Transport fluctuations in integrable models out of equilibrium

Myers, Jason; Bhaseen, M. J.; Harris, Rosemary J.; Doyon, Benjamin

doi:10.21468/scipostphys.8.1.007

Cited by 57 publications

(110 citation statements)

References 102 publications

(254 reference statements)

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“…In the second part, we conjecture that the cumulants of total currents are given by the exact same trees, up to only minor modifications of the weights. We compare our conjecture with the result of [3] and find perfect agreement up to the fourth cumulant.…”

Section: Introductionsupporting

confidence: 61%

“…We confirm our conjecture by a non-trivial matching with the result of [23] up to the fourth cumulant of the same current. We first remind how this quantity was derived in [14] and [3,23].…”

Section: Cumulants Of the Total Transport In Ghdmentioning

confidence: 99%

“…First, the simple combinatorial structure of the cumulants of total currents potentially translates into an analytic property of the full counting statistics. It is interesting to find a new relation in addition to the one established in [3]. Second, such structure provides hints about what the corresponding matrix elements would look like.…”

Section: Introductionmentioning

confidence: 95%

“…In the same paper the authors also computed this quantity by combining the current sum rule [19] with the long wavelength limit of the charge-charge correlation function [20]. The cumulant generating function of the total currents (also known as the full counting statistics) plays an important role in large deviation theory and has been studied in [3]. By using linear fluctuating hydrodynamics at Euler scale, the authors found a functional equation satisfied by this function.…”

Section: Introductionmentioning

confidence: 99%

“…Once the idea is clear, we present the generalization to higher cumulants. In section 3.1 we remind the result of [3] for the total transport cumulants. We then show, up to the fourth cumulant that they can be equivalently represented by the same diagrams.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Vu¹

2020

J. Stat. Mech.

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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]

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Section: Introductionsupporting

confidence: 61%

Section: Cumulants Of the Total Transport In Ghdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Vu¹

2020

J. Stat. Mech.

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$$ T\overline{T} $$ deformations and the width of fundamental particles

Cardy

Doyon

2022

J. High Energ. Phys.

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We provide a simple geometric meaning for deformations of so-called $$ T\overline{T} $$ T T ¯ type in relativistic and non-relativistic systems. Deformations by the cross products of energy and momentum currents in integrable quantum field theories are known to modify the thermodynamic Bethe ansatz equations by a “CDD factor”. In turn, CDD factors may be interpreted as additional, fixed shifts incurred in scattering processes: a finite width added to the fundamental particles (or, if negative, to the free space between them). We suggest that this physical effect is a universal way of understanding $$ T\overline{T} $$ T T ¯ deformations, both in classical and quantum systems. We first show this in non-relativistic systems, with particle conservation and translation invariance, using the deformation formed out of the densities and currents of particles and momentum. This holds at the level of the equations of motion, and for any interaction potential, integrable or not. We then argue, and show by similar techniques in free relativistic particle systems, that $$ T\overline{T} $$ T T ¯ deformations of relativistic systems produce the equivalent phenomenon, accounting for length contractions. We also show that, in both the relativistic and non-relativistic cases, the width of particles is equivalent to a state-dependent change of metric, where the distance function discounts the particles’ widths, or counts the additional free space. This generalises and explains the known field-dependent coordinate change describing $$ T\overline{T} $$ T T ¯ deformations. The results connect such deformations with generalised hydrodynamics, where the relations between scattering shifts, widths of particles and state-dependent changes of metric have been established.

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Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem

Horváth

2019

J. High Energ. Phys.

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We study Euler scale hydrodynamics of massless integrable quantum field theories interpolating between two non-trivial renormalisation group fixed points after inhomogeneous quantum quenches. Using a partitioning protocol with left and right initial thermal states and the recently developed framework of generalised hydrodynamics, we focus on current and density profiles for the energy and momentum as a function of ξ = x/t, where both x and t are sent to infinity. Studying the first few members of the A n and D n massless flows we carry out a systematic treatment of these series and generalise our results to other unitary massless models.In our analysis we find that the profiles exhibit extended plateaux and that non-trivial bounds exist for the energy and momentum densities and currents in the non-equilibrium stationary state, i.e. when ξ = 0. To quantify the magnitude of currents and densities, dynamical central charges are defined and it is shown that the dynamical central charge for the energy current satisfies a certain monotonicity property. We discuss the connection of the Landauer-Büttiker formalism of transport with our results and show that this picture can account for some of the bounds for the currents and for the monotonicity of the dynamical central charge. These properties are shown to be present not only in massless flows but also in the massive sinh-Gordon model suggesting their general validity and the correctness of the Landauer-Büttiker interpretation of transport in integrable field theories. Our results thus imply the existence of a non-equilibrium c-theorem as well, at least in integrable models. Finally we also study the interesting low energy behaviour of the A 2 model that corresponds to the massless flow from the tricritical to the critical Ising field theory.

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Transport fluctuations in integrable models out of equilibrium

Cited by 57 publications

References 102 publications

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

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

$$ T\overline{T} $$ deformations and the width of fundamental particles

Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem

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