Universal Spin Transport and Quantum Bounds for Unitary Fermions

Enss, Tilman; Thywissen, Joseph H.

doi:10.1146/annurev-conmatphys-031218-013732

Cited by 36 publications

(25 citation statements)

References 124 publications

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“…which agrees with previous literature [8]. The first term in (59) corresponds to Fick's law for SU (2), and encodes the diffusive behavior of the spin two-point function at long time.…”

Section: The Action Of Non-abelian Hydrodynamicssupporting

confidence: 89%

“…We emphasize that there is no contradiction between (8) and ( 9). Yet, in some sense, there is an intuitive tension about how (8) and ( 9) might both arise in hydrodynamics, where we aim to describe the slow dynamics of the densities of conserved quantities. How can we keep track of all the densities of conserved charges, if no quantum state actually has a definite charge (eigenvalue) under all Q A ?…”

Section: Non-abelian Continuous Symmetrymentioning

confidence: 99%

“…This paper is about the hydrodynamics of systems with continuous non-Abelian symmetries. Physical realizations include flavor charge in quark-gluon plasma [4] (or color charge at high temperatures), spin-orbit coupled solid-state systems [5,6], and SU(2)-symmetric cold atomic gases [7,8]. The "non-Abelian hydrodynamics" of these systems has been studied by many authors, for many decades [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamics in lattice models with continuous non-Abelian symmetries

et al. 2021

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We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles.As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

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“…which agrees with previous literature [8]. The first term in (59) corresponds to Fick's law for SU (2), and encodes the diffusive behavior of the spin two-point function at long time.…”

Section: The Action Of Non-abelian Hydrodynamicssupporting

confidence: 89%

Section: Non-abelian Continuous Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hydrodynamics in lattice models with continuous non-Abelian symmetries

et al. 2021

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“…This result for the bulk viscosity based on contact correlations is similar in structure to the fermionic Boltzmann calculation [12] but larger by a factor 4π 2 , which is necessary to satisfy the sum rule [42] and the highfrequency asymptotics with the contact density [47,48] technique is a diagrammatic strong-coupling approach to fermions in the BEC-BCS crossover [49,50] which treats fermions ψ σ and the pair field ∆ on equal footing. Its predictions for the unitary shear viscosity [9] agree well with recent data [51], and similarly for spin diffusion [52,53]. In this work, I extend the previous LW approach to compute the bulk viscosity (5) via the contact correlation function (6).…”

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confidence: 75%

Bulk Viscosity and Contact Correlations in Attractive Fermi Gases

Enss

2019

Phys. Rev. Lett.

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The bulk viscosity determines dissipation during hydrodynamic expansion. It vanishes in scale invariant fluids, while a nonzero value quantifies the deviation from scale invariance. For the dilute Fermi gas the bulk viscosity is given exactly by the correlation function of the contact density of local pairs. As a consequence, scale invariance is broken purely by pair fluctuations. These fluctuations give rise also to logarithmic terms in the bulk viscosity of the high-temperature nondegenerate gas. For the quantum degenerate regime I report numerical Luttinger-Ward results for the contact correlator and the dynamical bulk viscosity throughout the BEC-BCS crossover. The ratio of bulk to shear viscosity ζ/η is found to exceed the kinetic theory prediction in the quantum degenerate regime. Near the superfluid phase transition the bulk viscosity is enhanced by critical fluctuations and has observable effects on dissipative heating, expansion dynamics and sound attenuation.The bulk viscosity is a fundamental transport property which determines friction and dissipation in fluids during hydrodynamic expansion [1,2]. In particular, scale invariant fluids can expand isotropically without dissipation and therefore have zero bulk viscosity [3]. In a generic interacting fluid, instead, a nonzero value of the bulk viscosity quantifies the breaking of scale invariance in physical systems ranging from QCD [4-7] to condensed matter [8][9][10][11][12][13][14]. An intriguing example is the twodimensional dilute Fermi gas, where the classical model is scale invariant but a quantum scale anomaly breaks this symmetry [15][16][17][18]; this has recently been observed via breathing dynamics in cold-atom experiments [19][20][21].The bulk viscosity is necessary to understand and predict the real-time evolution and hydrodynamic modes of dissipative quantum fluids and to quantitatively interpret current experiments. However, measurements of the bulk viscosity remain challenging even for classical fluids [22]. Now a novel experimental probe via the dissipative heating rate due to a change in scattering length has been proposed for atomic gases [14]. It is therefore important to compute the bulk viscosity theoretically for quantum gases, which moreover includes predictions for the classical gas in the high-temperature limit.The bulk viscosity is defined as the correlation function of local pressure (the trace of the stress tensor). Since it vanishes in a scale invariant system, only the scale breaking part of the pressure contributes, the so-called trace anomaly [14,23,24]. This provides a formal link between the breaking of scale invariance and bulk viscosity. The bulk viscosity of the nonrelativistic, strongly interacting Fermi gas has been calculated from kinetic theory in the nondegenerate high-temperature limit [11,12] and in the low-temperature superfluid state [25,26]. Its value is largest in the strongly coupled region of the BEC-BCS crossover [27] near unitarity, but not precisely at unitarity where is must vanish by scale invarianc...

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“…Finally, diffusion with a short thermalization length has also been seen in spin transport in strongly interacting ultracold atoms in a trap [38]. The formulae we have developed can be applied directly to longitudinal spin diffusion in a magnetic field (to break spin reversal symmetry) or to transverse spin diffusion without a magnetic field or spontaneous magnetization (so that isotropy prevents mixing of the two transverse modes).…”

Section: Discussion and Applicationsmentioning

confidence: 95%

Theory of Diffusive Fluctuations

2019

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The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of non-linear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point half way to the diffusive pole, at frequency ω = − i 2 Dk 2 . We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.

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Universal Spin Transport and Quantum Bounds for Unitary Fermions

Cited by 36 publications

References 124 publications

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Hydrodynamics in lattice models with continuous non-Abelian symmetries

Bulk Viscosity and Contact Correlations in Attractive Fermi Gases

Theory of Diffusive Fluctuations

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