Thermodynamic bootstrap program for integrable QFT’s: form factors and correlation functions at finite energy density

Cubero, Axel Cortés; Panfil, Miłosz

doi:10.1007/jhep01(2019)104

Cited by 38 publications

(54 citation statements)

References 71 publications

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“…Strictly speaking, however, such a dilute gas picture only adequately describes physics at zero temperature. The computation of equilibrium correlation functions instead necessitates an expansion based on dressed (instead of bare) form factors of local densities, and these are given by matrix elements of particle-hole excitations on top of a finite-density thermal background [33,[67][68][69][70]. Considering the longitudinal magnetization component s z , the matrix element between a thermal state |ˆ T,h and an excited state with a single particle-hole excitation of 'type s', with momenta ∆k…”

Section: Spin Transport At Intermediate and High Temperaturesmentioning

confidence: 99%

Anomalous Spin Diffusion in One-Dimensional Antiferromagnets

et al. 2019

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The problem of characterizing low-temperature spin dynamics in antiferromagnetic spin chains has so far remained elusive. Here we reinvestigate it by focusing on isotropic antiferromagnetic chains whose low-energy effective field theory is governed by the quantum non-linear sigma model. Employing an exact non-perturbative theoretical approach, we analyze the low-temperature behaviour in the vicinity of non-magnetized states and obtain exact expressions for the spin diffusion constant and the NMR relaxation rate, which we compare with previous theoretical results in the literature. Surprisingly, in SU (2)-invariant spin chains in the vicinity of half-filling we find a crossover from the semi-classical regime to a strongly interacting quantum regime characterized by zero spin Drude weight and diverging spin conductivity, indicating super-diffusive spin dynamics. The dynamical exponent of spin fluctuations is argued to belong to the Kardar-Parisi-Zhang universality class. Furthermore, by employing numerical tDMRG simulations, we find robust evidence that the anomalous spin transport persists also at high temperatures, irrespectively of the spectral gap and integrability of the model.

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Section: Spin Transport At Intermediate and High Temperaturesmentioning

confidence: 99%

Anomalous Spin Diffusion in One-Dimensional Antiferromagnets

et al. 2019

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“…together with any other local (in real space) property of the system, according to the Quench Action approach [47,48,106]. The function q j (λ) in Eq.…”

mentioning

confidence: 99%

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

2019

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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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“…In this section we provide a short summary of the Thermodynamic Bootstrap Program. For a detailed presentation, we refer to [1]. The aim of the TBP is to provide a formalism for computing form factors in IQFTs at finite energy density.…”

Section: Thermodynamic Bootstrap Programmentioning

confidence: 99%

“…1 To agree with the GHD notation we use here a slightly different notation than in [1]. Namely, the integral equations are written in terms of the kernel T (θ , θ ), instead the standard IQFT notation uses ϕ(θ , θ ) = 2πT (θ , θ ).…”

Section: Thermodynamic Bootstrap Programmentioning

confidence: 99%

“…In this article, we explore the applications of the recently introduced Thermodynamic Bootstrap Program (TBP) [1] for correlation functions of integrable quantum field theories (IQFT) in the hydrodynamic regime. The thermodynamic bootstrap program is a set of axioms that strongly restrict form factors of physical operators between states of finite energy density, in IQFT's.…”

Section: Introductionmentioning

confidence: 99%

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Generalized hydrodynamics regime from the thermodynamic bootstrap program

Cubero

Panfil

2020

SciPost Phys.

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Within the generalized hydrodynamics (GHD) formalism for quantum integrable models, it is possible to compute simple expressions for a number of correlation functions at the Eulerian scale. Specializing to integrable relativistic field theories, we show the same correlators can be computed as a sum over form factors, the GHD regime corresponding to the leading contribution with one particle-hole pair on a finite energy-density background. The thermodynamic bootstrap program (TBP) formalism was recently introduced as an axiomatic approach to computing such finite-energy-density form factors for integrable field theories. We derive a new axiom within the TBP formalism from which we easily recover the predicted GHD Eulerian correlators. We also compute higher form factor contributions, with more particle-hole pairs, within the TBP, allowing for the computation of correlation functions in the diffusive, and beyond, GHD regimes. The two particle-hole form factors agree with expressions recently conjectured within the GHD.

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Thermodynamic bootstrap program for integrable QFT’s: form factors and correlation functions at finite energy density

Cited by 38 publications

References 71 publications

Anomalous Spin Diffusion in One-Dimensional Antiferromagnets

Anomalous Spin Diffusion in One-Dimensional Antiferromagnets

Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions

Generalized hydrodynamics regime from the thermodynamic bootstrap program

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