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Register a new userA Davidson-Lanczos iteration method for computation of continued-fraction expansion of the Greens function at very low temperatures: Applications to the dynamical mean field theory
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We present a combination method based on orignal version of Davidson algorithm for extracting few of the lowest eigenvalues and eigenvectors of a sparse symmetric Hamiltonian matrix and the simplest version of Lanczos technique for obtaining a tridiagonal representation of the Hamiltonian to compute the continued fraction expansion of the Greens function at a very low temperature. We compare the Davidson$+$Lanczos method with the full diagonalization on a one-band Hubbard model on a Bethe lattice of infinite-coordination using dynamical mean field theory.
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We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long, {it et al.} [Phys. Rev. B {bf 68}, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. {bf 111}, 010401 (2013)] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with $S=1/2$, we demonstrate that the proposed procedure is reasonably accurate even for relatively small systems.
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
We present the continued fraction method (CFM) as a new microscopic approximation to the spectral density of the Hubbard model in the correlated metal phase away from half filling. The quantity expanded as a continued fraction is the single particle Green function. Leading spectral moments are taken into account through a set of real expansion coefficients, as known from the projection technique. The new aspect is to add further stages to the continued fraction, with complex coefficients, thus defining a terminator function. This enables us to treat the entire spectral range of the Green function on equal footing and determine the energy scale of the Fermi liquid quasiparticles by minimizing the total energy. The solution is free of phenomenological parameters and remains well defined in the strong coupling limit, near the doping controlled metal-insulator transition. Our results for the density of states agree reasonably with several variants of the dynamical mean field theory. The CFM requires minimal numerical effort and can be generalized in several ways that are interesting for applications to real materials.
We present the design of a compact AC susceptometer for studies under arbitrarily oriented static magnetic fields, in particular magnetic fields oriented transverse to the AC excitation field. The small size of the susceptometer permits versatile use in conventional cryostats with superconducting magnet systems. The design of the susceptometer minimizes parasitic signal contributions while providing excellent thermal anchoring suitable for measurements in a wide range down to very low temperatures. The performance is illustrated by means of measurements of the transverse susceptibility at the magnetic field tuned quantum phase transition of the dipolar-coupled Ising ferromagnet LiHoF$_4$.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster Dynamical Mean Field Theory (DMFT). We compare cluster DMFT results with those of single site DMFT. We show that inclusion of the short range correlations on top of the on-site correlations, already treated exactly in single site DMFT, do not change the nature of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical $U$ and modify the shape of transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition, in particular in the region of the phase diagram where the two solutions coexist. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale at temperatures as low as $T=0.01t$. The insulating state is characterized by the relatively narrow Mott gap with pronounced peaks at the gap edge.
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