Hydrodynamic nonlinear response of interacting integrable systems

Fava, Michele; Biswas, Sounak; Gopalakrishnan, Sarang; Vasseur, Romain; Parameswaran, S. A.

doi:10.1073/pnas.2106945118

Cited by 26 publications

(24 citation statements)

References 60 publications

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“…The main general results for transport coefficients and correlations in integrable systems that are reviewed in the present work are the Drude weights (6.12), simply related to the flux Jacobian A (see (3.22)); the Euler-scale correlation functions (6.13) and (6.14); and the Onsager matrix (7.5) and (7.8), simply related to the diffusion matrix D (see (3.23)). More advanced aspects reviewed include the Euler-scale correlation functions in inhomogeneous backgrounds (8.4), and some aspects of nonlinear response including the full counting statistics for (generalised) charge transport and fluctuations (8.10) (because of lack of space, we do not review the more advanced diagrammatic theory for nonlinear response recently developed in [79]). We emphasise again that an important part of this review is to not only express these important results in integrable systems, but also explain the general framework of hydrodynamics that underlies them, section 3, and the form factor techniques, a powerful set of tools to obtain such exact results, section 5.…”

Section: Main Results Reviewedmentioning

confidence: 99%

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Correlation functions and transport coefficients in generalised hydrodynamics

et al. 2022

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We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.

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Section: Main Results Reviewedmentioning

confidence: 99%

“…Further general results, which we will not review here, are concerned with the 'nonlinear Drude weights', see for instance [99]. In the more special context of GHD, a diagrammatic theory for nonlinear response to external fields was proposed recently [79], which we also do not review.…”

Section: Non-linear Response: Higher-point Functionsmentioning

confidence: 98%

Correlation functions and transport coefficients in generalised hydrodynamics

et al. 2022

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“…For quantum distributions, much less is known beyond free fermions and systems with ballistic transport [20][21][22][23][24]. The question of FCS in interacting quantum systems was recently revived because of the surprising discovery that spin transport in the one-dimensional Heisenberg model appears to be described by the KPZ equation [25][26][27][28][29][30][31][32][33][34][35][36], although the Heisenberg model is an integrable quantum system with no stochasticity.…”

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confidence: 99%

Theory of anomalous full counting statistics in anisotropic spin chains

Gopalakrishnan¹,

Morningstar²,

Vasseur³

et al. 2022

Preprint

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We present an analytic theory of the full counting statistics of spin transport in the anisotropic one-dimensional XXZ spin chain. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the halfline. Although the magnetization transfer is diffusive on average, its distribution has a universal non-gaussian form at late times. We show that this distribution strongly violates the large-deviation principle, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.

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“…Recent study on the 2DCS of Kitaev model shows distinct signatures of matter Majorana fermions and gauge field excitations in the form of diagonal streak signals and their intercepts in 2D frequency domain, respectively 51 . According to this technique, one can reveal distinguishable spectroscopic characteristics of different types of gapped spin liquids 52 , signatures of interactions in many-body quantum systems [53][54][55][56][57][58] and extract different relaxation times in quantum systems with quenched disorders 59 . Very recently the 2DCS of one-dimensional Ising model has been investigated by implementing matrix-product state numerical simulations 60,61 .…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field

Negahdari

Langari

2023

Phys. Rev. B

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We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional coherent spectroscopy. We observe that at the isotropic point in the non-Abelian phase of this model, the nonlinear spectrum in the 2D frequency domain consists of sharp signals that originate from the flux excitations and Majorana bound states. Signatures of different flux excitations can be clearly observed in this spectrum, such that one can observe evidences of flux states with 4-adjacent, 2-non-adjacent, and 4-far-separated fluxes, which are not visible in linear response spectroscopy such as neutron scattering experiments. Moreover, in the Abelian phase we perceive that the spectrum in the frequency domain is composed of streak signals. These signals, as in the nonlinear response of the pure Kitaev model, represent a distinct signature of itinerant Majorana fermions. However, deep in the Abelian phase whenever a Kitaev exchange coupling is much stronger than the others, the streak signals are weakened and only single sharp spots are seen in the response, which resembles the dispersionless response of the conventional toric code.

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Hydrodynamic nonlinear response of interacting integrable systems

Cited by 26 publications

References 60 publications

Correlation functions and transport coefficients in generalised hydrodynamics

Correlation functions and transport coefficients in generalised hydrodynamics

Theory of anomalous full counting statistics in anisotropic spin chains

Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field

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