38,140 research outputs found
Coupled Luttinger Liquids
Many one--dimensional quantum systems, in particular interacting electron and
spin systems, can be described a Luttinger liquids. Here, some basic ideas of
this picture of one--dimensional systems are briefly reviewed. I then discuss
the effect of interchain coupling for a finite number of parallel chains. In
the case of spin chains coupled by exchange interactions, the low--energy
properties are radically different according to whether the number of coupled
chains is even or odd: even number of chains have a gap in the spin
excitations, whereas odd numbers of chains are gapless. The effect of
interchain tunneling is analyzed for two and three coupled chains of itinerant
fermions: for repulsive interactions, the two--chain system is ``universally''
found to be a d--wave superconductor, with a gap in the spin excitation
spectrum. On the other hand, for three chains the ground state depends both on
the boundary conditions in the transverse direction and on the strength of the
interactions. Weak repulsive interactions in all cases lead to dominant
superconducting pairing of d--type. An example of a three--leg spin ladder with
a spin gap is proposed. A general scheme to keep track of fermion
anticommutation in the bosonization technique is developed.Comment: 14 pages, Revtex with epsf, 3 figures included as Postscript files,
Rencontres de Moriond, Les Arcs, France, Jan. 199
Collective Diffusion and a Random Energy Landscape
Starting from a master equation in a quantum Hamiltonian form and a coupling
to a heat bath we derive an evolution equation for a collective hopping process
under the influence of a stochastic energy landscape. There results different
equations in case of an arbitrary occupation number per lattice site or in a
system under exclusion. Based on scaling arguments it will be demonstrated that
both systems belong below the critical dimension to the same universality
class leading to anomalous diffusion in the long time limit. The dynamical
exponent can be calculated by an expansion. Above the
critical dimension we discuss the differences in the diffusion constant for
sufficient high temperatures. For a random potential we find a higher mobility
for systems with exclusion.Comment: 15 pages, no figure
Quantum fluctuations in the spiral phase of the Hubbard model
We study the magnetic excitations in the spiral phase of the two--dimensional
Hubbard model using a functional integral method. Spin waves are strongly
renormalized and a line of near--zeros is observed in the spectrum around the
spiral pitch . The possibility of disordered spiral states is
examined by studying the one--loop corrections to the spiral order parameter.
We also show that the spiral phase presents an intrinsic instability towards an
inhomogeneous state (phase separation, CDW, ...) at weak doping. Though phase
separation is suppressed by weak long--range Coulomb interactions, the CDW
instability only disappears for sufficiently strong Coulomb interaction.Comment: Figures are NOW appended via uuencoded postscript fil
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