We study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL's) as a model for stripes in high- ${T}_{c}$ compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi-long-ranged along the stripes and short ranged in the transversal direction.We study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL's) as a model for stripes in high-${T}_{c}$ compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi-long-ranged along the stripes and short ranged in the transversal direction.

arXiv:cond-mat/0110265Physical review. B, Condensed matterMay 30, 20022 citations

Quantum Interference in Luttinger Liquids

E. A. Jagla, C. A. Balseiro

Springer eBooksJan 1, 19940 citations

Momentum-Space Entanglement and Loschmidt Echo in Luttinger Liquids after a Quantum Quench

Balázs Dóra, Rex Lundgren, Mark Selover +1 more

Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e., the overlap of the disentangled and final wave functions of the system. The second largest eigenvalue is the overlap of the first excited state of the disentangled system with zero total momentum and the final wave function. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e., the overlap of the disentangled and final wave functions of the system. The second largest eigenvalue is the overlap of the first excited state of the disentangled system with zero total momentum and the final wave function. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.

arXiv:1603.01997Physical Review LettersJun 29, 201617 citations

Quantum Monte Carlo Studies of Luttinger Liquids

Adrian Del Maestro

Bulletin of the American Physical SocietyMar 19, 20100 citations

We study effects of quenched disorder on coupled two-dimensional arrays of Luttinger liquids (LL's) as a model for stripes in high-

{T}_{c}

compounds. In the framework of a renormalization-group analysis, we find that weak inter-LL charge-density-wave couplings are always irrelevant as opposed to the pure system. By varying either disorder strength, intra- or inter-LL interactions, the system can undergo a delocalization transition between an insulator and a strongly anisotropic metallic state with LL-like transport. This state is characterized by short-ranged charge-density-wave order, the superconducting order is quasi-long-ranged along the stripes and short ranged in the transversal direction.