Cumulants of conserved charges in GGE and cumulants of total transport in GHD: exact summation of matrix elements?

Abstract

We obtain the cumulants of conserved charges in Generalized Gibbs Ensemble (GGE) by a direct summation of their finite-particle matrix elements. The Gaudin determinant that describes the norm of Bethe states is written as a sum over forests by virtue of the matrix-tree theorem. The aforementioned cumulants are then given by a sum over tree-diagrams whose Feynman rules involve simple Thermodynamic Bethe Ansatz (TBA) quantities. The internal vertices of these diagrams have the interpretation of virtual particles that carry anomalous corrections to bare charges. Our derivation follows closely the spirit of recent works [1,2]. We also conjecture that the cumulants of total transport in Generalized Hydrodynamics (GHD) are given by the same diagrams up to minor modifications. These cumulants play a central role in large deviation theory and were obtained in [3] using linear fluctuating hydrodynamics at Euler scale. We match our conjecture with the result of [3] up to the fourth cumulant. This highly non-trivial matching provides a strong support for our conjecture. 1 arXiv:1909.08852v3 [cond-mat.stat-mech]

Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz

“…Such a statistical description, which technically represents an exact cluster expansion, was obtained by several authors in [7][8][9][10][11][12]. The latter proved to be a useful tool to solve some concrete problems [13,14].…”

Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit

“…The predictions of this conjecture have been tested numerically with great success both in spin chains and in quantum gas models solvable by Bethe Ansatz [38][39][40][41][42] and have been verified even experimentally [43]. Moreover it has paved the way for interesting extensions and applications [38][39][40][41][44][45][46][47][48][49][50][51][52], as it essentially reduces the characterisation of macroscopic properties resulting from the complicated dynamics of quantum many-body systems to a relatively simple semiclassical description. At this point it is worth to recognise the important role played by integrability in understanding the physics of the quantum many-body problem in general, especially in the field of outof-equilibrium dynamics [12,[53][54][55][56][57][58][59][60].…”

Form factors and generalized hydrodynamics for integrable systems

“…But a microscopic derivation of the Drude weights as well as the diffusion matrix using the standard form factors are still outstanding tasks. Note that some hydrodynamic correlators were obtained along this line recently [96]. The form factor formalism may also prove capable of obtaining beyond-GHD regime corrections, including diffusive and quantum corrections, which can be compared to other current approaches [13,23,97].…”