Abstract
We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis and obtains real-frequency information in a final real-time evolution. Relative to computations on the real-frequency axis, required bath sizes are much smaller and no entanglement is generated, so much larger systems can be studied. The power of the method is demonstrated by solutions of a three-band model in the single- and two-site dynamical mean-field approximation. Technical issues are discussed, including details of the method, efficiency as compared to other matrix-product-state-based impurity solvers, bath construction and its relation to real-frequency computations and the analytic continuation problem of quantum Monte Carlo methods, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.
2 More- Received 31 July 2015
DOI:https://doi.org/10.1103/PhysRevX.5.041032
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Published by the American Physical Society
Popular Summary
Dynamical mean-field theory obtains an approximation to the electron self-energy of a full (typically infinite) system in terms of the solution of a simpler “quantum impurity” problem that consists of a set of localized, interacting levels coupled to a bath. While the approach has been very powerful, its applicability to interesting electronic phenomena occurring in broad classes of complex oxides has been limited because methods do not exist to solve large (many-orbital) impurity models with realistic interactions. Here, we significantly relax this limit, and we present a method for solving much more general classes of multiorbital impurity models.
Our key advance is a representation of the impurity model Green’s function via matrix product state-based computations formulated on the imaginary-time axis. Imaginary-time evolution does not create entanglement and hence dramatically increases the range of situations that can be studied. This development establishes, for the first time, the density matrix renormalization group, which is traditionally a computational approach to one-dimensional systems (and indeed to ground states and selected excited states), as a flexible, low-cost approach to a much wider class of problems. These problems include a general and previously inaccessible class of quantum impurity models relevant to the dynamical mean-field solution of realistic materials problems. We use our method to solve the lowest and next-to-lowest level of cluster dynamical mean-field approximation to study intersite physics of vanadate Ruddlesden-Popper materials with realistic rotationally invariant interactions.
We expect that with modest further optimization, many problems will be within reach, including ab initio studies of superconductivity in iron pnictide materials.