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arXiv:2011.04561 · Physical review. B./Physical review. B

Universal conductance of a PT -symmetric Luttinger liquid after a quantum quench

Cătălin Paşcu Moca, Balázs Dóra

Published Sep 17, 2021• 13 citations
arXivHTMLPDF

Abstract

We study the nonequilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular light cone, we find a universal conductance ${e}^{2}/h$, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution with a Hermitian LL Hamiltonian, the conductance is heavily renormalized by the Hermitian interaction as ${e}^{2}/hK$ with $K$ the LL parameter. Our analytical results are tested numerically, confirming the universality of the conductance in the non-Hermitian realm.

DOI
10.1103/physrevb.104.125124

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We study the nonequilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular light cone, we find a universal conductance e2/h{e}^{2}/he2/h, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution with a Hermitian LL Hamiltonian, the conductance is heavily renormalized by the Hermitian interaction as e2/hK{e}^{2}/hKe2/hK with KKK the LL parameter. Our analytical results are tested numerically, confirming the universality of the conductance in the non-Hermitian realm.
A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behavior in the non-Hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-Hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that are multiples of the conventional light cone velocity. This behavior is argued to be generic for correlators in non-Hermitian systems. In the long time limit, we find typical LL behavior, extending the LL universality to the nonequilibrium, non-Hermitian case. Our analytical results are benchmarked numerically and indicate that the dispersal of quantum information is much faster in non-Hermitian systems.
The quantized conductance was produced due to dissipation within the Luttinger liquid from the parity inversion and time reversal symmetric interaction. For unitary time with Hermitian Luttinger liquid Hamiltonian and produced nonequilibrium conductivity and was renormalized due to interaction. We have studied the nonequilibrium dynamics and transport of parity inversion symmetric Luttinger liquid and the model was quenched from domain wall. The study was extended to initial ground state of a Hermitian interacting Luttinger liquid. We have used the model using the time evolving block decimation and have found the conductance inside the light core and depended on post-quench Hamiltonian and was quantized when the system was quenched to the non Hermitian Hamiltonian. The conductance was found when the system was quenched from an interacting initial state and showed that the initial state had no effect on conductance. The strength of the initial or final interactions in the case of Hermitian dynamics showed the quenched displayed a conductance that remained universal.
Properties of one-dimensional (1D) transport strongly depend on the proper choice of boundary conditions. It has been frequently stated that the Luttinger-liquid (LL) conductance is renormalized by the interaction as ge2{ge}^{2}ge2/h. To contest this result I develop a model of 1D LL wire with the interaction switching off at the infinities. Its solution shows that there is no renormalization of the universal conductance while the electrons have a free behavior in the source and drain reservoirs.
We provide evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: the leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density-matrix renormalization group.
The transport dynamics of a quenched Luttinger liquid tunnel-coupled to a fermionic reservoir is investigated. In the transient dynamics, we show that for a sudden quench of the electron interaction universal power-law decay in time of the tunneling current occurs, ascribed to the presence of entangled compound excitations created by the quench. In sharp contrast to the usual nonuniversal power-law behavior of a zero-temperature nonquenched Luttinger liquid, the steady-state tunneling current is Ohmic and can be explained in terms of an effective quench-activated heating of the system. Our study unveils an unconventional dynamics for a quenched Luttinger liquid that could be identified in quenched cold Fermi gases.
We study the relaxation dynamics of the one-dimensional Tomonaga–Luttinger model after an interaction quench, paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical forms are investigated that all lead to universal Luttinger liquid (LL) physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the LL phenomenology. For generic regular potentials, the large time decay of the momentum distribution function toward the steady-state value is characterized by a power law with a universal exponent that depends only on the potential at zero momentum transfer. The commonly employed ad hoc procedure fails to give this exponent. In addition to quenches from zero to positive interactions, we also consider the abrupt changes in the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and that obtained in equilibrium at equal two-particle interaction.