Abstract The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, the interaction U and the temperature T. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB‐CDW), the AB phase separation region (PS‐AB/HOM; coexistence of AB‐CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS‐AB/IP; coexistence of AB‐CDW and IP). We identify three important values of the interaction UIPL = 0.572 < UIPH = 1.914 < UIP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below UIP/PS the IP appears. We propose a new general ansatz for the order parameter of this phase. A competition between the IP, the PS‐AB/IP and the PS‐AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.
The phase diagram for the spinless Falicov-Kimball model on a hypercubic lattice is reexamined in the limits of large and small dimensions (for the half-filled ion case). This model is identical to the thermodynamical problem of an annealed binary alloy with diagonal disorder. The phase diagram for the infinite-dimensional case is remarkably similar to the conjectured phase diagram for the one-dimensional case. The system orders in short-period phases, orders in long-period (possibly incommensurate) phases, or segregates, depending on the interaction strength and the electron concentration. The analysis for this simple model provides hope that recently proposed solutions for other interacting fermion models in infinite dimensions will accurately represent the solutions in two and three dimensions.
The Hubbard and spinless fermion chains are paradigms of strongly correlated systems, very well understood using the Bethe ansatz, density matrix renormalization group (DMRG), and field theory/renormalization group (RG) methods. They have been applied to one-dimensional materials and have provided important insights for understanding higher-dimensional cases. Recently, an interacting fermion model has been introduced, with possible applications to topological materials. It has a single Majorana fermion operator on each lattice site and interactions with the shortest possible range that involve four sites. We present a thorough analysis of the phase diagram of this model in one dimension using field-theory/RG and DMRG methods. It includes a gapped supersymmetric region and a gapless phase with coexisting Luttinger liquid and Ising degrees of freedom. In addition to a first-order transition, three critical points occur: tricritical Ising, Lifshitz, and a generalization of the commensurate-incommensurate transition. We also survey various gapped phases of the system that arise when the translation symmetry is broken by dimerization and find both trivial and topological phases with 0, 1, and 2 Majorana zero modes bound to the edges of the chain with open boundary conditions.
Spinless fermions with repulsion are treated non-perturbatively by classifying the diagrams of the generating functional Φ in powers of the inverse lattice dimension 1/d. The equations derived from the first two orders are evaluated on the one- and on the two-particle level. The order parameter of the AB-charge density wave (AB-CDW) occurring at larger interaction is calculated in d = 3. The Bethe-Salpeter equation is evaluated for the conductivity σ(ω) which is found to have two peaks within the energy gap 2∆ in the AB-CDW: a remnant of the Drude peak and an excitonic resonance. Unexpectedly, σ DC does not vanish for T → 0 1 The limit of infinite dimensions d → ∞ for itinerant fermion systems [1, 2] has proven very useful for the understanding of strongly interacting electron systems [3]. The research focusses on one-particle properties in the strict limit d = ∞. There exist also some results on transport properties [4, 5]. The present contribution extends the knowledge on the AC- and DC-conductivity including 1/d-corrections in the model of spinless fermions with repulsive interaction. The results cover and the non-symmetry broken (homogeneous) phase and the AB-CDW occurring on bipartite lattices. The techniques used in the description of the latter are certainly transferable to other symmetry broken phases in related models. The Hamiltonian of the spinless fermion model at half-filling (n = 0.5) is given in second quantisation
We show that the Gutzwiller variational wave function is very accurate for the computation of magnetic phase boundaries in the infinite-dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both the half-hypercubic and the hypercubic lattice, a large part of the phase diagram is occupied by an incommensurate phase, intermediate between the ferromagnetic and the paramagnetic phase. In case of the hypercubic lattice, the three phases join at a new quantum Lifshitz point at which the order parameter is critical and the stiffness vanishes.
We investigate the phase diagram of spinless fermions on a square lattice with nearest-neighbor interaction, using the recently developed projective truncation approximation in Green's function equation of motion. For attractive interaction, the ground state is in a homogeneous
p+ip superconducting (SC) phase at high or low fermion densities. Near half filling is a phase separation (PS) between the SC phases. Allowing inhomogeneous solution, we obtain
p-wave SC domains with positive interface energy. As temperature increases, the SC phases transit into normal phases above
Tsc, generating a homogeneous normal phase (far away from
n=1/2), or a PS between normal phases with different densities (close to
n=1/2). Further increasing temperature to
Tps, the PS disappears and the particle-hole symmetry of the Hamiltonian is recovered. For repulsive interaction, depending on the filling, the ground state is in charge-ordered phase (half filling), charge-disordered phase (large hole/particle doping), or PS between them (weak doping). At finite temperature, the regime of charge order phase moves to finite
V and extends to finite doping regime.