String-charge duality in integrable lattice models

Ilievski, Enej; Quinn, Eoin; Nardis, Jacopo De; Brockmann, Michael

doi:10.1088/1742-5468/2016/06/063101

Cited by 123 publications

(270 citation statements)

References 77 publications

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“…In other terms, the number of quasilocal charges is depends on the value of the coupling γ, a fact which has already been noticed by the authors of [73] in the case of the homogeneous XXZ chain. Taking for instance γ = •…”

Section: Quasilocal Lattice Chargesmentioning

confidence: 58%

“…In this limit one has ξ j (α) = − 2 log (f j (α)) , which can be accessed through the numerical knowledge of the functions a(j, γ) and b(j, γ) in (90). In the figure 3 of the main text, we display plots of the correlation lengths ξ j for α in the physical domain and various values of j, as a function of γ. Fron this figure it is concluded (see main text for details) that the correlation length ξ j is finite for γ < π j , and diverges otherwise, which gives an alternative illustration of the fact noticed in [73], namely that the quasilocal charge content is intimately related to the string content of the model.…”

Section: B Proof Of Quasilocalitymentioning

confidence: 69%

“…If these conditions are verified, we further check numerically that the corresponding transfer matrices T j satisfy the following inversion relation [21,73],…”

Section: Quasilocal Lattice Chargesmentioning

confidence: 97%

“…In the homogeneous XXZ case, analogously built quasilocal charges were shown [72][73][74] to determine completely the densities of all kinds of strings needed to describe the steady-state following a quantum quench.…”

Section: Construction Of the Ggementioning

confidence: 99%

“…From there one can follow the same steps as in the homogeneous case [72,73], resulting in the following relations between the light-cone charges and densities :…”

Section: From the Operators X J (α) To The String Densitiesmentioning

confidence: 99%

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Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Vernier¹,

Cubero²

2017

J. Stat. Mech.

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It has recently been shown that some integrable spin chains possess a set of quasilocal conserved charges, with the classic example being the spin-1 2 XXZ Heisenberg chain. These charges have been proven to be essential for properly describing stationary states after a quantum quench, and must be included in the generalized Gibbs ensemble (GGE). We find that similar charges are also necessary for the GGE description of integrable quantum field theories with non-diagonal scattering. A stationary state in a non-diagonal scattering theory is completely specified by fixing the mode-occupation density distributions of physical particles, as well auxiliary particles which carry no energy or momentum. We show that the set of conserved charges with integer Lorentz spin, related to the integrability of the model, are unable to fix the distributions of these auxiliary particles, since these charges can only fix kinematical properties of physical particles. The field theory analogs of quasilocal lattice charges are therefore necessary. As a concrete example, we find the complete set of charges needed in the sine-Gordon model, by using the fact that this field theory is recovered as the continuum limit of a spatially inhomogeneous version of the XXZ chain. The set of quasilocal charges of the lattice theory are shown to become a set local charges with fractional spin in the field theory.

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Section: Quasilocal Lattice Chargesmentioning

confidence: 58%

Section: B Proof Of Quasilocalitymentioning

confidence: 69%

“…If these conditions are verified, we further check numerically that the corresponding transfer matrices T j satisfy the following inversion relation [21,73],…”

Section: Quasilocal Lattice Chargesmentioning

confidence: 97%

Section: Construction Of the Ggementioning

confidence: 99%

“…From there one can follow the same steps as in the homogeneous case [72,73], resulting in the following relations between the light-cone charges and densities :…”

Section: From the Operators X J (α) To The String Densitiesmentioning

confidence: 99%

See 3 more Smart Citations

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Vernier¹,

Cubero²

2017

J. Stat. Mech.

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Perturbative post-quench overlaps in quantum field theory

Hódsági

Kormos

Takács

2019

J. High Energ. Phys.

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In analytic descriptions of quantum quenches, the overlaps between the initial pre-quench state and the eigenstates of the time evolving Hamiltonian are crucial ingredients. We construct perturbative expansions of these overlaps in quantum field theories where either the pre-quench or the post-quench Hamiltonian is integrable. Using the E 8 Ising field theory for concrete computations, we give explicit expressions for the overlaps up to second order in the quench size, and verify our results against numerical results obtained using the Truncated Conformal Space Approach. We demonstrate that the expansion using the post-quench basis is very effective, but find some serious limitations for the alternative approach using the pre-quench basis.

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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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String-charge duality in integrable lattice models

Cited by 123 publications

References 77 publications

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering

Perturbative post-quench overlaps in quantum field theory

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

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