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Register a new userTime-dependent variational principle in matrix-product state manifolds: pitfalls and potential
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We study the applicability of the time-dependent variational principle in matrix product state manifolds for the long time description of quantum interacting systems. By studying integrable and nonintegrable systems for which the long time dynamics are known we demonstrate that convergence of long time observables is subtle and needs to be examined carefully. Remarkably, for the disordered nonintegrable system we consider the long time dynamics are in good agreement with the rigorously obtained short time behavior and with previous obtained numerically exact results, suggesting that at least in this case the apparent convergence of this approach is reliable. Our study indicates that while great care must be exercised in establishing the convergence of the method, it may still be asymptotically accurate for a class of disordered nonintegrable quantum systems.
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We use the time dependent variational matrix product state (tVMPS) approach to investigate the dynamical properties of the single impurity Anderson model (SIAM). Under the Jordan-Wigner transformation, the SIAM is reformulated into two spin-1/2 XY chains with local magnetic fields along the z-axis. The chains are connected by the longitudinal Ising coupling at the end points. The ground state of the model is searched variationally within the space spanned by the matrix product state (MPS). The temporal Greens functions are calculated both by the imaginary and real time evolutions, from which the spectral information can be extracted. The possibility of using the tVMPS approach as an impurity solver for the dynamical mean field theory is also addressed. Finite temperature density operator is obtained by the ancilla approach. The results are compared to those from the Lanczos and the Hirsch-Fye quantum Monte-Carlo methods.
We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same tensor network structure that encodes the state is available. Often, such a representation can be found also for long-range terms in the Hamiltonian. As an application we use TDVP for the Fork Tensor Product States tensor network for multi-orbital Anderson impurity models. We demonstrate that TDVP allows to account for off-diagonal hybridizations in the bath which are relevant when spin-orbit coupling effects are important, or when distortions of the crystal lattice are present.
We present a unified framework for renormalization group methods, including Wilsons numerical renormalization group (NRG) and Whites density-matrix renormalization group (DMRG), within the language of matrix product states. This allows improvements over Wilsons NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Greens functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially emph{linear} scaling of complexity for $n$-channel problems.
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 less 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, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.
We derive an exact matrix product state representation of the Haldane-Rezayi state on both the cylinder and torus geometry. Our derivation is based on the description of the Haldane-Rezayi state as a correlator in a non-unitary logarithmic conformal field theory. This construction faithfully captures the ten degenerate ground states of this model state on the torus. Using the cylinder geometry, we probe the gapless nature of the phase by extracting the correlation length, which diverges in the thermodynamic limit. The numerically extracted topological entanglement entropies seem to only probe the Abelian part of the theory, which is reminiscent of the Gaffnian state, another model state deriving from a non-unitary conformal field theory.
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