No Arabic abstract
In recent experiments with ultracold atoms, both two-dimensional (2d) Chern insulators and one-dimensional (1d) topological charge pumps have been realized. Without interactions, both systems can be described by the same Hamiltonian, when some variables are being reinterpreted. In this paper, we study the relation of both models when Hubbard interactions are added, using the density-matrix renormalization-group algorithm. To this end, we express the fermionic Hofstadter model in a hybrid-space representation, and define a family of interactions, which connects 1d Hubbard charge pumps to 2d Hubbard Chern insulators. We study a three-band model at particle density $rho=2/3$, where the topological quantization of the 1d charge pump changes from Chern number $C=2$ to $C=-1$ as the interaction strength increases. We find that the $C=-1$ phase is robust when varying the interaction terms on narrow-width cylinders. However, this phase does not extend to the limit of the 2d Hofstadter-Hubbard model, which remains in the $C=2$ phase. We discuss the existence of both topological phases for the largest cylinder circumferences that we can access numerically. We note the appearance of a ferromagnetic ground state between the strongly interacting 1d and 2d models. For this ferromagnetic state, one can understand the $C=-1$ phase from a bandstructure argument. Our method for measuring the Hall conductivity could similarly be realized in experiments: We compute the current response to a weak, linear potential, which is applied adiabatically. The Hall conductivity converges to integer-quantized values for large system sizes, corresponding to the systems Chern number.
e provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t, t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux $phi$. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^{phi}$, a quantum phase transition in the 2D-topological insulator state is realized at $t_c$. The phase state is characterized by zero energy Majorana states localized at the boundaries. Taking into account the on-site Coulomb repulsion $U$ (where $U<<1$), the criterion for the stability of a topological insulator state is calculated at $t<<1$, $t sim U$. Thus, in the case of $ U > 4Delta $, the topological insulator state, which is determined by chiral gapless edge modes in the gap $Delta$, is destroyed.
We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^circ$ magnetic order, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a spinon Fermi surface or a fractionalized CI with nontrivial spinon topology, depending on the strength of Kitaev-like hopping. Our work highlights the rising field that interesting phases emerge from the interplay of band topology and Mott physics.
We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site ($U$) and next-nearest-neighbor ($V_2$) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-$V_2$ region by a CDW characterized by a 220200 (001122) charge configuration for smaller (larger) $U$, where 0, 1, and 2 denote essentially empty, singly occupied, and doubly occupied sites. Within the 001122-type CDW phase, we find a magnetic transition driven by an emergent coupled-dimer antiferromagnet on an effective square lattice of singly occupied sites. Possible realizations of the found states are discussed.
We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a non linear sigma model NL$sigma$M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity and string non-local order parameters, correlation functions between $x,y,z$ components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum and the entanglement entropy in order to characterize these two different phases. Finally, we identify one phase with a Mott insulator and the other one with a Haldane insulator.
One of the fundamental questions about the high temperature cuprate superconductors is the size of the Fermi surface (FS) underlying the superconducting state. By analyzing the single particle spectral function for the Fermi Hubbard model as a function of repulsion $U$ and chemical potential $mu$, we find that the Fermi surface in the normal state reconstructs from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the Luttinger Breaking (LB) phase, as the Mott insulator is approached. This transition into a non-Fermi liquid phase that violates the Luttinger count, is a continuous phase transition at a critical density in the absence of any other broken symmetry. We obtain the Fermi surface contour from the spectral weight $A_{vec{k}}(omega=0)$ and from an analysis of the poles and zeros of the retarded Greens function $G_{vec{k}}^{ret}(E=0)$, calculated using determinantal quantum Monte Carlo and analytic continuation methods.We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy and angle resolved photoemission spectroscopy.