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arXiv:1906.02637 · Physical Review Letters

Quantum Quench in P T -Symmetric Luttinger Liquid

Balázs Dóra, Cătălin Paşcu Moca

Published Mar 31, 2020• 50 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.136802

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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.
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.
We study operator correlations of a spinful Luttinger liquid after introducing a non-Hermitian interaction quench, yielding supersonic modes and dominant superconducting correlations as signatures of the nonunitary dynamics as well as spin-charge separation. A comparative analysis with the Hermitian counterpart, i.e., when the quench is Hermitian, shows a significant difference in the behavior of the model. We derive exact expressions for different operator correlations and show that the superconducting correlations decay slower than the charge and spin density wave correlations, especially within the short-time limit, and at the long-time limit all the operator correlations merge differed only by phase factors in the case of non-Hermitian interaction quench whereas they do not merge in the case of Hermitian interaction quench. In both cases known Luttinger liquid universality is retained at the long-time limit. We also analyze how the dynamics of operator correlations vary in the presence of anisotropy in the quenching parameters.
We study the nonequilibrium dynamics of the Luttinger model after suddenly turning on and off the bare Coulomb interaction between the fermions. We analyze several correlation functions such as the one particle density matrix and vertex correlations, its finite time dynamics, and the stationary state limit. Correlations exhibit a nonlinear light-cone effect: The spreading of the initial signal accelerates as a consequence of the quantum nature of the excitations, whose peculiar dispersion of plasmonic type in one dimension (1D) gives rise to a logarithmic divergence in the group velocity at q=0q=0q=0. In addition, we show that both the static and dynamic stationary state correlations can be reproduced with a simple generalized Gibbs ensemble despite the long-range character of the interactions which precludes the application of the Lieb-Robinson bounds. We propose a suitable experimental setup in which these effect can be observed based on ultracold ions loaded on linear traps.
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.
We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical Hermitian system, is time evolved with a non-Hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic of non-Hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as 1/x21/{x}^{2}1/x2, in sharp contrast to the usual 1/x1/x1/x decay of noninteracting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of nonlocal quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.
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.