Electron-phonon interaction and phonon dynamics in one-dimensional conductors: Spinless fermions

Long-range order in quasi-one-dimensional conductors

We study the formation of the charge-density wave long-range order in a system of repulsive 1D electrons coupled to 3D phonons. We show that the charge-density wave can be stabilized by interaction with phonons in quasi-1D crystals and semiconducting nanowires. In the case of metallic atomic chains, interaction with phonons of a 3D substrate is not enough, and violation of the translational invariance by commensurable perturbation or disorder is needed. The possibility of stabilization of superconductivity in 1D electrons with attraction by means of tunnel coupling to a 3D metal is considered.

Dissipation-driven quantum phase transitions in a Tomonaga-Luttinger liquid electrostatically coupled to a metallic gate

The dissipation induced by a metallic gate on the low-energy properties of interacting 1D electron liquids is studied. As a function of the distance to the gate, or the electron density in the wire, the system can undergo a quantum phase transition from a Tomonaga-Luttinger liquid to two kinds of dissipative phases, one of them with a finite spatial correlation length. We also define a dual model, which describes an attractive one-dimensional metal with a Josephson coupling to a dirty metallic lead.

Luttinger liquid of polarons in one-dimensional boson-fermion mixtures

We use the bosonization approach to investigate quantum phases of boson-fermion mixtures (BFM) of atoms confined to one dimension by an anisotropic optical lattice. For a BFM with a single species of fermions we find a charge-density wave phase, a fermion pairing phase, and a phase separation regime. We also obtain the rich phase diagram of a BFM with two species of fermions. We demonstrate that these phase diagrams can be understood in terms of polarons, i.e., atoms "dressed" by screening clouds of the other atom species. Techniques to detect the resulting quantum phases are discussed.

Phase diagram of an asymmetric spin ladder

We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.