Quantum physics in one dimension

  title={Quantum physics in one dimension},
  author={Thierry Giamarchi},
1. Peculiarities of d=1 2. Bosonization 3. Luttinger liquids 4. Refinements 5. Microscopic methods 6. Spin 1/2 chains 7. Interacting fermions on a lattice 8. Coupled fermionic chains 9. Disordered systems 10. Boundaries and isolated impurities 11. Significant others A. Basics of many body B. Not so important fine technical points C. Correlation functions D. Bosonization directory E. Sine-Gordon F. Numerical solution 

Fundamental aspects of electron correlations and quantum transport in one-dimensional systems

Table of contents 1. Introduction 2. Non-Fermi-liquid features of Fermi liquids: 1D physics in higher dimensions 3. Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model 4. Renormalization

Spectral functions of strongly interacting isospin-1/2 bosons in one dimension.

It is argued that the low-energy spectrum of the one-dimensional (iso)spin-1/2 bosons in the regime of strong repulsive interactions consists of acoustic density waves and the spin excitations described by an effective ferromagnetic spin chain with a small exchange constant J.

Spin 1/2 fermions on spin-dependent optical lattices

We study the phase diagram of one dimensional spin- 12 fermionic cold atoms. The two “spin” species can have different hopping or mass. The phase diagram at equal densities of the species is found to

Bosonization out of equilibrium

We develop a bosonization technique for one-dimensional fermions out of equilibrium. The approach is used to study a quantum wire attached to two electrodes with arbitrary energy distributions. The

Almost Perfect Metals in One Dimension.

We show that a one-dimensional quantum wire with as few as two channels of interacting fermions can host metallic states of matter that are stable against all perturbations up to qth order in fermion

Full counting statistics in the spin-1/2 Heisenberg XXZ chain

The spin-1/2 Heisenberg chain exhibits a quantum critical regime characterized by quasi long-range magnetic order at zero temperature. We quantify the strength of quantum fluctuations in the ground

Fractionalization Waves in Two-Dimensional Dirac Fermions: Quantum Imprint from One Dimension.

A simple measurement is proposed for an ultracold matter system, in which correlations in initially decoupled 1D chains are imprinted via quantum quench upon two-dimensional Dirac fermions.

Critical phenomena in one dimension from a Bethe ansatz perspective

This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase

Supersolids in confined fermions on one-dimensional optical lattices

Using quantum Monte Carlo simulations, we show that density-density and pairing correlation functions of the one-dimensional attractive fermionic Hubbard model in a harmonic confinement potential are

Density waves in strongly correlated quantum chains

Abstract We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fröhlich, Su-Schrieffer-Heeger, and