The variational cluster approach (VCA) is applied to study spontaneous ferromagnetism in the Hubbard model at zero temperature. We discuss several technical improvements of the numerical implementation of the VCA which become necessary for studies of a ferromagnetically ordered phase, e.g. more accurate techniques to evaluate the variational ground-state energy, improved local as well as global algorithms to find stationary points, and different methods to locate the magnetic phase transition. Using the single-site VCA, i.e. the dynamical impurity approximation (DIA), the ferromagnetic phase diagram of the model in infinite dimensions is worked out. The results are compared with previous dynamical mean-field studies for benchmarking purposes. The DIA results provide a unified picture of ferromagnetism in the infinite-dimensional model by interlinking different parameter regimes that are governed by different mechanisms for ferromagnetic order. Using the DIA and the VCA, we then study ferromagnetism in one-dimensional Hubbard chains with nearest and next-nearest-neighbor hopping t2. In comparison with previous results from the density-matrix renormalization group, the phase diagram is mapped out as a function of the Hubbard-U, the electron filling and t2. The stability of the ferromagnetic ground state against local and short-range non-local quantum fluctuations is discussed.
The two-orbital Hubbard model on a square lattice at quarter filling (electron number per site $n=1$) is investigated by the variational Monte Carlo method. For the variational wave function, we include short-range doublon-holon binding factors. We find that the energy of this wave function is lower than that of the density-density Jastrow wave function partially including long-range correlations used in a previous study. We introduce frustration to the model by the next-nearest-neighbor hopping $t'$ in addition to the nearest-neighbor hopping $t$. For $t'=0$, a ferromagnetic state with stagge…
We investigate the quantum phase diagram of t-J model on triangular lattice at 1/2 doping with various lattice sizes by using a combination of density matrix renormalization group (DMRG), variational Monte Carlo and quantum field theories. To sharply distinguish different phases, we calculated the symmetry quantum numbers of the ground state wave functions, and the results are further confirmed by studying correlation functions. Our results show there is a first order phase transition from ferromagnetism to d+id superconductivity, with the transition taking place at $J/t=0.4\pm0.2$.
We develop a diagrammatic method for the evaluation of general multi-band Gutzwiller wave functions in finite dimensions. Our approach provides a systematic improvement of the widely used Gutzwiller approximation. As a first application we investigate itinerant ferromagnetism and correlation-induced deformations of the Fermi surface for a two-band Hubbard model on a square lattice.
The first principles momentum dependent local ansatz wavefunction method (MLA) has been extended to the ferromagnetic state by introducing spin-dependent variational parameters. The theory is applied to the ferromagnetic Fe, Co, and Ni. It is shown that the MLA yields the magnetizations being comparable to the results obtained by the GGA (generalized gradient approximation) in the density functional theory. The projected momentum distribution functions as well as the mass enhancement factors are also calculated on the same footing, and are compared with those in the paramagnetic state. It is s…
We construct a multi-band Hubbard model on the lattice obtained by "decorating" a closely packed $d$-dimensional lattice $\mathcal{M}$ (such as the triangular lattice) where $d\ge2$. We take the limits in which the Coulomb interaction and the band gap become infinitely large. Then there remains only a single band with finite energy, on which electrons are supported. Let the electron number be $N_\mathrm{e}=|\mathcal{M}|-N_\mathrm{h}$, where $|\mathcal{M}|$ corresponds to the electron number which makes the lowest (finite energy) band half-filled, and $N_\mathrm{h}$ is the number of "holes". It…
Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density
用密度矩阵重整化群方法研究了双简并原子轨道的一维哈伯德模型的铁磁性，得到了基态相图。结果表明，当相互作用足够强时，铁磁性从低到高（0< n < 1.75）电子密度是稳定的。准长程序的三重态超导电性与铁磁有序共存的强Hund耦合区，其中轨道间相互作用U '-J是吸引的。在四分之一填充（n=1），绝缘铁磁态出现伴随着轨道准长程序。对于低密度（n<1），由于电子的虚跳跃引起的铁磁交换相互作用，铁磁性发生，与四分之一填充系统相同。这来自于强耦合极限中电荷和自旋-轨道自由度的分离。这种铁磁性对于能带结构的变化是脆弱的。对于高密度（n>1），铁磁相的相图类似于在无限维中获得的相图。在这种情况下，双交换机制是可操作的，以稳定的铁磁秩序和这种长程序是强大的对带色散的变化。在1.68<n<1.75的密度区出现部分极化态，在半填充区（n=2）的正下方出现相分离。
An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the doped Hubbard model in the strongly correlated regime ($U/t=8$, $n=0.875$) iPEPS yields lower variational energies than state-of-the-art variational methods in the large 2D limit, which demonstrates the competitiveness of the method. In order to obtain an accurate estimate of the energy in the exact infinite $D$ limit we introduce and test an extrapolation te…
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local Hamiltonian. The method is based on a systematic summation of Hamiltonian contributions using the corner transfer-matrix method. Benchmark results for challenging problems are presented, including the 2D Heisenberg model, the Shastry-Sutherland model, and the t-J model, which show that the variational scheme yields considerably more accurate resul…
We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with nearest (t) and next-nearest (t') neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of t' when we vary the electron density $(ρ)$ from half-filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin-polarized and paramagnetic states prevail. We find that the inclusion of a non-frustrating next nearest neighbor hopping stabilizes the fully spin-polarized phase up until |t'/…
We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform Matrix Product State algorithm (VUMPS) with infinite Density Matrix Renormalization Group (IDMRG) and with infinite Time Evolving Block Decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long range interactions…
Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of v…
