Eric Vernier

Exact steady states for quantum quenches in integrable Heisenberg spin chains

What is the long-time behavior of a quantum system after it is brought out of equilibrium? In a generic case, it has been proposed that an effective thermalization occurs, and the local properties of the system can then be described by a thermal Gibbs ensemble. However, in integrable systems, with infinitely many conservation laws, the answer is far more complicated. It was shown in several special cases that the long-time steady state can be exactly described by the so called complete generalized Gibbs ensemble. The latter can be obtained by maximizing the entropy with constraints imposed by the conservation of energy, but also by additional carefully chosen subset of the integrals of motion. In this work, the authors analyze more general initial states, focusing on integrable XXZ Heisenberg spin chains. They find that the complete generalized Gibbs ensemble indeed correctly describes the system at long times after the quench.

Non compact conformal field theory and the

The so-called regime III of the Izergin–Korepin 19-vertex model has defied understanding for many years. We show in this paper that its continuum limit involves in fact a non compact conformal field theory (the so-called Witten Euclidian black hole CFT), which leads to a continuous spectrum of critical exponents, as well as very strong corrections to scaling. Detailed numerical evidence based on the Bethe ansatz analysis is presented, involving in particular the observation of discrete states in the spectrum, in full agreement with the string theory prediction for the black hole CFT. Our results have important consequences for the physics of the O(n) model, which will be discussed elsewhere.

a_2^{(2)}

We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models, by combining Enting’s finite lattice method (FLM) with exact transfer matrix enumerations. The models encompass all integrable curves of the Q-state Potts model on the square and triangular lattices, including the antiferromagnetic transition curves and the Ising model (Q = 2) at temperature T, as well as a fully packed O(n) type loop model on the square lattice. The expansions are around the trivial fixed points at infinite Q, n or 1/T. By using a carefully chosen expansion parameter, q ≪ 1, all expansions turn out to be of the form , where the coefficients αk and βk are periodic functions of k. Thanks to this periodicity property, we can conjecture the form of the expansions to all orders (except in a few cases where the periodicity is too large). These expressions are then valid for all 0 ⩽ q < 1. We analyse in detail the q → 1− limit in which the models become critical. In this limit the divergence of the corner free energy defines a universal term which can be compared with the conformal field theory (CFT) predictions of Cardy and Peschel. This allows us to deduce the asymptotic expressions for the correlation length in several cases. Finally we work out the FLM formulae for the case where some of the system’s boundaries are endowed with particular (non-free) boundary conditions. We apply this in particular to the square-lattice Potts model with Jacobsen–Saleur boundary conditions, conjecturing the expansions of the surface and corner free energies to arbitrary order for any integer value of the boundary interaction parameter r. These results are in turn compared with CFT predictions.

(Izergin-Korepin) model in regime III

We consider the integrable one-dimensional spin-

Corner free energies and boundary effects for Ising, Potts and fully packed loop models on the square and triangular lattices

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Quasi-local conserved charges and spin transport in spin-1 integrable chains

chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-

Correlations and diagonal entropy after quantum quenches in XXZ chains

1/2

What is an integrable quench

model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-

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

1

On generalized Gibbs ensembles with an infinite set of conserved charges

Babujian-Takhtajan Hamiltonian. Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-