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The open-source library, irbasis, provides easy-to-use tools for two sets of orthogonal functions named intermediate representation (IR). The IR basis enables a compact representation of the Matsubara Greens function and efficient calculations of quantum models. The IR basis functions are defined as the solution of an integral equation whose analytical solution is not available for this moment. The library consists of a database of pre-computed high-precision numerical solutions and computational code for evaluating the functions from the database. This paper describes technical details and demonstrates how to use the library.
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Motivated by recent progress of quantum technologies, we study a discretized quantum adiabatic process for a one-dimensional free fermion system described by a variational wave function, i.e., a parametrized quantum circuit. The wave function is composed of $M$ layers of two elementary sets of time-evolution operators, each set being decomposed into commutable local operators. The evolution time of each time-evolution operator is treated as a variational parameter so as to minimize the expectation value of the energy. We show that the exact ground state is reached by applying the layers of time-evolution operators as many as a quarter of the system size. This is the minimum number $M_B$ of layers set by the limit of speed, i.e., the Lieb-Robinson bound, for propagating quantum entanglement via the local time-evolution operators. Quantities such as the energy $E$ and the entanglement entropy $S$ of the optimized variational wave function with $M < M_B$ are independent of the system size $L$ but fall into some universal functions of $M$. The development of the entanglement in these ansatz is further manifested in the progressive propagation of single-particle orbitals in the variational wave function. We also find that the optimized variational parameters show a systematic structure that provides the optimum scheduling function in the quantum adiabatic process. We also investigate the imaginary-time evolution of this variational wave function, where the causality relation is absent due to the non-unitarity of the imaginary-time evolution operators, thus the norm of the wave function being no longer conserved. We find that the convergence to the exact ground state is exponentially fast, despite that the system is at the critical point, suggesting that implementation of the non-unitary imaginary-time evolution in a quantum circuit is highly promising to further shallow the circuit depth.
The imaginary-time Greens function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Greens function can be constructed by decomposing its spectral representation. We investigate the performance of this so-called textit{intermedaite representation} (IR) from several points of view. First, for two simple models, we study the number of coefficients necessary to achieve a given tolerance in expanding the Greens function. We show that the number of coefficients grows only as $O(log beta)$ for fermions, and converges to a constant for bosons as temperature $T=1/beta$ decreases. Second, we show that this remarkable feature is ascribed to the properties of the physically constructed basis functions. The fermionic basis functions have features in the spectrum whose width is scaled as $O(T)$, which are consistent with the low-$T$ properties of quasiparticles in a Fermi liquid state. On the other hand, the properties of the bosonic basis functions are consistent with those of spin/orbital susceptibilities at low $T$. These results demonstrate the potential wide application of the IR to calculations of correlated systems.
We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Greens function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as single-particle and magnetic excitation spectra can be obtained by applying analytic continuation to imaginary-time data. However, analytic continuation is an ill-conditioned inverse problem and thus sensitive to noise and statistical errors. SpM provides stable analytic continuation against noise by means of a modern regularization technique, which automatically selects bases that contain relevant information unaffected by noise. This paper details the use of this program and shows some applications.
Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent background is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.
The MolMod database is presented, which is openly accessible at http://molmod.boltzmann-zuse.de/ and contains presently intermolecular force fields for over 150 pure fluids. It was developed and is maintained by the Boltzmann-Zuse Society for Computational Molecular Engineering (BZS). The set of molecular models in the MolMod database provides a coherent framework for molecular simulations of fluids. The molecular models in the MolMod database consist of Lennard-Jones interaction sites, point charges, and point dipoles and quadrupoles, which can be equivalently represented by multiple point charges. The force fields can be exported as input files for the simulation programs ms2 and ls1 mardyn, Gromacs, and LAMMPS. To characterise the semantics associated with the numerical database content, a force-field nomenclature is introduced that can also be used in other contexts in materials modelling at the atomistic and mesoscopic levels. The models of the pure substances that are included in the data base were generally optimised such as to yield good representations of experimental data of the vapour-liquid equilibrium with a focus on the vapour pressure and the saturated liquid density. In many cases, the models also yield good predictions of caloric, transport, and interfacial properties of the pure fluids. For all models, references to the original works in which they were developed are provided. The models can be used straightforwardly for predictions of properties of fluid mixtures using established combination rules. Input errors are a major source of errors in simulations. The MolMod database contributes to reducing such errors.
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