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arXiv:1903.10521 · Physical Review A

Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices

Yicheng Zhang, Lev Vidmar, Marcos Rigol

Published Jun 11, 2019• 23 citations
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Abstract

We study quantum quench dynamics in the Fermi-Hubbard model, and its $\mathrm{SU}(N)$ generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized N\'eel order, namely, initial states in which there is a periodic $N$-spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) N\'eel domain walls. Those correlations resemble the ones in the ground state of the $\mathrm{SU}(N)$ model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting $\mathrm{SU}(N)$ gas into the rapidity distribution after long times. Finally, we study equilibration in $\mathrm{SU}(N)$ gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated $\mathrm{SU}(N)$ fermions at large $U$.

DOI
10.1103/physreva.99.063605

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We study quantum quench dynamics in the Fermi-Hubbard model, and its SU(N)\mathrm{SU}(N)SU(N) generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized N'eel order, namely, initial states in which there is a periodic NNN-spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) N'eel domain walls. Those correlations resemble the ones in the ground state of the SU(N)\mathrm{SU}(N)SU(N) model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting SU(N)\mathrm{SU}(N)SU(N) gas into the rapidity distribution after long times. Finally, we study equilibration in SU(N)\mathrm{SU}(N)SU(N) gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated SU(N)\mathrm{SU}(N)SU(N) fermions at large UUU.
We study SU(N)\mathrm{SU}(N)SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.
We study the quantum relaxation dynamics for a lattice version of the one-dimensional (1D) NNN-flavor Gross-Neveu (GN) model after a Hamiltonian parameter quench. Allowing for a system-reservoir coupling γγγ, we numerically describe the system dynamics through a time-dependent self-consistent Lindblad master equation. For a closed (γ=0γ=0γ=0) finite-size system subjected to an interaction parameter quench, the order parameter dynamics exhibits oscillations and revivals. In the thermodynamic limit, our results imply that the order parameter reaches its post-quench stationary value in accordance with the eigenstate thermalization hypothesis (ETH). However, time-dependent finite-momentum correlation matrix elements equilibrate only if γ>0γ>0γ>0. Our findings are consistent with the system being described by a pertinent Generalized Gibbs Ensemble (GGE) and, accordingly, highlight subtle yet important aspects of the post-quench relaxation dynamics of quantum many-body systems.
We develop an exact approach to study the quench dynamics of hard-core bosons initially in thermal equilibrium in one-dimensional lattices. This approach is used to study the sudden expansion of thermal states after confining potentials are switched off. We find that a dynamical fermionization of the momentum distribution occurs at all temperatures. This phenomenon is studied for low initial site occupations, for which the expansion of the cloud is self-similar. In this regime, the occupation of the natural orbitals allows one to distinguish hard-core bosons from noninteracting fermions. We also study the free expansion of initial Mott insulating domains at finite temperature and show that the emergence of off-diagonal one-body correlations is suppressed gradually with increasing temperature. Surprisingly, the melting of the Mott domain is accompanied by an effective cooling of the system. We explain this phenomenon analytically using an equilibrium description based on an emergent local Hamiltonian.
We investigate the dynamics of correlation propagation in the one-dimensional Fermi-Hubbard model with SU(NNN) symmetry when the repulsive-interaction strength is quenched from a large value, at which the ground state is a Mott-insulator with 1/N1/N1/N filling, to an intermediate value. From approximate analytical insights based on a simple model that captures the essential physics of the doublon excitations, we show that entanglement in the initial state leads to collective enhancement of the propagation velocity vSU(N)v_{\text{SU}(N)}vSU(N)​ when N>2N>2N>2, becoming equal to the velocity of the Bose-Hubbard model in the large-NNN limit. These results are supported by numerical calculations of the density-density correlation in the quench dynamics for N=2,3,4,N=2,3,4,N=2,3,4, and 666.
Using the time-dependent density matrix renormalization-group method and exact diagonalization, we study the nonequilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the on-site interaction strength. We are particularly interested in the nonequilibrium evolution of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which, at finite spin polarizations and for attractive interactions, are the dominant two-body correlations in the ground state. For quenches from the noninteracting to the attractive regime, we investigate the dynamical emergence of FFLO correlations and their signatures in the pair quasi--momentum distribution function. We observe that the postquench double occupancy exhibits a maximum as the interaction strength becomes of the order of the bandwidth. Finally, we study quenches and ramps from attractive to repulsive interactions, which imprint FFLO correlations onto repulsively bound pairs. We show that a quite short ramp time is sufficient to wipe out the characteristic FFLO features in the postquench pair momentum distribution functions.
We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion; the asymptotic density dynamics is identical to that of initially localized, noninteracting particles, and the asymptotic velocity distribution is flat. The expansion velocity for initial correlated Mott insulating states is therefore independent of the interaction strength and particle statistics. Interestingly, this nonequilibrium dynamics is sensitive to the interaction driven quantum phase transition in the Bose-Hubbard model; while being constant in the Mott phase, the expansion velocity decreases in the superfluid phase and vanishes for large systems in the noninteracting limit. These results are compared to the setup of a recent experiment [Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013)], where the trap opening was combined with an interaction quench from infinitely strong interactions to finite values. In the latter case, the interaction quench breaks the universal dynamics in the asymptotic regime and the expansion depends on the interaction strength. We carry out an analogous analysis for a two-component Fermi gas, with similar observations. In addition, we study the effect of breaking the integrability of hard-core bosons in different ways; while the fast ballistic expansion from the ground state of Mott insulators in one dimension remains unchanged for finite interactions, we observe strong deviations from this behavior on a two-leg ladder even in the hard-core case. This change in dynamics bares similarities with the dynamics in the dimensional crossover from one to two dimensions observed in the aformentioned experimental study.