Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Abstract

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e., by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

Dynamics and level statistics of interacting fermions in the lowest Landau level

“…The Gaussian envelope at larger energies follows a well-distinguished set of eigenstates. Such eigenstate branches appear to be common in overlap distributions, e.g.in figure 5(a) of [138] and in figure 3(a) of [140]. In the present case, states in this branch have much smaller overlaps than the dominant eigenstates, and hence do not play any noticeable role in the dynamics, unlike the case of [140].…”

“…The dynamics of a quantum state is governed by the eigenstates of Hamiltonian with which the state has significant overlap. The distribution of overlaps-the overlaps with eigenstates as a function of corresponding eigenenergies, thus has been examined in the non-equilibrium literature for various Hamiltonians and initial states [75,86,[132][133][134][135][136][137][138][139][140].…”

Entanglement dynamics after quantum quenches in generic integrable systems

“…The results that we obtain here build on a large literature about the integrable quench dynamics of the XXZ chain [53][54][55][56][119][120][121][122][123][124][125][126][127][128][129][130] to which we refer for completeness.…”

What is an integrable quench?

“…Since integrable states will in general overlap with all eigenstates annihilated by odd conserved charges, it follows from this discussion that they will not posses the pair structure. This is explicitly shown in the case of the Néel state in [37], to which we refer for further detail. As a final remark, we note that the XX chain is closely related to the q → ∞ limit of the q-boson model studied in [134,135].…”