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Register a new userOne-dimensional repulsive Hubbard model with mass imbalance: orders and filling-anomaly
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We investigate the phase diagram of the one-dimensional repulsive Hubbard model with mass imbalance. Using DMRG, we show that this model has a triplet paired phase (dubbed $pi SG$) at generic fillings, consistent with previous theoretical analysis. We study the topological aspect of $pi SG$ phase, determining long-range string orders and the filling anomaly which refers to the relation among single particle gap, inversion symmetry and filling imbalance for open chains. We also find, using DMRG, that at $1/3$ filling, commensurate effects lead to two additional phases: a crystal phase and a trion phase; we construct a description of these phases using Tomonaga-Luttinger liquid theory.
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We propose a new combined approach of the exact diagonalization, the renormalization group and the Bethe ansatz for precise estimates of the charge gap $Delta$ in the one-dimensional extended Hubbard model with the onsite and the nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $Delta$ including the prefactor without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $Delta$ is exponentially small, beyond usual renormalization group methods and/or finite size scaling approaches. The detailed results of $Delta$ down to of order of $10^{-10}$ near the MIT are shown as contour lines on the $U$-$V$ plane.
We calculate the charge and spin Drude weight of the one-dimensional extended Hubbard model with on-site repulsion $U$ and nearest-neighbor repulsion $V$ at quarter filling using the density-matrix renormalization group method combined with a variational principle. Our numerical results for the Hubbard model (V=0) agree with exact results obtained from the Bethe ansatz solution. We obtain the contour map for both Drude weights in the $UV$-parameter space for repulsive interactions. We find that the charge Drude weight is discontinuous across the Kosterlitz-Thouless transition between the Luttinger liquid and the charge-density-wave insulator, while the spin Drude weight varies smoothly and remains finite in both phases. Our results can be generally understood using bosonization and renormalization group results. The finite-size scaling of the charge Drude weight is well fitted by a polynomial function of the inverse system size in the metallic region. In the insulating region we find an exponential decay of the finite-size corrections with the system size and a universal relation between the charge gap $Delta_c$ and the correlation length $xi$ which controls this exponential decay.
We investigate the effect of mass imbalance in binary Fermi mixtures loaded in optical lattices. Using dynamical mean-field theory, we study the transition from a fluid to a Mott insulator driven by the repulsive interactions. For almost every value of the parameters we find that the light species with smaller bare mass is more affected by correlations than the heavy one, so that their effective masses become closer than their bare masses before a Mott transition occurs. The strength of the critical repulsion decreases monotonically as the mass imbalance grows so that the minimum is realized when one of the species is localized. The evolution of the spectral functions testifies that a continuous loss of coherence and a destruction of the Fermi liquid occur as the imbalance grows. The two species display distinct properties and experimentally-observable deviations from the behavior of a balanced Fermi mixture.
The repulsive Fermi Hubbard model on the square lattice has a rich phase diagram near half-filling (corresponding to the particle density per lattice site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at $0.6 < n lesssim 0.8$, it is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions $U lesssim 4t$ in terms of the hopping $t$), and the region $1-n ll 1$ is most likely subject to phase separation. Much of this physics is preempted at finite temperatures and to an extent driven by strong magnetic fluctuations, their quantitative characteristics and how they change with the doping level being much less understood. Experiments on ultra-cold atoms have recently gained access to this interesting fluctuation regime, which is now under extensive investigation. In this work we employ a self-consistent skeleton diagrammatic approach to quantify the characteristic temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a large correlation length and identify their nature. Our results suggest that the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental access to this regime---are observed at $U/t approx 4-6$.
We investigate the $T=0$ phase diagram of a variant of the one-dimensional extended Hubbard model where particles interact via a finite-range soft-shoulder potential. Using Density Matrix Renormalization Group (DMRG) simulations, we evidence the appearance of Cluster Luttinger Liquid (CLL) phases, similarly to what first predicted in a hard-core bosonic chain [M. Mattioli, M. Dalmonte, W. Lechner, and G. Pupillo, Phys. Rev. Lett. 111, 165302]. As the interaction strength parameters change, we find different types of clusters, that encode the order of the ground state in a semi-classical approximation and give rise to different types of CLLs. Interestingly, we find that the conventional Tomonaga Luttinger Liquid (TLL) is separated by a critical line with a central charge $c=5/2$, along which the two (spin and charge) bosonic degrees of freedom (corresponding to $c=1$ each) combine in a supersymmetric way with an emergent fermionic excitation ($c=1/2$). We also demonstrate that there are no significant spin correlations.
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