Anomalous low-frequency conductivity in easy-plane XXZ spin chains

Agrawal, Utkarsh; Gopalakrishnan, Sarang; Vasseur, Romain; Ware, Brayden

doi:10.1103/physrevb.101.224415

Cited by 32 publications

(51 citation statements)

References 91 publications

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“…Combined with the expectation that the frequencyintegrated conductivity should be continuous everywhere due to sum rules, this hints at the possibility of superdiffusive corrections away from the commensurate points. This conjecture was put onto firmer grounds in (Agrawal et al, 2020). Let us consider a value ∆ = cos(πλ ∞ ) where λ ∞ is a generic irrational number.…”

Section: ∆ <mentioning

confidence: 99%

“…GHD allows one to obtain the exponents associated with the superdiffusive correction (Agrawal et al, 2020): The low-frequency conductivity behaves as σ(ω) ∝ ω −α with α = 1/2 for generic values of ∆. This divergence is cut-off at the rational points, leading to a diffusive correction.…”

Section: ∆ <mentioning

confidence: 99%

“…This divergence is cut-off at the rational points, leading to a diffusive correction. Furthermore, a qualitative picture emerges from GHD: the subleading correction arises from scattering of charged quasiparticles off neutral quasiparticles and an interpretation in terms of a Lévy flight has been put forward (Agrawal et al, 2020;.…”

Section: ∆ <mentioning

confidence: 99%

“…The approach allows to compute Drude weights (Ilievski and De Nardis, 2017b), diffusion constants (De Nardis et al, 2018) and can provide the full temperature dependence of both quantities. Moreover, subleading corrections to transport coefficients can be extracted such as diffusive or superdiffusive corrections in the presence of a Drude weight (Agrawal et al, 2020). Most importantly, GHD often allows for developing an intuition and interpretation as it is based on a kinetic theory of the characteristic excitations of integrable models.…”

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Finite-temperature transport in one-dimensional quantum lattice models

et al. 2021

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Section: ∆ <mentioning

confidence: 99%

Section: ∆ <mentioning

confidence: 99%

Section: ∆ <mentioning

confidence: 99%

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Finite-temperature transport in one-dimensional quantum lattice models

et al. 2021

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“…Intuitively, this kinetic approach remains valid even if the quasiparticle gas is not dilute, since scattering processes in integrable systems factorize. Recent developments include explaining how diffusive corrections to ballistic quasiparticle motion arise microscopically [75][76][77][78], and identifying the physical origin of the universal superdiffusive dynamics observed numerically in systems with non-Abelian symmetries [71,[79][80][81][82][83][84][85][86][87][88][89][90].…”

Section: Introductionmentioning

confidence: 99%

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Fava¹,

Ware

Gopalakrishnan

et al. 2020

Phys. Rev. B

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We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, which are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is subballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via x ∼ t 2/3 ) along both lines and at the SO(4)-symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

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Anomalous transport from hot quasiparticles in interacting spin chains

Gopalakrishnan¹,

Vasseur²

2023

Rep. Prog. Phys.

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Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, high-temperature spin transport can be diﬀusive or superdiﬀusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic ﬂuctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-fromequilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

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Anomalous low-frequency conductivity in easy-plane XXZ spin chains

Cited by 32 publications

References 91 publications

Finite-temperature transport in one-dimensional quantum lattice models

Finite-temperature transport in one-dimensional quantum lattice models

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Anomalous transport from hot quasiparticles in interacting spin chains

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