We propose two new methods to calculate exactly the spectrum of two spin-1 2 charge carriers moving in a ferromagnetic background, at zero temperature. We find that if the spins are located on a different sublattice than that on which the fermions move, magnon-mediated effective interactions are very strong and can bind the fermions into low-energy bipolarons with triplet character. This never happens in models where spins and charge carriers share the same lattice, whether they are in the same band or in different bands. This proves that effective one-lattice models do not describe correctly the low-energy part of the two-carrier spectrum of a two-sublattice model, even though they may describe the low-energy single-carrier spectrum appropriately. Such a composite object may describe well the lowenergy quasiparticle, although this is still debated [3]. Less clear is whether a model based on such states that mix together charge and spin degrees of freedom, can properly describe quasiparticle interactions, especially those mediated through spin fluctuations. Most oxides have at least one phase with long-range magnetic order, and magnon exchange is believed by some to be a key component determining their properties, eg. as the main "glue" for pairing in cuprates, which likely controls the value of T c [4].Here we show that effective one-lattice models severely underestimate the magnon-mediated attraction between carriers, compared to their two-sublattice "parent" model. The magnetic background is chosen as ferromagnetic (FM). This is much simpler than an antiferromagnetic (AFM) background, but it allows for exact solutions. Thus, any qualitative differences are inherent to the models themselves. Moreover, our conclusions are relevant to the modeling of carriers in AFM backgrounds, and raise serious questions about the ability of ZRS-like constructs to describe correctly low-energy twocarrier states.Our models are sketched in Fig. 1. For simplicity, we address the one-dimensional (1D) case; generalizations are straightforward. Model I is the "parent", twosublattice, two-band model. Model II is a two-band, single lattice effective model. Model III is an even simpler one-band effective model.In models I and II, one band hosts the spin S degrees of freedom, described by:This favours a FM ground-state |F M = | + S, . . . , +S for the undoped system. Spin-1 2 doping charge carriers occupy states in another band. In model I, this is located on a different sublattice, for example like in a CuO chain with spins on Cu and holes on O sites. In model II, they are on the same lattice. In both cases carriers are described by a Hubbard model: Interactions between charges and spins are described by the simplest exchange model. In model I, a carrier interacts with its two neighbour spins:II III FIG. 1. Models I and II have two bands: one occupied by spins (arrows), and one (empty circles) hosting carriers introduced by doping (filled circles, with arrow showing the spin).In the "parent" model I, these are on different sublattices....

There is major interest, in condensed matter physics, in understanding the role of topology: remarkable progress has been made in classifying topological properties of non-interacting electrons, and on understanding the interplay between topology and electron–electron interactions. We extend such studies to interactions with the lattice, and predict non-trivial topological effects in infinitely long-lived polaron bands. Specifically, for a two-dimensional many-band model with realistic electron–phonon coupling, we verify that sharp level crossings are possible for polaron eigenstates, and prove that they are responsible for a novel type of sharp transition in the ground state of the polaron that can occur at a fixed momentum. Furthermore, they result in the appearance of Dirac cones stabilized by electron–phonon coupling. Thus, electron–phonon coupling opens an avenue to create and control Dirac and Weyl semimetals.

We present exact diagonalization and momentum average approximation (MA) results for the single polaron properties of a one-dimensional two-band model with phonon-modulated hopping. At strong electron-phonon coupling, we find a novel type of sharp transition, where the polaron ground state momentum jumps discontinuously from $k=\pi$ to $k=0$. The nature and origin of this transition is investigated and compared to that of the Su-Schrieffer-Heeger (SSH) model, where a sharp but smooth transition was previously reported. We argue that such discontinuous transitions are a consequence of the multi-band nature of the model, and are unlikely to be observed in one-band models. We also show that MA describes qualitatively and even quantitatively accurately this polaron and its transition. Given its computationally efficient generalization to higher dimensions, MA thus promises to allow for accurate studies of electron-phonon coupling in multi-band models in higher dimensions

In two recent papers, we have shown how one-particle and few-particle lattice Green functions can be calculated efficiently for models with only nearestneighbor hopping, using continued fractions. Here, we show that a similar type of solution is possible for models with longer (but finite) range hopping.

We present numerically exact results for the spectral function of a single charge carrier that is injected into an Ising chain at finite temperature T . Both ferromagnetic and antiferromagnetic coupling between the Ising spins are considered. The interaction between the carrier and the Ising spins is assumed to be on-site and of Ising type, as well. We find that the carrier's spectral function exhibits a distinctive fine structure of resonances that are due to the temporary entrapping of the carrier inside small magnetic domains. The connection to models of disordered binary alloys where similar effects can occur is explained. We use these results to construct an accurate (quasi)analytic approximation for low and medium-T spectral functions.