受Mross和Senthil [Phys. Rev. B \textbf{84}，165126（2011）]的最近工作的启发，其提供了在两个空间维度中从费米液体到量子自旋液体的Mott转变的对偶描述，我们将他们的方法扩展到更高维的情况，并且我们提供了在三个空间维度中的明确形式。在二维情况下，是涡旋线导致了费米液体的不稳定性，而不是涡旋驱动传统费米液体进入量子自旋液体态。当涡线在不同的自由度上凝聚时，扩展的形式主义可以产生丰富的结果。例如，当涡线凝聚在电荷相自由度，所产生的有效的费米子作用被发现是等效的，通过充分研究的从粒子的方法获得的哈伯德和/或安德森晶格模型，这证实了扩展的对偶形式主义在3D中的有效性。当涡旋线在自旋相自由度上凝聚时，可以得到具有自旋能隙和对非常规超导对不稳定性的双金属。此外，当涡线在两个相位度上凝聚时，奇异的双U（1）规范理论出现，它描述了自旋相反的费米子激发的分离。值得注意的是，前两个功能已经在2D中以类似的方式进行了讨论，最后一个在以前的工作中没有报道。目前的工作预计是有用的理解莫特转变发生在两个空间维度之外。
英文摘要：
Motivated by recent work of Mross and Senthil [Phys. Rev. B \textbf{84}, 165126 (2011)] which provides a dual description for Mott transition from Fermi liquid to quantum spin liquid in two space dimensions, we extend their approach to higher dimensional cases, and we provide explicit formalism in three space dimensions. Instead of the vortices driving conventional Fermi liquid into quantum spin liquid states in 2D, it is the vortex lines to lead to the instability of Fermi liquid in 3D. The extended formalism can result in rich consequences when the vortex lines condense in different degrees of freedom. For example, when the vortex lines condense in charge phase degrees of freedom, the resulting effective fermionic action is found to be equivalent to that obtained by well-studied slave-particle approaches for Hubbard and/or Anderson lattice models, which confirm the validity of the extended dual formalism in 3D. When the vortex lines condense in spin phase degrees of freedom, a doublon metal with a spin gap and an instability to the unconventional superconducting pairing can be obtained. In addition, when the vortex lines condense in both phase degrees, an exotic doubled U(1) gauge theory occurs which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D, the last one has not been reported in the previous works. The present work is expected to be useful in understanding the Mott transition happening beyond two space dimensions.
We theoretically investigate pump-probe optical responses in the two-dimensional extended Hubbard model describing cuprates by using a time-dependent Lanczos method. At half filling, pumping generates photoinduced absorptions inside the Mott gap. A part of low-energy absorptions is attributed to the independent propagation of photoinduced holons and doublons. The spectral weight just below the Mott gap increases with decreasing the on-site Coulomb interaction $U$. We find that the next-nearest-neighbor Coulomb interaction $V_1$ enhances this $U$ dependence, indicating the presence of biexciton…
We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several features observed in studies using cluster dynamical mean-field theory. This includes a strong reduction of the critical interaction and inversion of the slope of the transition lines with respect to single-site dynamical mean-field theory. We show that these effects coincide with a much smaller momentum differentiation compared to cluster methods. We further…
We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site ($U$) and next-nearest-neighbor ($V_2$) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-$V_2$ region by a CDW chara…
We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\times 2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction $V$ causes "screening" effects close to the Mott phase transition, pushing the phase boundary to larger values of $U$. We also demonstrate the different effects of $V$ on correlations in metallic and insulating regimes and document the different correlation aspects of charge order and Mott states.
Inspired by the Nagaoka ferromagnetism, we propose an itinerant model to study the transition between the Mott singlet state and a ferromagnetic state by emulating a doping process in finite lattices. In the Nagaoka ferromagnetism, the total spin of the system takes the maximum value when an electron is removed from the half-filled system. To incorporate a procedure of the electron removal, our model contains extra sites as a reservoir of electrons, and the chemical potential of the reservoir controls the distribution of electrons. As a function of the chemical potential, the system exhibits g…
Extended Hubbard model with renormalized Wannier wave functions in the correlated state II: Quantum critical scaling of the wave function near the Mott-Hubbard transition
我们给出了一个由Slater s轨道组成的重正化单粒子Wannier函数的量子临界行为的模型例子，并在一个可调的高斯STO-7 G基表示，这是计算立方晶格的Gutzwiller关联态附近的金属-绝缘体转变（MIT）。讨论是在扩展的哈伯德模型和早先提出的方法[cf. EUR. J. B { \bf 66}，385（2008）]。组分原子波函数大小、Wannier函数最大值以及系统能量都随着晶格参数$R$的增加而成比例，如$[(R-R_{c})/R_{c}]^{s}$与$s$在间隔$[0.9,1.0]$中。这种标度律被解释为粒子间库仑排斥的主导作用的证据，这对于$R>R_c$是intersite字符。还得到了绝缘体-金属过渡晶格参数值$R=R_{c}$与原{ \em Mott判据}的关系。方法的可行性进行了测试，通过比较我们的结果与哈伯德链，其中Mott-Hubbard过渡是缺席的确切方法。鉴于我们的结果的独特功能，在定性方面也提供了广泛的讨论。
The microscopic mechanism of the metal-insulator transition is studied by orbital-resolved 51V NMR spectroscopy in a prototype of the quasi-one-dimensional system V6O13. We uncover that the transition involves a site-selective d orbital order lifting twofold orbital degeneracy in one of the two VO6 chains. The other chain leaves paramagnetic moments on the singly occupied dxy orbital across the transition. The two chains respectively stabilize an orbital-assisted spin-Peierls state and an antiferromagnetic long-range order in the ground state. The site-selective Mott transition may be a source…
The Heisenberg-Kitaev (HK) model on the triangular lattice is conceptually interesting for its interplay of geometric and exchange frustration. HK models are also thought to capture the essential physics of the spin-orbital entanglement in effective $j=1/2$ Mott insulators studied in the context of various 5d transition metal oxides. Here we argue that the recently synthesized Ba$_3$IrTi$_2$O$_9$ is a prime candidate for a microscopic realization of the triangular HK model. We establish that an infinitesimal Kitaev exchange destabilizes the 120$^\circ$ order of the quantum Heisenberg model and…
We propose the concept of "hybridization-switching induced Mott transition" which is relevant to a broad class of ABO$_3$ perovskite materials including BiNiO$_3$ and PbCrO$_3$ which feature extended $6s$ orbitals on the A-site cation (Bi or Pb), and A-O covalency induced ligand holes. Using {\it ab initio} electronic structure and slave rotor theory calculations, we show that such systems exhibit a breathing phonon driven A-site to oxygen hybridization-wave instability which conspires with strong correlations on the B-site transition metal ion (Ni or Cr) to induce a Mott insulator. These Mott…
Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity
We present a computational technique to calculate time and momentum resolved non-equilibrium spectral density of correlated systems using a tunneling approach akin scanning tunneling spectroscopy. The important difference is that our probe is extended, basically a copy of the sample, allowing one to extract the momentum information of the excitations. We illustrate the method by measuring the spectrum of a Mott-insulating extended Hubbard chain after a sudden quench with the aid of time-dependent density matrix renormalization group (tDMRG) calculations. We demonstrate that the system realizes…
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…
Mott transition plays a key role in strongly correlated physics but its nature is not yet fully understood. Motivated by recent development of Schwinger boson approach for the Kondo lattice, we propose in this work a novel slave fermion algorithm to study the Mott transition. Upon local approximation, our method yields a phase diagram with a zero-temperature continuous (Mott) metal-insulator transition at finite Coulomb interaction $U$ for the half-filled one-band Hubbard model on a square lattice, and the resistivity exhibits a critical scaling around the quantum Widom line. We argue that the…
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…
Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of the extended Hubbard model of hard-core bosons on the pyrochlore lattice with partial fillings. When the intersite repulsion is dominant, the system is in a cluster Mott insulator phase with an integer number of bosons localized inside the tetrahedral units of the pyrochlore lattice. We show that the full phase diagram contains three cluster Mott insulator phases with 1/4, 1/2, and 3/4 boson fillings, respectively. We further demonstrate that all three cluster Mott insulators are Coulomb liquid phases an…
We numerically investigate the dynamical properties of $κ$-type molecular conductors in their antiferromagnetic Mott insulating state. By treating the extended Hubbard model on the two-dimensional $κ$-type lattice within the Lanzcos exact diagonalization method, we calculate the one-particle spectral function $A(\boldsymbol{k}, ω)$ and the optical absorption spectra taking advantage of twisted boundary conditions. We find spin splitting in $A(\boldsymbol{k}, ω)$ predicted by a previous Hartree-Fock study [M. Naka et al., Nat. Commun. 10, 4305 (2019)]; namely, their up- and down-spin components…
Motivated by recent experiments on the quantum-spin-liquid candidate material LiZn2Mo3O8, we study a single-band extended Hubbard model on an anisotropic Kagome lattice with the 1/6 electron filling. Due to the partial filling of the lattice, the inter-site repulsive interaction is necessary to generate Mott insulators, where electrons are localized in clusters, rather than at lattice sites. It is shown that these cluster Mott insulators are generally U(1) quantum spin liquids with spinon Fermi surfaces. The nature of charge excitations in cluster Mott insulators can be quite different from co…
