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arXiv:2105.12649 · Physical review. B./Physical review. B

Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics

Stefano Scopa, Pasquale Calabrese, Lorenzo Piroli

Published Sep 20, 2021• 23 citations
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Abstract

We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings in the time domain by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provide an exact description, at large space-time scales, for arbitrary temperature $T$, particle density, and interactions. At $T=0$ and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low $T>0$ effects of SCS survive and characterize explicitly the value of $T$ for which the two distinguishable excitations melt.

DOI
10.1103/physrevb.104.115423

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We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings in the time domain by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provide an exact description, at large space-time scales, for arbitrary temperature TTT, particle density, and interactions. At T=0T=0T=0 and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low T>0T>0T>0 effects of SCS survive and characterize explicitly the value of TTT for which the two distinguishable excitations melt.
We study nonhomogeneous quantum quenches in a one-dimensional gas of repulsive spin-1/21/21/2 fermions, as described by the integrable Yang-Gaudin model. By means of generalized hydrodynamics (GHD), we analyze in detail the real-time evolution following a sudden change of the confining potential. We consider in particular release protocols and trap quenches, including a version of the quantum Newton's cradle. At zero temperature, we employ a simplified phase-space hydrodynamic picture to characterize the dynamics of the particle- and spin-density profiles. Away from zero temperatures, we perform a thorough numerical study of the GHD equations, and provide quantitative predictions for different values of the temperature, external magnetic field, and chemical potential. We highlight the qualitative features arising due to the multicomponent nature of the elementary excitations, discussing in particular effects of spin-charge separation and dynamical polarization.
Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires.
We study the transport properties of a one-dimensional spinful Fermi gas, after a junction of two semi-infinite subsystems held at different temperatures. The ensuing dynamics is studied by analyzing the space-time profiles of local observables emerging at large distances xxx and times ttt, as a function of $\ensuremath{\zeta}=x/t$. At equilibrium, the system displays two distinct species of quasiparticles, naturally associated with different physical degrees of freedom. By employing the generalized hydrodynamic approach, we show that when the temperatures are finite no notion of separation can be attributed to the quasiparticles. In this case, the profiles can not be qualitatively distinguished by those associated to quasiparticles of a single species that can form bound states. On the contrary, signatures of separation emerge in the low-temperature regime, where two distinct characteristic velocities appear. In this regime, we analytically show that the profiles display a piecewise constant form and can be understood in terms of two decoupled Luttinger liquids.
The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
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One of the key features of one-dimensional systems is the phenomenon of spin–charge separation. We show this separation of spin and charge in real time in the 1D Hubbard model by the application of the adaptive time-dependent density-matrix renormalization group method. It is found for single particle excitations and density wave packets far beyond the low-energy Luttinger liquid theory. An experimental set-up is proposed on how to observe the spin–charge separation with ultracold Fermi gases in a harmonic trap using the presence of the Mott-insulator region. Quantitative estimates for experimental parameters are given.