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Register a new userLuttinger liquids coupled by hopping
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Added by
Andre-Marie Tremblay
Publication date
1996
fields
Physics
and research's language is
English
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The stability of the Luttinger liquid to small transverse hopping has been studied from several points of view. The renormalization group approach in particular has been criticized because it does not take explicitly into account the difference between spin and charge velocities and because the interaction should be turned-on before the transverse hopping if the stability of the Luttinger liquid is a non-perturbative effect. An approach that answers both of these objections is explained here. It shows that the Luttinger liquid is unstable to arbitrarily small transverse hopping. The crossover temperatures below which either transverse coherent band motion or long-range order start to develop can be finite even when spin and charge velocities differ. Explicit scaling relations for these one-particle and two-particle crossover temperatures are derived in terms of transverse hopping, spin and charge velocities and anomalous exponents. The renormalization group results are recovered as special cases when spin and charge velocities are identical. The results compare well with recent experiments presented at this conference. Magnetic field effects are alluded to.
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One--particle interchain hopping in a system of coupled Luttinger liquids is investigated by use of exact diagonalizations techniques. Firstly, the two chains problem of spinless fermions is studied in order to see the behaviour of the band splitting as a function of the exponent $alpha$ which characterizes the $1D$ Luttinger liquid. Moderate intra-chain interactions can lead to a strong reduction of this splitting. The on-set of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by $alpha$. We give numerical evidence that inter-chain coherent hopping can be totally suppressed for $alphasim 0.4$ or even smaller $alpha$ values. The transverse conductivty is shown to exhibit a strong incoherent part. Even when coherent inter-chain hopping is believed to occur (at small $alpha$ values), it is shown that the coherent Drude weight is always significantly smaller than the incoherent weight. Implications for the optical experiments in quasi-1D organic or high-$T_c$ superconductors is outlined.
We study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub Bose-Luttinger liquids, which in some respects can be regarded as boson
Using functional renormalization group methods, we present a self-consistent calculation of the true Fermi momenta k_F^a (antibonding band) and k_F^b (bonding band) of two spinless interacting metallic chains coupled by small interchain hopping. In the regime where the system is a Luttinger liquid, we find that Delta = k_F^b - k_F^a is self-consistently determined by Delta = Delta_{1} [ 1 + {g}_0^2 ln (Lambda_0 / Delta)^2]^{-1} where g_0 is the dimensionless interchain backscattering interaction, Delta_{1} is the Hartree-Fock result for k_F^{b}-k_F^a, and Lambda_0 is an ultraviolet cutoff. If {g}_0^2 ln (Lambda_0 / Delta_{1})^2 is much larger than unity than even weak interachain backscattering leads to a strong reduction of the distance between the Fermi momenta.
We show that chiral co-propagating Luttinger liquids can be created and tuned by shining high frequency, circularly polarized light, normal to the layers, with different polarizations on two sections of bilayer graphene. By virtue of the broken time-reversal symmetry and the resulting mismatch of Chern number, the one-dimensional chiral modes are localized along the domain wall where the polarization changes. Single layer graphene hosts a single chiral edge mode near each Dirac node, whereas in bilayer graphene, there are two chiral modes near each of the Dirac nodes. These modes, under a high-frequency drive, essentially have a static charge distribution and form a chiral Luttinger liquid under Coulomb interaction, which can be tuned by means of the driving parameters. We also note that unlike the Luttinger liquids created by electrostatic confinement in bilayer graphene, here there is no back-scattering, and hence our wires along the node are stable to disorder.
We study electronic phase competition in a system of three coupled spinless Luttinger liquids using abelian bosonization, together with a perturbative renormalization group (RG) analysis. The scaling procedure generates off-diagonal contributions to the phase stiffness matrix, which require both rescaling as well as large rotations of the fields. These rotations, generally non-abelian in nature, are important for correctly obtaining the dominant electronic orders and critical behavior in different parameter regimes. They generate a coupling between different interaction channels even at the tree-level order in the coupling constant scaling equations. We study competing phases in this system, taking into account the aforementioned rotations, and determine its critical behavior in a variety of interaction parameter regimes where perturbative RG is possible. The phase boundaries are found to be of the Berezinskii-Kosterlitz-Thouless (BKT) type, and we specify the parameter regimes where valley-symmetry breaking, chiral orders, and restoration of $C_{3}$ symmetry may be observed. We discuss experimental systems where our approach and findings may be relevant.
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