Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Impurity in a Luttinger liquid: A numerical study of the finite-size energy spectrum and of the orthogonality catastrophe exponent

Qin SJ, Yu L., M. Fabrizio

Published Jan 1, 1996• 0 citations
OpenAlex

Related papers

Anomalous orthogonality catastrophe for Luttinger liquid with repulsion

Alexander O. Gogolin

•Jan 1, 1993•0 citations

Impurity in a Luttinger liquid: A numerical study of the finite-size energy spectrum and of the orthogonality catastrophe exponent

Shaojin Qin, Michele Fabrizio, Lu Yu

The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density-matrix renormalization group. By analyzing the finite-size scaling behavior of the low-energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the exponent of the orthogonality catastrophe, which gives a further support to the above theoretical prediction.

arXiv:cond-mat/9608024•Physical review. B, Condensed matter•Oct 1, 1996•33 citations

Impurity in a Luttinger liquid away from half-filling : a numerical study

Masaki Oshikawa

•Jan 1, 1997•0 citations

Local perturbation in a Tomonaga-Luttinger liquid at g=1/2: Orthogonality catastrophe, Fermi-edge singularity, and local density of states

Akira Furusaki

The orthogonality catastrophe in a Tomonaga-Luttinger liquid with an impurity is reexamined for the case when the interaction parameter or the dimensionless conductance is $g=1/2.$ By transforming bosons back to fermions, the Hamiltonian is reduced to a quadratic form, which allows for explicit calculation of the overlap integral and the local density of states at the defect site. The exponent of the orthogonality catastrophe due to a backward scattering center is found to be 1/8, in agreement with previous studies using different approaches. The time dependence of the core-hole Green's function is computed numerically, which shows a clear crossover from a nonuniversal short-time behavior to a universal long-time behavior. The local density of states vanishes linearly in the low-energy limit at $g=1/2.$

arXiv:cond-mat/9702195•Physical review. B, Condensed matter•Oct 15, 1997•42 citations

Instability of a quasi-1D Luttinger liquid

V. S. Babichenko, Andrey Nikolaevich Kozlov

ZhETF Pisma Redaktsiiu•May 1, 1995•0 citations

Loschmidt Echo and the Many-Body Orthogonality Catastrophe in a Qubit-Coupled Luttinger Liquid

Balázs Dóra, Frank Pollmann, József Fortágh +1 more

We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry.

arXiv:1303.7169•Physical Review Letters•Jul 23, 2013•88 citations
The behavior of a single impurity in a one-dimensional Luttinger liquid is numerically investigated by means of the density-matrix renormalization group. By analyzing the finite-size scaling behavior of the low-energy spectrum, we confirm the theoretical prediction of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)] both for attractive and repulsive interactions. Moreover, we calculate the exponent of the orthogonality catastrophe, which gives a further support to the above theoretical prediction.
The orthogonality catastrophe in a Tomonaga-Luttinger liquid with an impurity is reexamined for the case when the interaction parameter or the dimensionless conductance is g=1/2.g=1/2.g=1/2. By transforming bosons back to fermions, the Hamiltonian is reduced to a quadratic form, which allows for explicit calculation of the overlap integral and the local density of states at the defect site. The exponent of the orthogonality catastrophe due to a backward scattering center is found to be 1/8, in agreement with previous studies using different approaches. The time dependence of the core-hole Green's function is computed numerically, which shows a clear crossover from a nonuniversal short-time behavior to a universal long-time behavior. The local density of states vanishes linearly in the low-energy limit at g=1/2.g=1/2.g=1/2.
We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry.