In the Cellular Dynamical Mean Field Theory (CDMFT), a strongly correlated system is represented by a small cluster of correlated sites, coupled to an adjustable bath of uncorrelated sites simulating the cluster's environment; the parameters governing the bath are set by a self-consistency condition involving the local Green function and the lattice electron dispersion. Solving the cluster problem with an exact diagonalization method is only practical for small bath sizes (8 sites). In that case the self-consistency condition cannot be exactly satisfied and is replaced by a minimization procedure. There is some freedom in the definition of the `merit function' to optimize. We use Potthoff's Self-Energy Functional Approach on the one- and two-dimensional Hubbard models to gain insight into the best choice for this merit function. We argue that several merit functions should be used and preference given to the one that leads to the smallest gradient of the Potthoff self-energy functional. We propose a new merit function weighted with the self-energy that seems to fit the Mott transition in two dimensions better than other merit functions.
We study the dynamics of correlation functions of a class of $d-$dimensional integrable models coupled linearly to a fermionic or bosonic bath in the presence of a periodic drive with a square pulse protocol. It is well known that in the absence of the bath, these models exhibit a dynamical phase transition; all correlators decay to their steady state values as $n_0^{-(d+1)/2}$[$n_0^{-d/2}]$ above [below] a critical frequency $ω_c$, where $n_0$ is the number of drive cycles. We find that the presence of a linearly coupled fermionic bath which maintains integrability of the system preserves thi…
We derive an effective time independent Hamiltonian for the transverse Ising model coupled to a spin bath, in the presence of a high frequency AC magnetic field. We show that the spin blocking mechanism that removes the quantum phase transition can be suppressed by the AC field, allowing high tunability of the quantum critical point. Finally, we calculate the phase diagram within the RPA approximation for the case of spin $7/2$ nuclei, appropriate to the $LiHo_{x}Y_{1-x}F_{4}$ system.
Abstract We discuss the quantum dynamics of the central spin model in a regime where the central spin and bath are slaved to each other. The exact solution is found when the bath is static, and is compared with the effect of an external field, finding that they are inequivalent due to the quantum nature of the environment. When the bath has dynamics, we analyze the differences between the numerical simulation using time-dependent perturbation theory and the equation of motion technique, which shows better accuracy. We demonstrate that the use of dynamical Renormalization Group (dRG), simultane…
We demonstrate an algebraic construction of frequency-dependent bath orbitals which can be used in a robust and rigorously self-consistent DMFT-like embedding method, here called $ω-$DMFT, suitable for use with Hamiltonian-based impurity solvers. These bath orbitals are designed to exactly reproduce the hybridization of the impurity to its environment, while allowing for a systematic expansion of this bath space as impurity interactions couple frequency points. In this way, the difficult non-linear fit of bath parameters necessary for many Hamiltonian-formulation impurity solvers in DMFT is av…
Exponential Convergence of Cellular Dynamical Mean Field Theory: Reply to the comment by K. Aryanpour, Th. Maier and M. Jarrell (cond-mat/0301460)
我们对K. Aryanpour，Th. Maier和M. J. J. II（cond-mat/0301460）在我们的论文（Phys. Rev. B { \bf 65} 155112（2002））上。我们证明使用一般的参数和明确的例子，每当相关长度是有限的，本地观测值收敛指数快速的集群大小，$L_{c}$，细胞动力学平均场论（CDMFT）。这是一个更快的收敛速度比$1/L_{c}^{2}$行为的动态集群近似（DCA），从而驳斥了中央断言他们的评论。
Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems
Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）；Institute of Information Systems Engineering, TU Wien（维也纳工业大学信息系统工程学院）；Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）；Department of Physics, Friedrich-Alexander-Universität Erlangen/Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学物理系）
We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we defi…
We introduce a nested optimization procedure using semi-definite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory (DMFT) methodologies. We show that the proposed method is more efficient and flexible than state-of-the-art fitting schemes, which allows us to treat as large a number of bath sites as the impurity solver at hand allows. We characterize its robustness to initial conditions and symmetry constraints, thus providing conclusive evidence that in the presence of a large bath, our semi-definite relaxation approach can find the correct set of bath pa…
We develop a semi-analytical approach beyond the Born-Markov approximation to study the quench dynamics of the spin-boson model in the strong-coupling regime ($α\leq1/2$) for the Ohmic bath. The basic idea in our approach is to write an effective time-dependent model for the dynamics of the system coupled to the bosonic bath after integrating out high-frequency bath modes. By applying this procedure to the Heisenberg equations of motion, we derive a set of flow equations for the system parameters as a function of time. The final flow equations look similar to those of the equilibrium renormali…
