Efficient representation of fully many-body localized systems using tensor networks

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of $\ell$ contiguous sites. We argue this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.Comment: Version 2, 16 pages, 16 figures. Larger systems and greater efficienc

S3 Quantum Hall Wavefunctions

We construct a family of quantum Hall Hamiltonians whose ground states, at least for small system sizes, give correlators of the S3 conformal field theories. The ground states are considered as trial wavefunctions for quantum Hall effect of bosons at filling fraction nu=3/4 interacting either via delta function interaction or delta function plus dipole interaction. While the S3 theories can be either unitary or nonunitary, we find high overlaps with exact diagonalizations only for the nonunitary case, suggesting that these wavefunctions may correspond to critical points, possibly analogous to the previously studied Gaffnian wavefunction. These wavefunctions give an explicit example which cannot be fully characterized by their thin-torus limit or by their pattern of zeros.Comment: 4+epsilon pages. 1 figure. Revised version includes: 1 additional author; additional numerical work; several minor corrections. Our main results are unchange

Correlators of N=1 Superconformal Currents

We give an explicit expression for the M-point correlator of the superconformal current in two dimensional N=1 superconformal field theories.Comment: 8 pages. Some typos fixed. Unfortunately, these typos exist in the published version in J Phys

Activation of the phosphosignaling protein CheY. I. Analysis of the phosphorylated conformation by 19F NMR and protein engineering

CheY, the 14-kDa response regulator protein of the Escherichia coli chemotaxis pathway, is activated by phosphorylation of Asp57. In order to probe the structural changes associated with activation, an approach which combines 19F NMR, protein engineering, and the known crystal structure of one conformer has been utilized. This first of two papers examines the effects of Mg(II) binding and phosphorylation on the conformation of CheY. The molecule was selectively labeled at its six phenylalanine positions by incorporation of 4-fluorophenylalanine, which yielded no significant effect on activity. One of these 19F probe positions monitored the vicinity of Lys109, which forms a salt bridge to Asp57 in the apoprotein and has been proposed to act as a structural "switch" in activation. 19F NMR chemical shift studies of the labeled protein revealed that the binding of the cofactor Mg(II) triggered local structural changes in the activation site, but did not perturb the probe of the Lys109 region. The structural changes associated with phosphorylation were then examined, utilizing acetyl phosphate to chemically generate phsopho-CheY during NMR acquisition. Phosphorylation triggered a long-range conformational change extending from the activation site to a cluster of 4 phenylalanine residues at the other end of the molecule. However, phosphorylation did not perturb the probe of Lys109. The observed phosphorylated conformer is proposed to be the first step in the activation of CheY; later steps appear to perturb Lys109, as evidenced in the following paper. Together these results may give insight into the activation of other prokaryotic response regulators

Derivative relation for thermopower in the quantum Hall regime

Recently, Tieke et al (to be published in PRL) have observed the relation S_{yx} = alpha B dS_{xx}/dB for the components of the thermopower tensor in the quantum Hall regime, where alpha is a constant and B is the magnetic field. Simon and Halperin (PRL 73, 3278 (1994)) have suggested that an analogous relation observed for the resistivity tensor R_{xx} = \alpha B dR_{xy}/dB can be explained with a model of classical transport in an inhomogeneous medium where the local Hall resistivity is a function of position and the local dissipative resistivity is a small constant. In the present paper, we show that this new thermopower relation can be explained with a similar model.Comment: This paper supercedes cond-mat/9705001 which was withdrawn. 4 pages, Revte

Composite Fermions with Orbital Magnetization

For quantum Hall systems, in the limit of large magnetic field (or equivalently small electron band mass $m_b$), the static response of electrons to a spatially varying magnetic field is largely determined by kinetic energy considerations. This response is not correctly given in existing approximations based on the Fermion Chern-Simons theory of the partially filled Landau level. We remedy this problem by attaching an orbital magnetization to each fermion to separate the current into magnetization and transport contributions, associated with the cyclotron and guiding center motions respectively. This leads to a Chern-Simons Fermi liquid description of the $\nu=\frac{1}{2m}$ state which correctly predicts the $m_b$ dependence of the static and dynamic response in the limit $m_b \rightarrow 0$.Comment: 4 pages, RevTeX, no figure