Chebyshev matrix product state approach for time evolution

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the non-projective method and more efficient information storage, data compression, and less computational effort.Comment: 14 pages, 8 figure

Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux

We perform a density-matrix renormalization-group study of strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux. Focusing on one-third filling, we explore the phase diagram in dependence of the magnetic flux and the inter-leg tunneling strength. We find several phases including a Meissner phase, vortex liquids, a vortex lattice, as well as a staggered-current phase. Moreover, there are regions where the chiral current reverses its direction, both in the Meissner and in the staggered-current phase. While the reversal in the latter case can be ascribed to spontaneous breaking of translational invariance, in the first it stems from an effective flux increase in the rung direction. Interactions are a necessary ingredient to realize either type of chiral-current reversal

Entanglement spectroscopy of SU(2)-broken phases in two dimensions

In magnetically ordered systems, the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite-size energy spectra, the so-called tower of states (TOS). In the present work, we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground-state entanglement spectrum (ES). Using state-of-the-art density matrix renormalization group (DMRG) calculations, we examine the ES of the 2D antiferromagnetic J(1)-J(2) Heisenberg model on both the triangular and kagome lattice. At large ferromagnetic J(2), the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite-size scaling in the thermodynamic limit) sharply reflects TOS features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes, TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG

Phase diagram of the J1-J2 Heisenberg model on the kagome lattice

We perform an extensive density matrix renormalization group (DMRG) study of the ground-state phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J_2=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J_2\approx 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J_2 the ground state displays signatures of the magnetic order of the \sqrt{3}\times\sqrt{3} and the q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.Comment: 9 pages, 10 figures. Figure added, minor modifications, as publishe

Role of Correlation and Exchange for Quasi-particle Spectra of Magnetic and Diluted Magnetic Semiconductors

Theoretical foundation and application of the generalized spin-fermion (sp-d) exchange lattice model to magnetic and diluted magnetic semiconductors are discussed. The capabilities of the model to describe spin quasi-particle spectra are investigated. The main emphasis is made on the dynamic behavior of two interacting subsystems, the localized spins and spin density of itinerant carriers. A nonperturbative many-body approach, the Irreducible Green Functions (IGF) method, is used to describe the quasi-particle dynamics. Scattering states are investigated and three branches of magnetic excitations are calculated in the regime, characteristic of a magnetic semiconductor. For a simplified version of the model (Kondo lattice model) we study the spectra of quasi-particle excitations with special attention given to diluted magnetic semiconductors. For this, to include the effects of disorder, modified mean fields are determined self-consistently. The role of the Coulomb correlation and exchange is clarified by comparing of both the cases.Comment: 34 page

Evolution of the Ace-1 and Gste2 Mutations and Their Potential Impact on the Use of Carbamate and Organophosphates in IRS for Controlling Anopheles gambiae s.l., the Major Malaria Mosquito in Senegal

Widespread of insecticide resistance amongst the species of the Anopheles gambiae complex continues to threaten vector control in Senegal. In this study, we investigated the presence and evolution of the Ace-1 and Gste2 resistance genes in natural populations of Anopheles gambiae s.l., the main malaria vector in Senegal. Using historical samples collected from ten sentinel health districts, this study focused on three different years (2013, 2017, and 2018) marking the periods of shift between the main public health insecticides families (pyrethroids, carbamates, organophosphates) used in IRS to track back the evolutionary history of the resistance mutations on the Ace-1 and Gste2 loci. The results revealed the presence of four members of the Anopheles gambiae complex, with the predominance of An. arabiensis followed by An. gambiae, An. coluzzii, and An. gambiae-coluzzii hybrids. The Ace-1 mutation was only detected in An. gambiae and An. gambiae-coluzzii hybrids at low frequencies varying between 0.006 and 0.02, while the Gste2 mutation was found in all the species with a frequency ranging between 0.02 and 0.25. The Ace-1 and Gste2 genes were highly diversified with twenty-two and thirty-one different haplotypes, respectively. The neutrality tests on each gene indicated a negative Tajima's D, suggesting the abundance of rare alleles. The presence and spread of the Ace-1 and Gste2 resistance mutations represent a serious threat to of the effectiveness and the sustainability of IRS-based interventions using carbamates or organophosphates to manage the widespread pyrethroids resistance in Senegal. These data are of the highest importance to support the NMCP for evidence-based vector control interventions selection and targeting

The one dimensional Kondo lattice model at partial band filling

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure