Detecting phases in one-dimensional many-fermion systems with the functional renormalization group

Abstract

The functional renormalization group (FRG) has been used widely to investigate phase diagrams, in particular the one of the two-dimensional Hubbard model. So far, the study of one-dimensional models has not attracted as much attention. We use the FRG to investigate the phases of a onedimensional spinless tight-binding chain with nearest and next-nearest neighbor interactions at half filling. The phase diagram of this model has already been established with other methods, and phase transitions from a metallic phase to ordered phases take place at intermediate to strong interactions. The model is thus well suited to analyze the potential and the limitations of the FRG in this regime of interactions. We employ flow equations that are exact up to second order in the interaction, which implies that we take into account the frequency dependence of the two-particle vertex as well as the feedback of the dynamic self-energy. For intermediate nearest neighbor interactions, our scheme captures the phase transition from a metallic phase to a charge density wave with alternating occupation. The critical interaction, at which this transition occurs, is underestimated due to our approximations. Similarly, for intermediate next-nearest neighbor interactions, we observe a transition to a charge density wave with occupation pattern ..00110011... We show that taking into account a feedback of the two-particle vertex in the flow equation is essential for the detection of those phases. arXiv:1803.00272v2 [cond-mat.str-el]

Nonequilibrium Properties of Berezinskii-Kosterlitz-Thouless Phase Transitions

“…In contrast to both mean-field and perturbation theory, our RG approach yields a finite value of U crit in the limit Γ ¼ E ¼ 0 in accord with the analytic solution [36]. Moreover, we quantitatively reproduce an exact result for the phase boundary at Γ > 0 in the limit U → ∞.…”

“…Phase diagram.-To probe spontaneous symmetry breaking and the transition into a CDW phase, we add a small staggered on site potential s to the Hamiltonian [36] and compute the susceptibility…”

Second-order functional renormalization group approach to quantum wires out of equilibrium

“…In this work, we aim to account for all second-order terms. This has so far only been achieved in thermal equilibrium [21][22][23][24][25] as well as for the singleimpurity Anderson model out of equilibrium [26].…”

“…In contrast to previous approaches to this problem [17], we incorporate second-order contributions and can therefore describe inelastic processes and heating effects. Due to the significant numerical cost, second-order FRG schemes have so far only been implemented for electronic systems in thermal equilibrium [21][22][23][24][25] as well as for the single-impurity Anderson model out of equilibrium [26].…”

Efficient learning of a one-dimensional density functional theory

“…The particles are subject to a repulsive interaction on nearest-and nextnearest-neighbor sites, which we fix to U = 1 and U = 0.5 so as to model a lattice analog of the Coulomb interaction. This parameter choice places the system in a metallic, but strongly correlated phase in absence of a potential V i , even at half filling [39].…”