A note on generalized hydrodynamics: inhomogeneous fields and other  concepts

Doyon, Benjamin; Yoshimura, Takato

doi:10.21468/scipostphys.2.2.014

Cited by 182 publications

(300 citation statements)

References 58 publications

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“…Starting from an inhomogeneous initial state, the method has been very successful in describing the time-evolved profiles of various observables (e.g. spin or energy densities and currents) in a hydrodynamic scaling regime, for a number of different situations and model systems [13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Front dynamics and entanglement in the XXZ chain with a gradient

Eisler

Bauernfeind

2017

Phys. Rev. B

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We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

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Section: Introductionmentioning

confidence: 99%

Front dynamics and entanglement in the XXZ chain with a gradient

Eisler

Bauernfeind

2017

Phys. Rev. B

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“…After long time evolution from such a state a non-vanishing flow can still be present and the system relaxes to a non-equilibrium steady state. This setup is the most relevant for transport properties and can be treated within the generalized hydrodynamics approach [15][16][17]. The essence of this approach lies in the existence of the Euler scale, which roughly determines sizes of cells in the system where the local conserved quantities (number of particles, momentum, energy etc) change slowly enough, in both space and time.…”

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Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

2020

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We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

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“…There are however fundamental questions that can not be addressed within 1 st GHD; diffusive transport [64][65][66][67][68][69] and large-time corrections [20][21][22][23] are two of them. The importance of these issues results in a considerable urge to fill these gaps [61], passing through refinements and reinterpretations of the theory [57,[70][71][72][73].…”

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Higher-order generalized hydrodynamics in one dimension: The noninteracting test

2017

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We derive a Moyal dynamical equation that describes exact time evolution in generic (inhomogeneous) noninteracting spin-chain models. Assuming quasistationarity, we develop a hydrodynamic theory. The question at hand is whether some large-time corrections are captured by higher-order hydrodynamics. We consider in particular the dynamics after that two chains, prepared in different conditions, are joined together. In these situations a light cone, separating regions with macroscopically different properties, emerges from the junction. In free fermionic systems some observables close to the light cone follow a universal behavior, known as Tracy-Widom scaling. Universality means weak dependence on the system's details, so this is the perfect setting where hydrodynamics could emerge. For the transverse-field Ising chain and the XX model, we show that hydrodynamics captures the scaling behavior close to the light cone. On the other hand, our numerical analysis suggests that hydrodynamics fails in more general models, whenever a condition is not satisfied.Over the past few years, we are experiencing an increasing interest in the physics behind the nonequilibrium time evolution of inhomogeneous states. An example is the time evolution of two semi-infinite chains that are joined together after having been prepared in different equilibrium conditions [1,2]. This kind of settings allows one to investigate the transport properties of quantum many-body systems even if the system is isolated from the environment.The first analytic results in this context were obtained in noninteracting models . There, under the assumption of quasistationarity, a semiclassical picture applies where the information about the initial state is carried by free stable quasiparticles moving throughout the system. Similar results were obtained in the framework of conformal field theory and Luttinger liquid descriptions [25][26][27][28][29][30][31][32][33][34][35][36][37]. In the presence of interactions the situation was less clear [38][39][40][41][42][43][44][45][46][47], but, eventually, Refs [48,49] have shown that the continuity equations satisfied by the (quasi)local conserved quantities are sufficient to characterize the late-time behavior. The framework developed in Refs [48,49] is now known as generalized hydrodynamics [48], where "generalized" is used to emphasize that integrable models have infinitely many (quasi)local charges [50]. We will generally omit "generalized" and refer to the system of equations derived in [48,49] as first-order hydrodynamics, 1 st GHD, to emphasize that it is a system of first-order partial differential equations.Within 1 st GHD, it was possible to compute the profiles of local observables [48,49,[51][52][53][54][55][56][57], to conjecture an expression for the time evolution of the entanglement entropy [58], and to efficiently calculate Drude weights [59][60][61][62][63]. There are however fundamental questions that can not be addressed within 1 st GHD; diffusive transport [64][65][66][67][68][69] and large-tim...

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A note on generalized hydrodynamics: inhomogeneous fields and other concepts

Cited by 182 publications

References 58 publications

Front dynamics and entanglement in the XXZ chain with a gradient

Front dynamics and entanglement in the XXZ chain with a gradient

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

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