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arXiv:2205.12970 · Physical review. B./Physical review. B

Tunable transport in the mass-imbalanced Fermi-Hubbard model

Philip Zechmann, Alvise Bastianello, Michael Knap

Published Aug 5, 2022• 13 citations
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Abstract

Transport dominates the late-time dynamics of quantum many-body systems with conserved quantities and is described by the laws of hydrodynamics. Within the framework of a quantum kinetic theory, the authors study the recently experimentally realized mass-imbalanced Fermi-Hubbard model in one dimension and investigate the emergence of diffusive hydrodynamics. Excellent agreement with both tensor network computations and experimental data is found. Furthermore, they analyze the influence of external potentials and show that the presence of a tilt gives rise to a more exotic type of subdiffusive transport.

DOI
10.1103/physrevb.106.075115

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Transport dominates the late-time dynamics of quantum many-body systems with conserved quantities and is described by the laws of hydrodynamics. Within the framework of a quantum kinetic theory, the authors study the recently experimentally realized mass-imbalanced Fermi-Hubbard model in one dimension and investigate the emergence of diffusive hydrodynamics. Excellent agreement with both tensor network computations and experimental data is found. Furthermore, they analyze the influence of external potentials and show that the presence of a tilt gives rise to a more exotic type of subdiffusive transport.
We study transport in the one-dimensional mass-imbalanced Fermi-Hubbard model in the high-temperature limit, focusing on the case of strong interactions. Prior theoretical and experimental investigations have revealed unconventionally long transport timescales, with complications due to strong finite-size effects. We compute the dynamical current-current correlation function directly in the thermodynamic limit using infinite tensor network techniques. We show that transport in the strong-imbalance limit is dominated by AC resonances, which we compute with an analytic expansion. We study the dephasing of these resonances with mass imbalance, $\ensuremath{\eta}$. In the small-imbalance limit, the model is nearly integrable. We connect these unusual limits by computing the DC conductivity and transport decay time as a function of $\ensuremath{\eta}$ and the interaction strength U/tU/tU/t. We propose an experimental protocol to measure these correlation functions in cold atom experiments.
Constraints in the dynamics of quantum many-body systems can dramatically alter transport properties and relaxation timescales even in the absence of static disorder.Here, we report on the observation of such constrained dynamics arising from the distinct mobility of two species in the one-dimensional massimbalanced Fermi-Hubbard model, realized with ultracold ytterbium atoms in a state-dependent optical lattice.By displacing the trap potential and monitoring the subsequent dynamical response of the system, we identify suppressed transport and slow relaxation with a strong dependence on the mass imbalance and interspecies interaction strength, consistent with eventual thermalization for long times.Our observations demonstrate the potential for quantum simulators to provide insights into unconventional relaxation dynamics arising from constraints.
We study three aspects of quantum nonequilibrium dynamics; (1) transport of conserved quantities, (2) entanglement spreading, and (3) construction of local operators which slowly relax to thermal equilibrium. Motivated by recent progresses in ultracold atom experiments, we first analyze transport phenomena of a population imbalanced two-component fermi gas with arbitrary strength of inter-species interaction in three dimension. Using the Boltzmann kinetic equation at dilute regime, we obtain the transport coefficients of linear responses to gradients of temperature and chemical potential imbalance. We identify the magneto-caloric effects, and determine how these effects depend on interaction strength and population imbalance. Then, we propose an experimental protocol to observe these effects in an experiment with ultracold atoms. Next, we study entanglement spreading in a one-dimensional quantum Ising chain with longitudinal and transverse fields, which is diffusive and nonintegrable. Fully diagonalizing the Hamiltonian matrix, we explicitly show that the entanglement spreading is ballistic, thus faster than diffusive transport of conserved quantities. We provide a local spreading picture of entanglement entropy in terms of logarithmic negativity. Then, we discuss a role of energy conservation in entanglement spreading through analyzing a Floquet system. Lastly, we construct local operators that relax slowly to equilibrium with the same one-dimensional Hamiltonian. By showing that the Hamiltonian satisfies the eigenstate thermalization hypothesis, we first conclude that this model relaxes local operators to thermal equilibrium. Then, we systematically construct local operators that relax slower than conventional diffusive modes.
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.
Hydrodynamics governs diverse collective phenomena in nature, from the expansion of a quarkgluon plasma to viscous electron flow in quantum materials. In strongly interacting hydrodynamic fluids, the transport of spin remains poorly understood. Here, we investigate spin transport in the hydrodynamic regime of a spin-imbalanced unitary Fermi gas confined in a uniform optical box. By quenching a spatially periodic optical potential that modulates both the density and spin polarization, we observe the relaxation of the many-body system, which determines both the spin diffusivity and the spin Seebeck/Peltier coefficients in a homogeneous quantum gas. Our measurements provide parameter-free benchmarks for microscopic theories and establish an ultracold atom platform for studying spin caloritronics in strongly correlated matter.