1,720,971 research outputs found
Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces
No full textQuantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L = 501 while accounting for N-ph = 63 phonons per site with high precision in the CDW phase
Matrix product state based band Lanczos solver for quantum cluster approaches
No full textWe present a matrix-product state (MPS) based band Lanczos method as solver for quantum cluster methods such as the variational cluster approximation. While a na & iuml;ve implementation of MPS as cluster solver would barely improve its range of applicability, we show that our approach makes it possible to treat cluster geometries well beyond the reach of exact diagonalization methods. The key modifications we introduce are a continuous energy truncation combined with a convergence criterion that is more robust against approximation errors introduced by the MPS representation and provides a bound to deviations in the resulting Green's function. The potential of the resulting cluster solver is demonstrated by computing the self-energy functional for the single-band Hubbard model at half filling in the strongly correlated regime, on different cluster geometries. Here, we find that only when treating large cluster sizes, observables can be extrapolated to the thermodynamic limit, which we demonstrate at the example of the staggered magnetization. Treating clusters sizes with up to 6 x 6 sites we obtain significant improvement over the extrapolation accessible with exact diagonalization solvers when comparing with quantum Monte Carlo results. Finally, we illustrate the applicability of the MPS cluster solver to more complex models by calculating spectral properties as relevant for the electron-doped cuprate CaCuO2
Automated construction of -invariant matrix-product operators from graph representations
Full text linkWe present an algorithmic construction scheme for
matrix-product-operator (MPO) representations of arbitrary
U(1)U(1)-invariant
operators whenever there is an expression of the local structure in
terms of a finite-states machine (FSM). Given a set of local operators
as building blocks, the method automatizes two major steps when
constructing a U(1)U(1)-invariant
MPO representation: (i) the bookkeeping of auxiliary bond-index shifts
arising from the application of operators changing the local quantum
numbers and (ii) the appearance of phase factors due to particular
commutation rules. The automatization is achieved by post-processing the
operator strings generated by the FSM. Consequently, MPO representations
of various types of U(1)U(1)-invariant
operators can be constructed generically in MPS algorithms reducing the
necessity of expensive MPO arithmetics. This is demonstrated by
generating arbitrary products of operators in terms of FSM, from which
we obtain exact MPO representations for the variance of the Hamiltonian
of a S=1S=1
Heisenberg chain.</jats:p
Time-evolution methods for matrix-product states
Full text linkMatrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W-I,W-II method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics. (C) 2019 The Author(s). Published by Elsevier Inc
Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert spaces without U(1) symmetry
No full textLattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches.</p
Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models
Full text linkFor the characterization of the dynamics in quantum many-body systems the question of how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling, and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to what extent the initially localized information can be recovered only by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking, we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as a scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
