Generalized hydrodynamics of classical integrable field theory: the  sinh-Gordon model

Bastianello, Alvise; Doyon, Benjamin; Watts, Gérard; Yoshimura, Takato

doi:10.21468/scipostphys.4.6.045

Cited by 117 publications

(160 citation statements)

References 89 publications

(288 reference statements)

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“…These intuitions are confirmed on Fig. 10 where we show the time evolution of both quantities for the initial perturbation given by the Gaussian packet (33). Figure 10: The time evolution of the ballistic and diffusive "occupation numbers" C ballistic (t) and C diffusive (t) from equations (36) and (37).…”

Section: Localized Initial Statesupporting

confidence: 65%

“…The equation (40) can be now solved numerically with the techniques introduced in the previous sections. Figure 11: Left panel: The dynamics of the k = 0 mode following an initial state (32) with 3 different values of the momentum k. Right panel: The dynamics of the k = 0 mode following an initial Gaussian state of (33). Additionally to the density moments (j = 0) we plot the the second and fourth moments.…”

Section: Quadratic Correctionsmentioning

confidence: 99%

“…Such bi-partite quenches or similar inhomogeneous initial states were studied in different contexts ranging from the CFT [1][2][3][4][5][6][7] and more generally QFT [8][9][10] to lattice models including 1d spin chains [11][12][13][14][15][16][17][18][19][20][21][22] and 1d Hubbard-like models [23][24][25]. The hydrodynamics solution to bi-partite quench protocol was originally proposed in [26,27] and further developed [28][29][30][31][32][33][34]. The resulting theory, Generalized Hydrodynamics (GHD), was successfully applied to variants of bi-partite quench protocols [27,[35][36][37][38] and other inhomogeneous setups [28,39].…”

Section: Introductionmentioning

confidence: 99%

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Linearized regime of the generalized hydrodynamics with diffusion

Panfil

Pawełczyk

2019

SciPost Phys. Core

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We consider the generalized hydrodynamics including the recently introduced diffusion term for an initially inhomogeneous state in the Lieb-Liniger model. We construct a general solution to the linearized hydrodynamics equation in terms of the eigenstates of the evolution operator and study two prototypical classes of initial states: delocalized and localized spatially. We exhibit some general features of the resulting dynamics, among them, we highlight the difference between the ballistic and diffusive evolution. The first one governs a spatial scrambling, the second, a scrambling of the quasi-particles content. We also go one step beyond the linear regime and discuss the evolution of the zero momentum mode that does not evolve in the linear regime.

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Section: Localized Initial Statesupporting

confidence: 65%

Section: Quadratic Correctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Linearized regime of the generalized hydrodynamics with diffusion

Panfil

Pawełczyk

2019

SciPost Phys. Core

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“…4 we benchmark the GHD in the classical Sinh-Gordon model (see Ref. [117] and [89] for the TBA). The model describes a scalar field φ with Lagrangian L = dx {∂ µ φ∂ µ φ/2 − (m/g) 2 [cosh(gφ) − 1]}, with m the mass and g the interaction parameter.…”

mentioning

confidence: 99%

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

2019

Self Cite

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We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently-introduced Generalized Hydrodynamics (GHD). The method allows to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally-motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the classical Sinh-Gordon model.Introduction. -Exploring the out-of-equilibrium behavior of quantum many-body systems is nowadays among the most active research areas in physics, due to a successful synergy between theoretical and experimental advances [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].How, and in which sense, does a coarse-grained thermodynamic description emerge through dynamical evolution in isolated out-of-equilibrium many-body systems? One-dimensional systems represent an ideal playground to address this question: there, remarkably powerful tools exist, both theoretical (such as conformal field theory [18] and integrability [19,20]) and computational (such as Matrix Product States methods [21]).Integrability is ubiquitous in the low-dimensional world, with applications ranging from spin chains [19] to continuum models (having Lorentz [20] or Galilean [22,23] invariance, or neither [24]). Amazingly, many of these examples have been experimentally realized [9][10][11][12][13][14][15][16][17].Integrable models are characterized by the presence of infinitely many conserved chargesQ j , which can be used to exactly determine their thermodynamics [25]. In recent times, the importance of quasi-local charges has moreover been underlined [26][27][28][29][30][31][32][33][34][35].The last decade has witnessed exact results reaching out-of-equilibrium protocols as well: great attention has been devoted to the homogeneous sudden quantum quench [36] (see also Ref. [37] and reference therein). Due to the conserved quantities, the system exhibits local relaxation to a state that is not thermal [38][39][40][41][42][43][44][45][46], but rather emerges from a Quench Action [47,48] or (where applicable) a Generalized Gibbs Ensemble [49,50] which accounts for all the relevant charges.More recently, the focus has been on quenches from spatially inhomogeneous systems. A new theoretical toolbox, dubbed Generalized Hydrodynamics (GHD) [51,52] allows to address this problem. In Ref. [51,52] GHD dealt with inhomogeneous states evolving under a homogeneous Hamiltonian. Several applications have been explored , extending the initial findings to describe the entanglement spreading [79][80][81][82][83][84], including diffusive corrections [85][86][87][88] or applying it to classical field theories [89][90][91][92]. Very recently, it has been shown that GHD FIG. 1: Prototypical experimental setup that can be addressed with our method...

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“…An hydrodynamic description taking into account the local conserved quantities was developed, which is now called "generalized hydrodynamics" (GHD) [9,10]. It has lead to many fruitful developments in the last few years [7,[11][12][13][14][14][15][16][17][18][19][20][21], including on the experimental side [22].…”

mentioning

confidence: 99%

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

2019

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We study the dynamics of a spin-1 2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schrödinger equation is used to construct a variational solution capturing several aspects of the problem.

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Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model

Cited by 117 publications

References 89 publications

Linearized regime of the generalized hydrodynamics with diffusion

Linearized regime of the generalized hydrodynamics with diffusion

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

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