We investigate the two-dimensional Hubbard model on the triangular lattice with anisotropic hopping integrals at half filling. By means of a self-energy functional approach, we discuss how stable the non-magnetic state is against magnetically ordered states in the system. We present the zero-temperature phase diagram, where the normal metallic state competes with magnetically ordered states with $(π, π)$ and $(2π/3, 2π/3)$ structures. It is shown that a non-magnetic Mott insulating state is not realized as the ground state, in the present framework, but as a meta-stable state near the magnetically ordered phase with $(2π/3, 2π/3)$ structure.
单能带哈伯德模型的顺磁相的莫特-哈伯德金属-绝缘体转变长期以来一直被用来描述像V $_2$ O $_3$这样的真实材料中的类似特征。在这里，我们表明，这种转变是隐藏在一个相当强大的反铁磁绝缘体，即使在存在比较强的磁挫折。这一结果提出了一个问题的相关性的莫特-哈伯德金属-绝缘体转变的通用相图的单带哈伯德模型。
We demonstrate that supervised machine learning (ML) with entanglement spectrum can give useful information for constructing phase diagram in the half-filled one-dimensional extended Hubbard model. Combining ML with infinite-size density-matrix renormalization group, we confirm that bond-order-wave phase remains stable in the thermodynamic limit.
Models of interacting Majorana modes may be realized in vortex lattices in superconducting films in contact with topological insulators and may be tuned to the strong-interaction regime by adjusting the chemical potential. Extending the results on one- and two-dimensional Majorana-Hubbard models, here we determine the phase diagrams of two- and four-leg ladders using both field theory and the density-matrix renormalization group (DMRG) methods.
Efficient calculation of the antiferromagnetic phase diagram of the 3D Hubbard model
用Betts集团的动力学集团近似方法计算了三维哈伯德模型在半充满时的反铁磁相图。Betts团簇是一组周期性团簇，其最好地反映了晶格在热力学极限下的性质，并提供了作为团簇大小的函数的最佳有限尺寸标度。利用系统的有限尺寸标度作为团簇时空维数的函数，我们计算了反铁磁相图。我们的结果是定性一致的结果Staudt等人[Eur. B 17 411（2000）]，但是需要使用小得多的簇：48个簇与1000个簇相比。
受最近数值结果的启发，我们研究了Kane-Mele-Hubbard（KHM）模型的相图，特别是它的量子临界点的性质。Kane-Mele-哈伯德模型的相图可以通过打破我们以前工作的SO（4）对称性而理解为U（1）_spin x U（1）_charge x PH对称性。面内Neel相的涡旋携带电荷，带电磁涡旋的扩散驱动面内Neel相和QSH绝缘体相之间的转变，这种转变属于3dXY普适类。液相和面内Neel相之间的转变是各向异性的O（4）转变，由于量子涨落，该转变最终变为一级。根据1/N计算，预测液态-QSH相变为一级相变。
We show that the numerically exact bold-line diagrammatic theory for the $2d$ Hubbard model exhibits a non-Fermi-liquid (NFL) strange metal state, which is connected to the SYK NFL in the strong-interaction limit. The solution for the doped system features the expected phenomenology with the NFL near half-filling at strong couplings and in a wide temperature range enclosed by the atomic state at high temperatures and a Fermi liquid at low temperatures. We demonstrate, however, that this behavior in the weakly doped regime is due to the unphysical branch of the Luttinger-Ward functional. On the…
We present an algorithm to evaluate Matsubara sums for Feynman diagrams comprised of bare Green's functions with single-band dispersions with local U Hubbard interaction vertices. The algorithm provides an exact construction of the analytic result for the frequency integrals of a diagram that can then be evaluated for all parameters $U$, temperature $T$, chemical potential $μ$, external frequencies and internal/external momenta. This method allows for symbolic analytic continuation of results to the real frequency axis, avoiding any ill-posed numerical procedure. When combined with diagrammati…
Comment on ``Ground State Phase Diagram of a Half-Filled One-Dimensional Extended Hubbard Model''
In Phys. Rev. Lett. 89，236401（2002）中，Jeckelmann论证了最近发现的一维扩展哈伯德模型的键序波（BOW）相在（U，V）平面中不具有有限范围，而是仅存在于一阶SDW-CDW相边界的一段上。在这里，我们提出了更高的精度和更大的系统尺寸比以前的量子Monte Carlo结果，并再次确认，BOW相确实存在一个有限的距离，从相边界，因此是一个BOW-CDW过渡曲线。
The dynamical structure factor is an important observable of quantum magnets but due to numerical and theoretical limitations, it remains a challenge to make predictions for Hubbard-like models beyond one dimension. In this work, we study the magnetic excitations of the triangular lattice Hubbard model including next-nearest neighbor hopping. Starting from the 120$^{\circ}$ and stripe magnetic orders we compute the magnon spectra within a self-consistent random phase approximation. In the stripe phase, we generically find accidental zero modes related to a classical degeneracy known from the c…
Diagrammatic Monte Carlo -- the technique for numerically exact summation of all Feynman diagrams to high orders -- offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the non-analyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this techniqu…
We study the phase diagram of the interacting spin-$1/2$ Haldane model with chiral phase $ϕ= π/2$ at half-filling. Both on-site and long-range Coulomb repulsive interactions (Haldane-Hubbard-Coulomb model) are considered. The problem with on-site interaction $U$ alone was addressed in the past by a variety of approximate and finite size methods that produced results in disagreement with each other both quantitatively and qualitatively. Here we employ the Diagrammatic Monte Carlo technique to accurately locate phase transition points to the topologically nontrivial phases in the $(Δ, U)$-plane,…
