What is an integrable quench?

Abstract

Inspired by classical results in integrable boundary quantum field theory, we propose a definition of integrable initial states for quantum quenches in lattice models. They are defined as the states which are annihilated by all local conserved charges that are odd under space reflection. We show that this class includes the states which can be related to integrable boundary conditions in an appropriate rotated channel, in loose analogy with the picture in quantum field theory. Furthermore, we provide an efficient method to test integrability of given initial states. We revisit the recent literature of global quenches in several models and show that, in all of the cases where closed-form analytical results could be obtained, the initial state is integrable according to our definition. In the prototypical example of the XXZ spin-s chains we show that integrable states include two-site product states but also larger families of matrix product states with arbitrary bond dimension. We argue that our results could be practically useful for the study of quantum quenches in generic integrable models.Comment: 44 pages, 10 figures; v2: minor revisio

Spin chain overlaps and the twisted Yangian

“…They can be constructed starting from a four-dimensional representation of the Clifford algebra so (5) {γ i , γ j } = 2δ i,j I 4×4 , (2.4) and symmetrizing the n-fold tensor product…”

“…The commutators of the G i then generate a d G -dimensional irreducible representation of so (5). We refer to section 5 for a discussion of further properties of the G i .…”

“…In statistical physics the latter type of state typically constitutes the initial state in a quantum quench of an integrable system and the overlaps are key to investigating the time development after the quench, see f.inst. [1][2][3][4][5][6][7][8]. In holography the typical state of interest is a so-called matrix product state which encodes information about the vacuum of the holographic system and the overlaps give the expectation value of the theory's operators in the vacuum state [9][10][11][12][13][14].…”

“…One class of such quantities are the overlaps with the Bethe eigenstates of the system. Based on the experience from a number of concrete studies of overlaps [9][10][11][12][22][23][24][25] a proposal for an integrability criterion was put forward in [5]. An initial state or matrix product state was said to be integrable if it was annihilated by all the conserved charges of the integrable system, which were odd under space-time parity.…”

Entanglement spreading and quasiparticle picture beyond the pair structure

“…In the original formulation [33], quasi-particles are assumed to be produced in pairs of opposite momenta: this is the simplest assumption which respects the translational invariance of the protocol, and it is the common situation in most of free-to-free quenches and in exactly solvable quenches in integrable models [66]. This is, for example, the case for the protocol studied in Refs.…”