Quasilocal charges in integrable lattice systems

Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž; Zadnik, Lenart

doi:10.1088/1742-5468/2016/06/064008

Cited by 311 publications

(535 citation statements)

References 202 publications

(438 reference statements)

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“…On the one hand, integrable systems are characterized by a macroscopic number of (quasi)local conservation laws [29][30][31][32][33] and the overlap with these conserved quantities leads to unconventional equilibration and thermalization [34][35][36] and nondecaying currents [37][38][39]. On the other hand, the overlap with one of the conserved quantities is not guaranteed for all parameters * jonasrichter@uos.de † rsteinig@uos.de of the model, observables, and initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Real-time dynamics of typical and untypical states in nonintegrable systems

Richter¹,

Jin²,

Raedt³

et al. 2018

Phys. Rev. B

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Understanding (i) the emergence of diffusion from truly microscopic principles continues to be a major challenge in experimental and theoretical physics. At the same time, isolated quantum many-body systems have experienced an upsurge of interest in recent years. Since in such systems the realization of a proper initial state is the only possibility to induce a nonequilibrium process, understanding (ii) the largely unexplored role of the specific realization is vitally important. Our work reports a substantial step forward and tackles the two issues (i) and (ii) in the context of typicality, entanglement as well as integrability and nonintegrability. Specifically, we consider the spin-1/2 XXZ chain, where integrability can be broken due to an additional next-nearest neighbor interaction, and study the real-time and real-space dynamics of nonequilibrium magnetization profiles for a class of pure states. Summarizing our main results, we show that signatures of diffusion for strong interactions are equally pronounced for the integrable and nonintegrable case. In both cases, we further find a clear difference between the dynamics of states with and without internal randomness. We provide an explanation of this difference by a detailed analysis of the local density of states.

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Section: Introductionmentioning

confidence: 99%

Real-time dynamics of typical and untypical states in nonintegrable systems

Richter¹,

Jin²,

Raedt³

et al. 2018

Phys. Rev. B

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“…[1][2][3] for recent reviews. Particularly interesting is the case of integrable models in one dimension, where the dynamics is constrained by a large set of conserved charges [4], leading to peculiar features in the transport properties [5] or the relaxation towards a stationary state [6]. A key paradigm of closedsystem dynamics is the quantum quench, where one typically prepares the pure ground state of a Hamiltonian which is then abruptly changed into a new one and the subsequent unitary time evolution is monitored [7].…”

Section: Introductionmentioning

confidence: 99%

Universal front propagation in the quantum Ising chain with domain-wall initial states

2016

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We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

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“…where the different kernels are again those of equations (69,72). As mentioned previously the ground state, or physical vacuum, corresponds to ρ …”

Section: String Bethe Ansatz Equations At Rational Values Of the Coupmentioning

confidence: 94%

“…As was first unveiled recently in the context of the XXZ chain in a series of papers by Prosen and collaborators (see in particular [64][65][66][67][68]72] as well as [69] for a review, and [70] by different authors and [71,74] for generalizations to chains of higher spin), the algebraic structures underlying quantum integrable lattice models may allow for more conserved charges to be built, which have a weaker (but still physically essential) form of locality called quasilocality. This term indicates that such charges can be written as sums of densities with arbitrarily large support, but with Hilbert-Schmidt norm decreasing exponentially with the length of the support.…”

Section: Quasilocal Lattice Chargesmentioning

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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Quasilocal charges in integrable lattice systems

Cited by 311 publications

References 202 publications

Real-time dynamics of typical and untypical states in nonintegrable systems

Real-time dynamics of typical and untypical states in nonintegrable systems

Universal front propagation in the quantum Ising chain with domain-wall initial states

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

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