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arXiv:1909.05251 · Physical Review Letters

Energy Drag in Particle-Hole Symmetric Systems as a Quantum Quench

William Berdanier, Thomas Scaffidi, Joel E. Moore

Published Dec 13, 2019• 12 citations
arXivHTMLPDF

Abstract

Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry-for instance, the half filled Hubbard model or graphene near the Dirac point-the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analog, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's golden rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.

DOI
10.1103/physrevlett.123.246603

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Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry-for instance, the half filled Hubbard model or graphene near the Dirac point-the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analog, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's golden rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.
In the situation of two electrostatically coupled conductors, a current in one conductor may induce a current in the other one. We will study this phenomenon, called Coulomb drag, in the Hubbard chain where the two 'conductors' are given by fermions with different spin orientations. With the aid of a Monte Carlo approach, which we presented in a recent paper, we calculate the trans-conductance in different variants of the Hubbard chain (with/without impurity and additional (long-ranged) interactions) for different fillings.
Charge carriers moving in a quantum wire may induce, via the Coulomb interaction and momentum conservation, a drag current in another quantum wire located nearby. In addition, tunnelling of carriers between the two parallel wires is considered. For spinless carriers the problem can be mapped onto the one-dimensional Hubbard model. The exact solution of the Hubbard chain and conformal field theory are used to calculate the critical exponents for the temperature dependence of the drag current between the two wires. The exponents are non-universal and depend on the interaction strength, the band filling and the tunnelling amplitude. For a repulsive interaction the drag current is opposite to the driving current, while for an attractive interaction they are parallel.
We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length LLL attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors acquire energy gap MMM. At energies larger than $\ensuremath{\Gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{const}\ifmmode\times\else\texttimes\fi{}{v}_{\ensuremath{-}}\mathrm{exp}(\ensuremath{-}LM/{v}_{\ensuremath{-}})/L+{\ensuremath{\Gamma}}_{+}$, where ${\ensuremath{\Gamma}}_{+}$ is the impurity scattering rate, and, for $L>{v}_{\ensuremath{-}}/M$, where ${v}_{\ensuremath{-}}$ is the fluctuation velocity, the gap leads to an ``ideal'' drag with almost equal currents in the conductors. At low energies the drag is suppressed by coherent instanton tunneling, and the zero-temperature transconductance vanishes, indicating the Fermi-liquid behavior.
We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.
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This thesis focuses on several examples of strongly correlated electronic quantum fluids. In chapter 2 we use a kinetic theory approach to describe the transport properties of bilayer graphene near charge neutrality. After solving the semiclassical Boltzmann equation, we find that the results are well approximated by a hydrodynamic two-fluid model. A fluid of electrons and a fluid of holes interact with each other via Coulomb drag. Chapter 3 looks at quantum Hall edges. We consider a quantum Hall edge coupled to a driven quantum dot and compute the current on the edge downstream from the contact. We show that Coulomb interactions between the dot and the edge renormalize the charge in the current pulses. Chapter 4 focuses on the bilayer quantum Hall system. Two layers of quantum Hall fluid are separated by a variable distance. At large interlayer separation, we have two well-separated composite Fermi liquids and we consider the pairing between the two layers as the interlayer separation is decreased. We propose a new trial state for this paired phase of matter and use exact diagonalization numerics to investigate this proposal.