Particle number conservation in quantum many-body simulations with matrix product operators

Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in simulation where the dynamically evolving entities are matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that in this case often the entanglement imposed by the global constraint of fixed particle number is the limiting factor.Comment: minor changes, 18 pages, 5 figure

Biorthonormal Matrix-Product-State Analysis for Non-Hermitian Transfer-Matrix Renormalization-Group in the Thermodynamic Limit

We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the thermodynamic limit. The BMPS is built on a dual series of reduced biorthonormal bases for the left and right Perron states of a non-Hermitian matrix. We propose two alternative infinite-size Biorthonormal TMRG (iBTMRG) algorithms and compare their numerical performance in both finite and infinite systems. We show that both iBTMRGs produce a dual infinite-BMPS (iBMPS) which are translationally invariant in the thermodynamic limit. We also develop an efficient wave function transformation of the iBTMRG, an analogy of McCulloch in the infinite-DMRG [arXiv:0804.2509 (2008)], to predict the wave function as the lattice size is increased. The resulting iBMPS allows for probing bulk properties of the system in the thermodynamic limit without boundary effects and allows for reducing the computational cost to be independent of the lattice size, which are illustrated by calculating the magnetization as a function of the temperature and the critical spin-spin correlation in the thermodynamic limit for a 2D classical Ising model.Comment: 14 pages, 9 figure

Spin-charge separation in two-component Bose-gases

We show that one of the key characteristics of interacting one-dimensional electronic quantum systems, the separation of spin and charge, can be observed in a two-component system of bosonic ultracold atoms even close to a competing phase separation regime. To this purpose we determine the real-time evolution of a single particle excitation and the single-particle spectral function using density-matrix renormalization group techniques. Due to efficient bosonic cooling and good tunability this setup exhibits very good conditions for observing this strong correlation effect. In anticipation of experimental realizations we calculate the velocities for spin and charge perturbations for a wide range of parameters

Magnetism in the dilute Kondo lattice model

The one dimensional dilute Kondo lattice model is investigated by means of bosonization for different dilution patterns of the array of impurity spins. The physical picture is very different if a commensurate or incommensurate doping of the impurity spins is considered. For the commensurate case, the obtained phase diagram is verified using a non-Abelian density-matrix renormalization-group algorithm. The paramagnetic phase widens at the expense of the ferromagnetic phase as the $f$-spins are diluted. For the incommensurate case, antiferromagnetism is found at low doping, which distinguishes the dilute Kondo lattice model from the standard Kondo lattice model.Comment: 11 pages, 2 figure

Modulation spectroscopy with ultracold fermions in an optical lattice

We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time dependent density-matrix renormalization group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott-insulator, respectively. In the Mott-insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations

Strontium and neodymium isotopic variations in early Archean gneisses affected by middle to late Archean high-grade metamorphic processes: West Greenland and Labrador

Relicts of continental crust formed more than 3400 Ma ago are preserved fortuitously in most cratons. The cratons provide the most direct information about crust and mantle evolutionary processes during the first billion years of Earth history. In view of their polymetamorphic character, these terrains are commonly affected by subsequent tectonothermal events. Hence, their isotope systematics may be severely disturbed as a result of bulk chemical change or local isotopic homogenization. This leads to equivocal age and source information for different components within these terrains. The Sr and Nd isotopic data are presented for early Archean gneisses from the North Atlantic Craton in west Greenland and northern Labrador which were affected by younger metamorphic events

Detection of trend changes in time series using Bayesian inference

Change points in time series are perceived as isolated singularities where two regular trends of a given signal do not match. The detection of such transitions is of fundamental interest for the understanding of the system's internal dynamics. In practice observational noise makes it difficult to detect such change points in time series. In this work we elaborate a Bayesian method to estimate the location of the singularities and to produce some confidence intervals. We validate the ability and sensitivity of our inference method by estimating change points of synthetic data sets. As an application we use our algorithm to analyze the annual flow volume of the Nile River at Aswan from 1871 to 1970, where we confirm a well-established significant transition point within the time series.Comment: 9 pages, 12 figures, submitte

Lanczos algorithm with Matrix Product States for dynamical correlation functions

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex-post reorthogonalization method allows to avoid several shortcomings of the original approach, namely the multi-targeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.Comment: final version 11 pages, 11 figure

From density-matrix renormalization group to matrix product states

In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the original DMRG formulation and the MPS approach, demonstrating the additional flexibility that arises from constructing both the wavefunction and the Hamiltonian in MPS form. We also show how to make use of global symmetries, for both the Abelian and non-Abelian cases.Comment: Numerous small changes and clarifications, added a figur

Residential Load Variability and Diversity at Different Sampling Time and Aggregation Scales

The increasing use of large-scale intermittent distributed renewable energy resources on the electrical power system introduces uncertainties in both network planning and management. In addition to architectural changes to the power system, the applications of demand side response (DSR) also add a dimension of complexity - thereby converting the traditionally passive customers into active prosumers (customers that both produce and consume electricity). It has therefore become important to conduct detailed studies on system load profiles to uncover the nature of the system load. These studies could help distribution network operators (DNOs) to adopt relevant strategies that can accommodate new resources such as distributed generation and energy storage on the evolving distribution network and ensure updated design and management approaches. This paper investigates the relationship between both the system load diversity and variability when different customers are aggregated at different scales. Additionally, the implication of sampling time scales is investigated to capture its effect on load diversity and variability. The study looks at the diversity and variability that is observable from the viewpoint of higher power levels, when interconnecting different sized groupings of customers, at different sampling resolutions. The paper thus concludes that the per-customer capacity requirement of the network decreases as the size of customer groupings increases. The load variability also decreases as the aggregation level increases. For active network management, faster time scales are required at lower aggregation scales due to high load variability