Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model.

Accurate simulations of the two-dimensional (2D) Hubbard model constitute one of the most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for the calculations of the 2D Hubbard model at finite temperature. An optimal evolution of the density operator is achieved in tanTRG with a mild O(D^{3}) complexity, where the bond dimension D controls the accuracy. With the tanTRG approach we boost the low-temperature calculations of large-scale 2D Hubbard systems on up to a width-8 cylinder and 10×10 square lattice. For the half-filled Hubbard model, the obtained results are in excellent agreement with those of determinant quantum Monte Carlo (DQMC). Moreover, tanTRG can be used to explore the low-temperature, finite-doping regime inaccessible for DQMC. The calculated charge compressibility and Matsubara Green's function are found to reflect the strange metal and pseudogap behaviors, respectively. The superconductive pairing susceptibility is computed down to a low temperature of approximately 1/24 of the hopping energy, where we find d-wave pairing responses are most significant near the optimal doping. Equipped with the tangent-space technique, tanTRG constitutes a well-controlled, highly efficient and accurate tensor network method for strongly correlated 2D lattice models at finite temperature.

Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas.

We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wave functions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a nonmonotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.

Reaching the Continuum Limit in Finite-Temperature Ab Initio Field-Theory Computations in Many-Fermion Systems.

Finite-temperature grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and the lattice gauge theory. However, these calculations have computational costs scaling as N_{s}^{3} with the size of the lattice or basis set, N_{s}. We report a new approach based on systematically controllable low-rank factorization that reduces the scaling of such computations to N_{s}N_{e}^{2}, where N_{e} is the average number of fermions in the system. In any realistic calculations aiming to describe the continuum limit, N_{s}/N_{e} is large and needs to be extrapolated effectively to infinity for convergence. The method thus fundamentally changes the prospect for finite-temperature many-body computations in correlated fermion systems. Its application, in combination with frameworks to control the sign or phase problem as needed, will provide a powerful tool in ab initio quantum chemistry and correlated electron materials. We demonstrate the method by computing exact properties of the two-dimensional Fermi gas with zero-range attractive interaction as a function of temperature in both the normal and superfluid states.

Quantum effect enhanced magnetism of C-doped phosphorene nanoribbons: first-principles calculations.

Manipulating magnetism of low-dimensional materials is of great importance for their practical applications. Here, using first-principles calculations, we report a systematic investigation of the magnetic properties of C-doped H saturated zigzag phosphorene nanoribbons (H-ZPNRs), which are rather different from those of 2D periodic systems due to the quantum size effect. First of all, we observed a greatly enhanced magnetic moment locating mainly on the C atom and also slightly on its surrounding P atoms. Our results also indicated a strong dependence of the magnetic moment of the C atom on its location, which decays from the edge to the center site of the nanoribbons with an odd-even oscillating behavior originating from Friedel oscillation in low-dimensional materials. As for the C atom on a specific location, its magnetic moment decreases gradually with increasing width of H-ZPNRs, degenerating to the 2D case. What is more, we found that both the magnitude and the oscillating behavior of the magnetic moment on the C atom can be tuned by the edge saturation atoms. In addition, the case of two C atoms co-doping H-ZPNRs was also studied, showing non-magnetic (NM), ferromagnetic (FM) and antiferromagnetic (AFM) states depending on the locations of the two C atoms. Our findings suggest a plausible route for manipulating magnetism of the sp element doped H-ZPNRs, which are expected to have potential applications in spintronics.

Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization.

We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.