INTRODUCTORY REMARKSIn recent years the theory of quantum phase transitions has been in the focus of very active research. 1-3The quantum phase transitions take place at zero temperature by changing a control parameter and emerge as a result of competing different ground-state phases. Importantly, quantum phase transitions can influence the behavior of systems over a wide range of the phase diagram at nonzero (sometimes quite large) temperatures. Exactly solvable quantum models exhibiting a quantum phase transition are notoriously rare. A well-known example of a solvable model is the spin-1/2 Ising chain in a transverse field, where a zero-temperature transition from the ordered quantum Ising phase (small transverse fields) to the disordered quantum paramagnetic phase (large transverse fields) takes place. This model is often used for illustration of basic concepts in the quantum phase transition theory.2,4-8 In general, spin-1/2 XY chains 9 provide an excellent ground for various statistical mechanics studies since in many cases the calculations can be performed without any approximation. Moreover, there are some real-life compounds which can be viewed as realizations of one-dimensional spin-1/2 XY models. 10-13Quite recently, two other classes of solvable models have been found, namely a two-dimensional Kitaev model 14 and a spin-1/2 XY chain with multi-site interactions 15-17 (see also Ref. 18). The model belonging to the latter class is of interest in this paper. This model has an essentially richer ground-state phase diagram as the standard one-dimensional spin-1/2 XY model. In particular, it may exhibit several gapless spinliquid phases and quantum phase transitions between them. 16,17On the other hand, quantum models with random Hamiltonian parameters present another class of models for which an exact solution cannot be found easily. A solvable model with diagonal Lorentzian disorder was introduced by Lloyd.19 Later on Lloyd's idea was used to study random spin-1/2 XX chains.20...
Recently, we demonstrated rigorously the stability of charge-stripe phases in quantumparticle systems that are described by extended Falicov-Kimball Hamiltonians, with the quantum hopping particles being either spinless fermions or hardcore bosons. In this paper, by means of the same methods, we show that any anisotropy of nearestneighbor hopping eliminates the π/2-rotation degeneracy of the so called dimeric and axial-stripe phases and orients them in the direction of a weaker hopping. Moreover, due to the same anisotropy the obtained phase diagrams of fermions show a tendency to become similar to those of hardcore bosons.
We study a system composed of fermions (electrons), hopping on a square lattice, and of immobile particles (ions), that is described by the spinless Falicov-Kimball Hamiltonian augmented by a next-nearest-neighbor attractive interaction between the ions (a nearest-neighbor repulsive interaction between the ions can be included and does not alter the results). A part of the grand-canonical phase diagram of this system is constructed rigorously, when the coupling between the electrons and ions is much stronger than the hopping intensity of electrons. The obtained diagram implies that, at least for a few rational densities of particles, by increasing the hopping intensity the system can be driven from a state of phase separation to a state with a long-range order. This kind of transitions occurs also, when the hopping fermions are replaced by hopping hard-core bosons.
We consider a classical lattice gas that consists of more than one "species" of particles (like a spin-3 2 Ising model or the atomic limit of the extended Hubbard model), whose ground-state phase diagram is macroscopically degenerate. This gas is coupled component-wise and in the Falicov-Kimball-like manner to a multicomponent free-fermion gas. We show rigorously that a component-wise coupling of the classical subsystem to the quantum one orders the classical subsystem so that the macroscopic degeneracy is removed.
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