The underlying Fermi surface is a key concept for strongly-interacting electron models and has been introduced to generalize the usual notion of the Fermi surface to generic (superconducting or insulating) systems. By using improved correlated wave functions that contain backflow and Jastrow terms, we examine the two-dimensional $t{-}t^\prime$ Hubbard model and find a non-trivial renormalization of the topology of the underlying Fermi surface close to the Mott insulator. Moreover, we observe a sharp crossover region, which arises from the metal-insulator transition, from a weakly interacting metal at small coupling to a resonating valence-bond superconductor at intermediate coupling. A violation of the Luttinger theorem is detected at low hole dopings.
Many-Body Renormalization of Semiconductor Quantum Wire Excitons: Absorption, Gain, Binding, Unbinding, and Mott Transition
通过求解动态屏蔽的Bethe-Salpeter库仑相互作用方程，从理论上研究了GaAs量子线结构中准一维多体激子在外部光激发条件下的形成和稳定性.与最近的几个实验结果一致，计算的激子峰显示出非常弱的载流子密度依赖性高达（甚至高于）莫特跃迁密度，$n_c\sim3\times10^5$ cm $^{-1}$。在$n_c$之上，我们发现了相当大的光学增益，有力地证明了一维量子线激光器运行的可能性。
We examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr$_2$CuO$_3$. The low-energy spin excitation does not contribute to t…
The real part of optical conductivity $\text{Re}σ(ω)$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}σ(ω)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}σ(ω)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum …
We study the fully gapped chiral Mott insulator (CMI) of frustrated Bose-Hubbard models on ladders and two-dimensional lattices by perturbative strong-coupling analysis and density matrix renormalization group (DMRG). First we show the existence of a low-lying exciton state on all geometries carrying the correct quantum numbers responsible for the condensation of excitons and formation of the CMI in the intermediate interaction regime. Then we perform systematic DMRG simulations on several two-leg ladder systems with $π$-flux and carefully characterize the two quantum phase transitions. We dis…
Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physi…
We define, compute and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals $(i)$ mid-gap states related to parity-forbidden optical states, and $(ii)$ strong renormalization and hybridization of the excitonic resonance and the absorption…
We study the effects of electronic correlations on fragile topology using dynamical mean-field theory. Fragile topological insulators (FTIs) offer obstruction to the formation of exponentially localized Wannier functions, but they can be trivialized by adding certain trivial degrees of freedom. For the same reason, FTIs do not host symmetry-protected flow of edge states between bulk bands in cylindrical boundary conditions but are expected to have a spectral flow between the fragile bands and other bands under certain twisted boundary conditions. We here analyze commonly observed effects of st…
Precise Determination of Phase Diagram for Two-Dimensional Hubbard Model with Filling- and Bandwidth-Control Mott Transitions: Grand-Canonical Path-Integral Renormalization Group Approach
In many transition-metal oxides and dichalcogenides, the electronic and lattice degrees of freedom are strongly coupled, giving rise to remarkable phenomena, such as metal-insulator transition (MIT) and charge-density wave (CDW) order. We study this interplay by tracing the instant electronic structure under ab initio molecular dynamics. Applying this method to a 1T-TaS2 layer, we show that the CDW-triggered Mott gap undergoes a continuous reduction as the lattice temperature raises, despite a nearly constant CDW amplitude. Before the CDW order undergoes a sharp first-order transition around t…
利用密度矩阵重整化群计算了具有次近邻跳跃t'的半满Hubbard链对外电场的响应，研究了Mott跃迁随相互作用强度的变化.当从绝缘侧接近临界点时，电极化率χ发散。我们证明了表征这种跃迁的相关长度xi与极化涨落成正比，并且chi ~ xi ^[2]。临界行为表明，对于所有的t '，无论是否存在自旋能隙，跃迁都是无限阶的，并且超标度成立。
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the 2nd nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fe…
We describe the critical behavior of electric field-driven (dynamic) Mott insulator-to-metal transitions in dissipative Fermi and Bose systems in terms of non-Hermitian Hamiltonians invariant under simultaneous parity (P) and time-reversal (T) operations. The dynamic Mott transition is identified as a PT symmetry-breaking phase transition, with the Mott insulating state corresponding to the regime of unbroken PT symmetry with a real energy spectrum. We establish that the imaginary part of the Hamiltonian arises from the combined effects of the driving field and inherent dissipation. We derive …
Employing the density-matrix renormalization group technique in the matrix-product-state representation, we investigate the photoexcited superconducting correlations induced by the $η$-pairing mechanism in the half-filled Hubbard chain. We estimate the characteristic pair correlation function and verify the accuracy of our numerical results by comparison with exact-diagonalization data for small systems. The optimal parameter set of the pump that most enhances the $η$-pair correlations, is calculated in the strong-coupling regime. For such a pump, we explore the possibility of quasi-long-range…
