First-principle construction of U(1) symmetric matrix product states

The algorithm to calculate the sets of symmetry sectors for virtual indices of U(1) symmetric matrix product states (MPS) is described. Principal differences between open (OBC) and periodic (PBC) boundary conditions are stressed, and the extension of PBC MPS algorithm to projected entangled pair states (PEPS) is outlined.Comment: 7 pages (13 pages in the journal version), 1 figur

Efficient MPS algorithm for periodic boundary conditions and applications

We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS), and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of about 100 sites and more than for small quantum systems. We apply the formalism to calculate the ground state and first excited state of a spin-1 Heisenberg ring and deduce the size of the Haldane gap. The results are compared to previous high-precision DMRG calculations. Furthermore, we study spin-1 systems with a biquadratic nearest-neighbor interaction and show first results of an application to a mesoscopic Hubbard ring of spinless Fermions which carries a persistent current.Comment: 7 pages, 3 figures, 3 tables, the article was accepted for Ukrainian Journal of Physic

Bilinear-biquadratic spin-1 rings: an SU(2)-symmetric MPS algorithm for periodic boundary conditions

An efficient algorithm for SU(2) symmetric matrix product states (MPS) with periodic boundary conditions (PBC) is proposed and implemented. It is applied to a study of the spectrum and correlation properties of the spin-1 bilinear-biquadratic Heisenberg model. We characterize the various phases of this model by the lowest states of the spectrum with angular momentum J = 0, 1, 2 for systems of up to 100 spins. Furthermore, we provide precision results for the dimerization correlator as well as the string correlator.Comment: 17 pages, 9 figures, 4 tables, improved numbers, new references adde

Dimerization in ultracold spinor gases with Zeeman splitting

Two recent publications report different boundaries for the dimerized phase of the bilinear-biquadratic spin-1 Heisenberg model with quadratic Zeeman effect. We address these discrepancies for the biquadratic model with quadratic Zeeman term and explain the differences. Based on our numerical results the phase boundaries of the dimerized phase are determined.Comment: 5 pages, 5 figure

Symmetries and entanglement in the one-dimensional spin-1/2 XXZ model

An efficient and stable algorithm for U(1) symmetric matrix product states (MPS) with periodic boundary conditions (PBC) is proposed. It is applied to a study of correlation and entanglement properties of the eigenstates of the spin-1/2 XXZ model with different spin projections. Convergence properties and accuracy of the algorithm are studied in detail.Comment: 10 pages, 4 figures, 4 table

Phase diagram of one-, two-, and three-dimensional quantum spin systems derived from entanglement properties

We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is obtained from a tensor network representation of the ground state wave-function. Three spin-1/2 models (Ising, XY, XXZ, all in a transverse field) are investigated. Imaginary-time evolution (TEBD in 1D, `simple update' in 2D and 3D) is used to determine the ground states of these models. The phase structure of the models is discussed for all three dimensions.Comment: 13 pages, 10 figure

Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models

We investigate entanglement properties of infinite 1D and 2D spin-1/2 quantum Ising and XXZ models. Tensor network methods (MPS in 1D and TERG and CTMRG in 2D) are used to model the ground state of the studied models. Different entanglement measures, such as one-site entanglement entropy, one-tangle, concurrence of formation and assistance, negativity and entanglement per bond are calculated and their `characterizing power' to determine quantum phase transitions is compared. A special emphasis is made on the study of entanglement monogamy properties.Comment: 19 pages, 24 figure

Influence of resonant tunneling on the imaging of atomic defects on InAs(110) surfaces by low-temperature scanning tunneling microscopy

We have used a low-temperature scanning tunneling microscope (STM) to study the surface of heavily doped semiconductor InAs crystals. The crystals are cleaved in situ along the (110) plane. Apart from atomically flat areas, we also observe two major types of atomic scale defects which can be identified as S dopant atoms and as As vacancies, respectively. The strong bias voltage dependence of the STM image of the impurities can be explained in terms of resonant tunneling through localized states which are present near the impurity.Comment: 3 pages, 4 figures, published in Appl. Phys. A 66, 171 (1998

Luttinger liquid parameters from tensor network data

We study the XXZ Heisenberg model in a staggered magnetic field using the HOTRG tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization step. We determine the phase diagram of the model from the low lying spectrum, and from the finite size dependence of the spectrum we extract scaling dimensions, which are compared to predictions of low energy field theory.Comment: 7 pages, 7 multi-panel figures, 1 table in Version

Spin-1/2 XXZ Heisenberg chain in a longitudinal magnetic field

We study the XXZ Heisenberg model in a longitudinal magnetic field using a tensor renormalization method. Built into the tensor representation of the XXZ model is the U(1) symmetry, which is systematically maintained at each renormalization step. This enables rather large tensor representations. We extract ground state properties as well as the low lying spectrum from the fixed point tensors. With rather moderate numerical effort we achieve a very good accuracy as demonstrated by comparison with Bethe Ansatz calculations. The phase structure of the model can be accurately reproduced just from the largest fixed point tensor elements.Comment: 10 pages (9 pages in a journal version), 7 multi-panel figures, 1 tabl