We consider the effect of weak nonmagnetic disorder on two chains of interacting fermions (with and without spins) coupled by interchain hopping. For the spinless case, interchain hopping increases localization for repulsive interactions but stabilizes the
s-wave superconducting phase for attractive interactions. For the case with spin, the
d-wave phase arising from purely repulsive interactions in the clean system is destroyed by an infinitesimal disorder, while for attractive interactions, the
s-wave superconductivity is more resistant to disorder than in the one-chain case. In each case we compute the localization length and the conductivity.
We analyze an anisotropic spin-1/2 two-leg ladder in the presence of various types of random perturbations. The generic phase diagram for the pure system, in a way similar to spin one chains, consists of four phases: an antiferromagnet, a Haldane gap or a singlet phase (depending on the sign of interchain coupling), and two
XY phases designated by
XY1 and
XY2. The effects of disorder depend crucially on whether it preserves
XY symmetry (random field along
z and random exchange) or not (random anisotropy or random
XY fields). In all cases we computed the new phase diagram and the correlation length for the disordered system. The ladder exhibits a remarkable stability to disorder with
XY symmetry. Not only the singlet phases but also the massless
XY1 phase are totally unaffected by disorder in stark contrast with the single chain case. Even in the presence of an external magnetic field breaking the spin gap most of the phase diagram (including the
XY point) remains unaffected by the disorder, again in opposition with the single chain case. This stabilization towards disorder is similar, albeit stronger, to the one occurring for fermionic ladders. On the other hand, the
XY2 phase is very strongly suppressed. Disorder breaking
XY symmetry has much stronger effects and most of the phases at the exception of the singlet one are now destroyed. Interestingly, the disordered
XY1 phase has a much shorter correlation length than the disordered
XY2 phase contrarily with the case of perturbations preserving the rotation symmetry around the
z axis. The ladder system is thus in fact much more anisotropic than its single chain counterpart with identical exchanges. Finally we examine the case of strong disorder or weak interchain exchange for
XY symmetric disorder. Close to the isotropic point, when the interchain exchange is increased the system undergoes a transition between two decoupled disordered spin-1/2 chains to a singlet ladder unaffected by disorder. For more
XY like systems, the transition occurs in two steps with a nondisordered
XY1 phase occurring between the decoupled chains and the singlet phase. Comparison with other disordered gapped systems such as spin one chains is discussed.
Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one-dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation-invariant system a so-called site-impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so-called bond-impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site-impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond-impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.
Abstract Using the density matrix renormalization group (DMRG) method, we study the quantum coherence in one‐dimensional disordered spin chains and Fermi systems. We consider in detail spinless fermions on a ring, and compare the influence of several kinds of impurities in a gapless and a dimerized, gapped system. In the translation‐invariant system a so‐called site‐impurity, which can be realized by a local potential or a modification of one link, increases for repulsive interaction, and decreases for attractive interaction, upon renormalization. The weakening of two neighbouring bonds, which is a realization of a so‐called bond‐impurity, on the other hand, is healed for repulsive interaction, but enhanced for intermediate attractive interactions. This leads to a strong suppression of the quantum coherence measured by the phase sensitivity, but not to localization. Adding a local distortion to a dimerized system, we find that even the presence of a single site‐impurity increases the metallic region found in the dimerized model. For a strong dimerization and a high barrier, an additional sharp maximum, is seen in the phase sensitivity as a function of interaction, already for systems with about 100 sites. A bond‐impurity in the dimerized system also opens a small metallic window in the otherwise isolating regime.
The phase diagram of two bosonic chains coupled by interchain hopping and interchain boson-boson repulsion is investigated by means of bosonization and renormalization-group techniques. It comprises two types of charge-density waves, a conventional superfluid phase, and a superfluid phase made of condensed boson pairs. The effect of a random potential on that system is also derived. Compared with the one-chain case, interchain hopping strongly stabilizes the conventional superfluid phase with respect to Anderson localization. By contrast, the superfluid phase made of condensed boson pairs is much more unstable with respect to Anderson localization than the superfluid phase of the one-chain system. An exact mapping of the two strongly correlated bosonic chains onto two coupled vortex planes gives us the phase diagram of the latter system without any further calculation. The vortex system exhibits two types of vortex lattice phase (one with entanglement and another one without entanglement), a normal phase and a phase with bound pairs of vortices. The results for Anderson localization of the bosons allow us to study vortex pinning by columnar defects or twin boundaries and obtain the correlation length of the pinned vortex lattice. We show that interplane vortex hopping strongly reduces vortex pinning by columnar defects but not by twin boundaries. We obtain the melting temperature of the entangled solid. We also derive the critical current by modified Larkin-Ovchinnikov arguments and find a very sharp decrease of critical currents when the system moves into the entangled phase in the case of columnar pins. For strong columnar pins, there is a transition into a pinned solid phase with dislocations. We argue that two multicritical points may exist in the phase diagram.
The effect of a weak random potential on two-leg Hubbard ladders is investigated. The random potential is shown to induce Anderson localization except for attractive enough interactions, supressing completely d-wave superconductivity. These localization effects remain very strong even for many ladders coupled by Josephson coupling. Both dc and ac conductivities and localization lengths are obtained. Consequences for the superconducting ladder compound SrxCa14−xCu24O41+δ are discussed. The two-chain Hubbard ladder is a toy model of a metal with a spin-gap, reminiscent of the metallic phase of underdoped cuprates. Recent experiments[1] on the superconducting transition in Sr14−xCaxCu24O41 have been interpreted in the framework of this model. However, impurities are only considered as a source of holes and not a source of random potential although it is known that an infinitesimal disorder localizes all electronic states in one dimension. It is therefore important to investigate the disordered Hubbard ladder. The disordered Hubbard ladder is defined by the Hamiltonian: H = −t ‖ (c † i+1,p,σci,p,σ + c † i,p,σci+1,p,σ) − t⊥ i,p,σ i,σ