We study the ground state of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction $U$ ($V$) and nearest-neighbor hopping $t$. In order to obtain an accurate phase diagram, we consider various physical quantities such as the charge gap, spin gap, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter using the density-matrix renormalization group technique. We confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to do a cross-check to demonstrate the validity of our estimations. Thus, our results agree quantitatively with the renormalization group results in the weak-coupling regime ($U \lesssim 2t$), with the perturbation results in the strong-coupling regime ($U \gtrsim 6t$), and with the quantum Monte Carlo results in the intermediate-coupling regime. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point $(U_{\rm t}, V_{\rm t}) \approx (5.89t, 3.10t)$ and the BOW phase vanishes at the critical end point $(U_{\rm c}, V_{\rm c}) \approx (9.25t, 4.76t)$.
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.
We investigate the antiferromagnetically ordered state in the half-filled Hubbard model on the Socolar dodecagonal tiling. When the interaction is introduced, the staggered magnetizations suddenly appear, which results from the existence of the macroscopically degenerate states in the tightbinding model. The increase of the interaction strength monotonically increases the magnetizations although its magnitude depends on the local environments. Magnetization profile is discussed in the perpendicular space. The similarity and difference are also addressed in magnetic properties in the Hubbard mo…
We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra- and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic st…
We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin $S=1/2$ anisotropic $XXZ$ Heisenberg chain with alternating next-nearest-neighbor and three-spin couplings in the presence of a uniform and a staggered magnetic field.
In this paper we investigate effects of a lattice dimension on strongly correlated electronic systems at $T=0 K$. The model for numerical calculations is formalized in terms of the integral equations which were obtained previously for the half -- filled paramagnetic Hubbard model. The assumption that all relevant functions of the system have a magnitude dependence of momentus vectors makes ultimately possible treating a lattice dimension $D$ as an external parameter. We here submit for consideration the number of doubly occupied lattice sites, the electronic density of states, and the momentum…
利用自洽的Hartree-Fock近似研究了扩展的$t$ - $t'$哈伯德模型中各种条纹相的相对稳定性。人们发现，一个负的比例的次近邻跳跃$t'/t<0$驱逐反铁磁畴的空穴，并加强条纹秩序。因此，半填充的条纹不仅容纳空穴，而且重新分布空穴，从而获得动能，并且这些条纹在适合于YBa $_2$ Cu $_3$ O $_{6+δ}$的$t'/t\simeq -0.3$的区域中接管。
By the example of the Hubbard model we analytically and numerically examine the formating and coexisting of localized electron--electron pairs (doublons) and localized electron--hole pairs (Frenkel--type excitons) . Here we demonstrate that at a variation of the on-site Coulomb repulsion U there occurs a quantum transition from the doublon to the exciton regime that is conditioned by the low-energy effective hybridization of the valence and conductivity subbands. We calculate momentum distribution functions and electronic spectrum functions for different U, which reveal topologically nontrivia…
The electronic system of the 1D Hubbard model is not stable due to Peierls instability; the correlations are strong even for the weak Coulomb interaction. The resulting strongly correlated state without Landau quisi--particle excitations is known as the Luttinger liquid. Critical exponents of a power--law dependence of correlation functions at low energies differ substantially for the Luttinger and Fermi liquids. In this paper we evaluate two critical exponents that define non--trivial behavior of the density of electronic states at low frequences and the momentum distribution of the occupatio…
We study the time evolution of a half-filled Hubbard layer coupled to a magnon bath after a quench of the Hubbard interaction. Qualitatively different regimes, regarding the asymptotic long-time dynamics, are identified and characterized within the mean-field approximation. In the absence of the bath, the dynamics of the closed system is similar to that of a quenched BCS condensate. Though the presence of the bath introduces an additional relaxation mechanism, our numerical results and analytical arguments show that equilibration with the bath is not necessarily attained within the approximati…
Motivated by Mo$_3$S$_7$(dmit)$_3$, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second order perturbation theory, that in the molecular limit, the ground state and the low energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangul…
Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory
Half-filled Hubbard Model on a Bethe lattice with next-nearest neighbor hopping
研究了具有最近邻和次最近邻跃迁$t_1$和$t_2$的Bethe晶格上Néel反铁磁性与顺磁金属-绝缘体跃迁（PMIT）之间的相互作用.我们在本文中集中在半填充的情况。对于$t_2/t_1\to 1$，PMIT超过反铁磁相，并显示出类似于V $_2$ O $_3$的情况。在这个参数制度，我们还观察到一个新的磁相。
We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a $2^{nd}$ order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied w…
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。
We study magnetic, transport and thermodynamic properties of the half-filled two-dimensional ($2D$) Hubbard model with layered distributed repulsive interactions using unbiased finite temperature quantum Monte Carlo simulations. Antiferromagnetic long-ranged correlations at $T=0$ are confirmed by means of the magnetic structure factor and the onset of short-ranged ones is at a minimum temperature which can be obtained by peaks in susceptibility and specific heat following an RPA prediction. We also show that transport is affected in the large interaction limit and is enhanced in the non-repuls…
