Imke Schneider

Wigner crystal versus Friedel oscillations in the one-dimensional Hubbard model

We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical density matrix renormalization group calculations. For finite systems we find a relatively sharp crossover even for moderate short-range interactions into a region with 4kF density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultracold fermionic gases in optical lattices and in finite quantum wires.

Real-time dynamics in the one-dimensional Hubbard model

We consider single-particle properties in the one-dimensional repulsive Hubbard model at commensurate fillings in the metallic phase. We determine the real-time evolution of the retarded Greens function by matrix-product state methods. We find that at sufficiently late times the numerical results are in good agreement with predictions of nonlinear Luttinger liquid theory. We argue that combining the two methods provides a way of determining the single-particle spectral function with very high frequency resolution.

Two-bath spin-boson model: Phase diagram and critical properties

The spin-boson model, describing a two-level system coupled to a bath of harmonic oscillators, is a generic model for quantum dissipation, with manifold applications. It has also been studied as a simple example for an impurity quantum phase transition. Here, we present a detailed study of a U(1)-symmetric two-bath spin-boson model, where two different components of an SU(2) spin

Recursive method for the density of states in one dimension.

\frac{1}{2}

Spin-charge-separated quasiparticles in one-dimensional quantum fluids

are coupled to separate dissipative baths. Nontrivial physics arises from the competition of the two dissipation channels, resulting in a variety of phases and quantum phase transitions. We employ a combination of analytical and numerical techniques to determine the properties of both the stable phases and the quantum critical points. In particular, we find a critical intermediate-coupling phase which is bounded by a continuous quantum phase transition which violates the quantum-to-classical correspondence.

Two-channel pseudogap Kondo and Anderson models: Quantum phase transitions and non-Fermi liquids

We derive a powerful yet simple method for analyzing the local density of states (DOS) in gapless one-dimensional fermionic systems, including extensions such as momentum dependent interaction parameters and hard-wall boundaries. We study the crossover of the local DOS from individual density waves to the well-known asymptotic power laws and identify characteristic signs of spin charge separation in possible STM experiments. For semi-infinite systems a closed analytic expression is found in terms of hypergeometric functions.

Local density of states for individual energy levels in finite quantum wires.

We revisit the problem of dynamical response in spin-charge separated one dimensional quantum fluids. In the framework of Luttinger liquid theory, the dynamical response is formulated in terms of noninteracting bosonic collective excitations carrying either charge or spin. We argue that, as a result of spectral nonlinearity, long-lived excitations are best understood in terms of generally strongly interacting fermionic holons and spinons. This has far reaching ramifications for the construction of mobile impurity models used to determine threshold singularities in response functions. We formulate and solve the appropriate mobile impurity model describing the spinon threshold in the single-particle Greens function. Our formulation further raises the question whether it is possible to realize a model of noninteracting fermionic holons and spinons in microscopic lattice models of interacting spinful fermions. We investigate this issue in some detail by means of density matrix renormalization group (DMRG) computations.

Low-energy local density of states of the 1D Hubbard model

We discuss the two-channel Kondo problem with a pseudogap density of states,

Highest weight state description of the isotropic spin-1 chain

\rho(\w)\propto|\w|^r

Even-odd effect in short antiferromagnetic Heisenberg chains

, of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic