Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

Agrawal, Utkarsh; Gopalakrishnan, Sarang; Vasseur, Romain

doi:10.1103/physrevb.99.174203

Cited by 31 publications

(26 citation statements)

References 90 publications

(137 reference statements)

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“…It has however some limitations, and it was often blamed to be valid only in limits in which the system behaves essentially in a classical way (indeed, does not appear in first-order GHD). In addition, the theory is unable to capture diffusive behaviour in interacting systems, a subject that has been attracting more and more attention [66,67,70,71,[78][79][80]. In order to overcame this weakness, there have been proposals to go beyond the lowest order (of an implicit asymptotic expansion in the limit of low inhomogeneity) in interacting integrable systems [78,79,81,82], but, at the same time, some issues in noninteracting spin chains were uncovered.…”

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confidence: 99%

Locally quasi-stationary states in noninteracting spin chains

Fagotti

2020

SciPost Phys.

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Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections"). Contents4 The two-temperature scenario revisited 18 5 Continuum scaling limit 19 6 Conclusion 22 A Non-equilibrium dynamics in inhomogeneous systems 24 B Weak inhomogeneous limit: an asymptotic expansion 26 B.1 Locally quasi-stationary states 28 B.2 Off-diagonal states 29 References 30 1 A spin operator O ℓ is quasi-localised around a given site ℓ if there is a sequence of connected subsystems Sn ⊂ Sn+1 (Sn is a proper subset of Sn+1), centred around ℓ, such that O ℓ − tr Sn [O ℓ ] tr Sn [I] ⊗ I Sn < e −α|Sn| , with α > 0 and |Sn| the extent of Sn. A quasilocal charge is an additive charge with quasi-localised density -see Ref. [84] for a review on quasilocal charges in integrable spin chains.

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confidence: 99%

Locally quasi-stationary states in noninteracting spin chains

Fagotti

2020

SciPost Phys.

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“…Discussion and conclusion. We presented an exact hydrodynamic description of the out-of-equilibrium dynamics of integrable systems in the presence of dephasing noise, where the extension to inhomogeneous setups is now obvious [110,111]. For future perspectives, it would be interesting to extend our treatment to include subleading terms, operators which do not conserve particles' number, and to effectively describe three-body losses, one of the leading effects in cold-atom setups involving quantum gases [38,100].…”

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confidence: 99%

Generalized hydrodynamics with dephasing noise

2020

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We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the system based on a hydrodynamic formulation. This results in an additional term to the standard generalized hydrodynamics theory describing diffusive dynamics in the momentum space of the quasiparticles of the system, with a time-and momentum-dependent diffusion constant. Our analytical predictions are then benchmarked in the classical limit by comparison with a microscopic simulation of the nonlinear Schrödinger equation, showing perfect agreement. In the quantum case, our predictions agree with state-of-the-art numerical simulations of the anisotropic Heisenberg spin in the accessible regime of times and with bosonization predictions in the limit of small dephasing times and temperatures.

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“…For such a random CFT, we showed in [22] that there are both normal and anomalous diffusive contributions to heat transport on top of the usual ballistic one that is the sole contribution in standard CFT. We mention that the diffusive effect due to the type of randomness in [22] was recently demonstrated numerically for random quantum spin chains in [30] using generalized hydrodynamics [31,32]. This makes clear that the generalization to the inhomogeneous dynamics given by H in (1.1) is important as it opens up a mechanism for diffusion within CFT.…”

Section: Introductionmentioning

confidence: 77%

Inhomogeneous Conformal Field Theory Out of Equilibrium

Moosavi

2021

Ann. Henri Poincaré

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We study the non-equilibrium dynamics of conformal field theory (CFT) in 1+1 dimensions with a smooth position-dependent velocity v(x) explicitly breaking translation invariance. Such inhomogeneous CFT is argued to effectively describe 1+1-dimensional quantum many-body systems with certain inhomogeneities varying on mesoscopic scales. Both heat and charge transport are studied, where, for concreteness, we suppose that our CFT has a conserved U(1) current. Based on projective unitary representations of diffeomorphisms and smooth maps in Minkowskian CFT, we obtain a recipe for computing the exact non-equilibrium dynamics in inhomogeneous CFT when evolving from initial states defined by smooth inverse-temperature and chemical-potential profiles $$\beta (x)$$ β ( x ) and $$\mu (x)$$ μ ( x ) . Using this recipe, the following exact analytical results are obtained: (i) the full time evolution of densities and currents for heat and charge transport, (ii) correlation functions for components of the energy–momentum tensor and the U(1) current as well as for any primary field, and (iii) the thermal and electrical conductivities. The latter are computed by direct dynamical considerations and alternatively using a Green–Kubo formula. Both give the same explicit expressions for the conductivities, which reveal how inhomogeneous dynamics opens up the possibility for diffusion as well as implies a generalization of the Wiedemann–Franz law to finite times within CFT.

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Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

Cited by 31 publications

References 90 publications

Locally quasi-stationary states in noninteracting spin chains

Locally quasi-stationary states in noninteracting spin chains

Generalized hydrodynamics with dephasing noise

Inhomogeneous Conformal Field Theory Out of Equilibrium

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