Magnetic and superconducting instabilities in the two-dimensional t-t'-Hubbard model are discussed within a functional renormalization group approach. The fermionic four-point vertex is efficiently parametrized by means of partial bosonization. The exchange of composite bosons in the magnetic, charge density and superconducting channels accounts for the increase of the effective couplings with increasing length scale. We compute the pseudocritical temperature for the onset of local order in various channels.
We design an efficient and balanced approach that captures major effects of collective electronic fluctuations in strongly correlated fermionic systems using a simple diagrammatic expansion on a basis of dynamical mean-field theory. For this aim we perform a partial bosonization of collective fermionic fluctuations in leading channels of instability. We show that a simultaneous account for different bosonic channels can be done in a consistent way that allows to avoid the famous Fierz ambiguity problem. The present method significantly improves a description of an effective screened interactio…
We study the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice within a bosonization scheme for flat-band Chern insulators, focusing on the calculation of the spin-wave excitation spectrum. We consider the Haldane-Hubbard model with the noninteracting lower bands in a nearly-flat band limit, previously determined for the spinless model, and at 1/4-filling of its corresponding noninteracting limit. Within the bosonization scheme, the Haldane-Hubbard model is mapped into an effective interacting boson model, whose quadratic term allows us to determine the spin-wav…
The Mott metal-insulator transition is a typical strong correlation effect triggered by the Umklapp scattering. However, in a physical system, the Umklapp scattering coexists with the normal scattering, including both forward and backward scattering, which conserves the total momentum of scattered electrons. Therefore, it is not easy to quantify the contribution of the Umklapp scattering in a Mott metal-insulator transition. To resolve this difficulty, we propose to explore these scattering processes separately. We study the contribution of each scattering process in the one-dimensional Hubbar…
We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contains Chern-Simons-like terms. Finally, we write down a fermionic dual of the gauged Ising model (the Fr…
Comment on ``Electron-phonon Vertex in the Two-dimensional One-band Hubbard Model''
In cond-mat/0306131 Huang { \em et al.}首次报道了小声子动量在电子关联引起的电子-声子耦合中占优势的数值证据。他们还报告了一个向上翻转的电子声子顶点功能的小动量的哈伯德排斥$U$足够大的$U$的功能。在这篇评论中，我们比较了他们的量子蒙特卡罗数据与分析结果的基础上从玻色子技术的通用$U$。我们关联的电子-声子顶点函数的向上翻转，在大的温度下的相分离不稳定的趋势。
We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. Guided by analytic bosonization results, we quantitatively determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By computing various local quantities as well as the half-system entanglement, we are able to distinguish between Mott, metallic and superconducting phases. We point out the compressible nature of the Mo…
The parquet approach to vertex corrections is unbiased but computationally demanding. Most applications are therefore restricted to small cluster sizes or rely on various simplifying approximations. We have recently shown that the bosonization of the parquet diagrams provides interpretative and algorithmic advantages over the original purely fermionic formulation. Here we present first results of the numerical implementation of this method by applying it to the half-filled Hubbard model on the square lattice at weak coupling. The improved algorithmic performance allows us to evaluate the parqu…
We present a consistent fusion of functional renormalization group and mean-field theory which explicitly introduces a bosonic field via a Hubbard-Stratonovich transformation at the critical scale, at which the order sets in. We show that a minimal truncation of the flow equations, that neglects order parameter fluctuations, is integrable and fulfills fundamental constraints as the Goldstone theorem and the Ward identity connected with the broken global symmetry. To introduce the bosonic field, we present a technique to factorize the most singular part of the vertex, even when the full depende…
We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent …
Two-particle generalized susceptibilities and their irreducible vertex functions play a prominent role in the quantum many-body theory for correlated electron systems. They act as basic building blocks in the parquet formalism which provides a flexible scheme for the calculation of spectral and response functions. The irreducible vertices themselves have recently attracted increased attention as unexpected divergences in these functions have been identified. Remarkably, such singularities appear already for one of the simplest strongly interacting systems: the atomic limit of the half-filled H…
The optical conductivity contains information about energy absorption and the underlying physical processes. In finite-dimensional systems, vertex corrections to the bare bubble need to be considered, which is a computationally challenging task. Recent numerical studies showed that in the weak coupling limit, near an ordering instability with wave vector $π$, $π$-tons (or Maki-Thompson diagrams) yield the most relevant vertex corrections. This provides a route for including vertex corrections into, for example, dynamical mean field theory estimates of the optical conductivity. By implementing …
Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results and the question of the exact solution for the conductivity in the Hubbard model remained open. In this letter we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity, and identify the best available result to be compared to experiment. We find that at relevant (high) temperatures, the sel…
Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase
In this work, we adapt the formalism of the dynamical vertex approximation (D$Γ$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$Γ$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attrac…
Here we analyze the divergences of the irreducible vertex function in dynamical mean field theory, which may indicate either a non-physical breakdown of the perturbation theory or a response to some physical phenomenon. To investigate this question, we construct a quasiparticle vertex from the diverging irreducible vertex functions. This vertex describes the scattering between quasiparticles and quasiholes in a Fermi liquid. We show that the quasparticle vertex \textit{does not} diverge in the charge channel, wherein the irreducible vertex \textit{does} diverge; and we show that the quasiparti…
The parquet equations are a self-consistent set of equations for the effective two-particle vertex of an interacting many-fermion system. The application of these equations to bulk models is, however, demanding due to the complex emergent momentum and frequency structure of the vertex. Here, we show how a channel-decomposition by means of truncated unities, which was developed in the context of the functional renormalization group to efficiently treat the momentum dependence, can be transferred to the parquet equations. This leads to a significantly reduced numerical effort scaling only linear…
Bosonization and density-matrix renormalization group studies of Fulde-Ferrell-Larkin-Ovchinnikov phase and irrational magnetization plateaus in coupled chains
Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model
Universität Hamburg（汉堡大学）；Orebro University（厄勒布鲁大学）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）；European X-Ray Free-Electron Laser Facility（欧洲X射线自由电子激光设施）；CNRS, École polytechnique, Institut Polytechnique de Paris（法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）；Collège de France（法兰西公学院）
