Sam T. Carr

Full counting statistics in the self-dual interacting resonant level model

We present a general technique to obtain the zero temperature cumulant generating function of the full counting statistics of charge transfer in interacting impurity models out of equilibrium from time-dependent simulations on a lattice. We demonstrate the technique with application to the self-dual interacting resonant level model, where very good agreement between numerical simulations using the density matrix renormalization group and those obtained analytically from the thermodynamic Bethe ansatz is found. We show from the exact form of counting statistics that the quasiparticles involved in transport carry charge 2e in the low bias regime and e/2 in the high bias regime.

Effect of a local perturbation in a fermionic ladder.

We study the effect of a local external potential on a system of two parallel spin-polarized nanowires placed close to each other. For single-channel nanowires with repulsive interaction we find that transport properties of the system are highly sensitive to the transverse gradient of the perturbation: the asymmetric part completely reflects the electrons leading to vanishing conductance at zero temperature, while the flat potential remains transparent. We envisage a possible application of this unusual property in the sensitive measurement of local potential field gradients.

Phase diagram of two interacting helical states

We consider two coupled time-reversal-invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low-energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges.We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spin-nematic phase. However, in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities.

Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling

We present analysis of a single channel interacting quantum wire problem in the presence of spin-orbit interaction. The spin-orbit coupling breaks the spin-rotational symmetry from SU(2) to U(1) and breaks inversion symmetry. The low-energy theory is then a two band model with a difference of Fermi velocities

Lifshitz transitions and crystallization of fully polarized dipolar fermions in an anisotropic two-dimensional lattice

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Full counting statistics in the not-so-long-time limit

. Using bosonization and a two-loop renormalization group procedure we show that electron-electron interactions can open a gap in the spin sector of the theory when the interaction strength

Transport through nanostructures: Finite time versus finite size

U

Superfluid, solid, and supersolid phases of dipolar bosons in a quasi-one-dimensional optical lattice

is smaller than

Helical quantum Hall Edge modes in bilayer graphene: a realization of quantum spin-ladders

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Effect of paramagnetic fluctuations on a Fermi-surface topological transition in two dimensions

in appropriate units. For repulsive interactions, the resulting strong coupling phase is of the spin-density-wave type. We show that this phase has peculiar emergent topological properties. The gapped spin sector behaves as a topological insulator, with zero-energy edge modes with fractional spin. On the other hand, the charge sector remains critical, meaning the entire system is metallic. However, this bulk electron liquid as a whole exhibits properties commonly associated with the one-dimensional edge states of two-dimensional spin-Hall insulators, in particular, the conduction of