Super Rogers-Szeg\"o polynomials associated with BCNBC_N type of Polychronakos spin chains

As is well known, multivariate Rogers-Szeg\"o polynomials are closely connected with the partition functions of the $A_{N-1}$ type of Polychronakos spin chains having long-range interactions. Applying the `freezing trick', here we derive the partition functions for a class of $BC_N$ type of Polychronakos spin chains containing supersymmetric analogues of polarized spin reversal operators and subsequently use those partition functions to obtain novel multivariate super Rogers-Szeg\"o (SRS) polynomials depending on four types of variables. We construct the generating functions for such SRS polynomials and show that these polynomials can be written as some bilinear combinations of the $A_{N-1}$ type of SRS polynomials. We also use the above mentioned generating functions to derive a set of recursion relations for the partition functions of the $BC_N$ type of Polychronakos spin chains involving different numbers of lattice sites and internal degrees of freedom.Comment: 33 pages, minor typos corrected, journal reference give

First-Principles Study of Integer Quantum Hall Transitions in Mesoscopic Samples

We perform first principles numerical simulations to investigate resistance fluctuations in mesoscopic samples, near the transition between consecutive Quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of real devices. The Hall and longitudinal resistances extracted from the generalized Landauer formula reproduce all the experimental features uncovered recently. We then use a simple generalization of the Landauer-B\"uttiker model, based on the interplay between tunneling and chiral currents -- the co-existing mechanisms for transport -- to explain the three distinct types of fluctuations observed, and identify the central region as the critical region.Comment: changes to acknowledgements onl

Quantum leakage detection using a model-independent dimension witness

Users of quantum computers must be able to confirm they are indeed functioning as intended, even when the devices are remotely accessed. In particular, if the Hilbert space dimension of the components are not as advertised -- for instance if the qubits suffer leakage -- errors can ensue and protocols may be rendered insecure. We refine the method of delayed vectors, adapted from classical chaos theory to quantum systems, and apply it remotely on the IBMQ platform -- a quantum computer composed of transmon qubits. The method witnesses, in a model-independent fashion, dynamical signatures of higher-dimensional processes. We present evidence, under mild assumptions, that the IBMQ transmons suffer state leakage, with a $p$ value no larger than $5{\times}10^{-4}$ under a single qubit operation. We also estimate the number of shots necessary for revealing leakage in a two-qubit system.Comment: 11 pages, 5 figure

Simulating STM transport in alkanes from first principles

Simulations of scanning tunneling microscopy measurements for molecules on surfaces are traditionally based on a perturbative approach, most typically employing the Tersoff-Hamann method. This assumes that the STM tip is far from the sample so that the two do not interact with each other. However, when the tip gets close to the molecule to perform measurements, the electrostatic interplay between the tip and substrate may generate non-trivial potential distribution, charge transfer and forces, all of which may alter the electronic and physical structure of the molecule. These effects are investigated with the ab initio quantum transport code SMEAGOL, combining non-equilibrium Green's functions formalism with density functional theory. In particular, we investigate alkanethiol molecules terminated with either CH3 or CF3 end-groups on gold surfaces, for which recent experimental data are available. We discuss the effects connected to the interaction between the STM tip and the molecule, as well as the asymmetric charge transfer between the molecule and the electrodes.Comment: 10 pages, 18 figure

Efficient atomic self-interaction correction scheme for non-equilibrium quantum transport

Density functional theory calculations of electronic transport based on local exchange and correlation functionals contain self-interaction errors. These originate from the interaction of an electron with the potential generated by itself and may be significant in metal-molecule-metal junctions due to the localized nature of the molecular orbitals. As a consequence, insulating molecules in weak contact with metallic electrodes erroneously form highly conducting junctions, a failure similar to the inability of local functionals of describing Mott-Hubbard insulators. Here we present a fully self-consistent and still computationally undemanding self-interaction correction scheme that overcomes these limitations. The method is implemented in the Green's function non-equilibrium transport code Smeagol and applied to the prototypical cases of benzene molecules sandwiched between gold electrodes. The self-interaction corrected Kohn-Sham highest occupied molecular orbital now reproduces closely the negative of the molecular ionization potential and is moved away from the gold Fermi energy. This leads to a drastic reduction of the low bias current in much better agreement with experiments.Comment: 4 pages, 5 figure

Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators

We derive the exact spectra as well as partition functions for a class of $BC_N$ type of spin Calogero models, whose Hamiltonians are constructed by using supersymmetric analogues of polarized spin reversal operators (SAPSRO). The strong coupling limit of these spin Calogero models yields $BC_N$ type of Polychronakos-Frahm (PF) spin chains with SAPSRO. By applying the freezing trick, we obtain an exact expression for the partition functions of such PF spin chains. We also derive a formula which expresses the partition function of any $BC_N$ type of PF spin chain with SAPSRO in terms of partition functions of several $A_K$ type of supersymmetric PF spin chains, where $K\leq N-1$. Subsequently we show that an extended boson-fermion duality relation is obeyed by the partition functions of the $BC_N$ type of PF chains with SAPSRO. Some spectral properties of these spin chains, like level density distribution and nearest neighbour spacing distribution, are also studied.Comment: 36 pages, 2 figures. arXiv admin note: text overlap with arXiv:1402.275

Weak Localization and Transport Gap in Graphene Antidot Lattices

We fabricated and measured antidot lattices in single layer graphene with lattice periods down to 90 nm. In large-period lattices, a well-defined quantum Hall effect is observed. Going to smaller antidot spacings the quantum Hall effect gradually disappears, following a geometric size effect. Lattices with narrow constrictions between the antidots behave as networks of nanoribbons, showing a high-resistance state and a transport gap of a few mV around the Dirac point. We observe pronounced weak localization in the magnetoresistance, indicating strong intervalley scattering at the antidot edges. The area of phase-coherent paths is bounded by the unit cell size at low temperatures, so each unit cell of the lattice acts as a ballistic cavity.Comment: some revisions, to appear in New Journal of Physics, Special Issue Graphen

Subtleties of witnessing quantum coherence in non-isolated systems

Identifying non-classicality unambiguously and inexpensively is a long-standing open challenge in physics. The No-Signalling-In-Time protocol was developed as an experimental test for macroscopic realism, and serves as a witness of quantum coherence in isolated quantum systems by comparing the quantum state to its completely dephased counterpart. We show that it provides a lower bound on a certain resource-theoretic coherence monotone. We go on to generalise the protocol to the case where the system of interest is coupled to an environment. Depending on the manner of the generalisation, the resulting witness either reports on system coherence alone, or on a disjunction of system coherence with either (i) the existence of non-classical system-environment correlations or (ii) non-negligible dynamics in the environment. These are distinct failure modes of the Born approximation in non-isolated systems.Comment: 16pp, 2 figs, 5 thms. v2: typos corrected, references added and small change to title to reflect that of published versio