How order melts after quantum quenches

Abstract

Injecting a sufficiently large energy density into an isolated many-particle system prepared in a state with long-range order will lead to the melting of the order over time. Detailed information about this process can be derived from the quantum mechanical probability distribution of the order parameter. We study this process for the paradigmatic case of the spin-1/2 Heisenberg XXZ chain. We determine the full quantum mechanical distribution function of the staggered subsystem magnetization as a function of time after a quantum quench from the classical Néel state. This provides a detailed picture of how the Néel order melts and reveals the existence of an interesting regime at intermediate times that is characterized by a very broad probability distribution.Introduction. -A fundamental objective of quantum theory is to determine probability distribution functions of observables in given quantum states. In fewparticle systems the time evolution of such probability distributions provides a lot of useful information beyond what is contained in the corresponding expectation values. Recent advances in cold-atom experiments have made possible not only the study of non-equilibrium time evolution of (almost) isolated many-particle systems [1][2][3][4][5][6][7][8][9][10][11][12][13], but given access to the full quantum mechanical probability distributions of certain observables [14][15][16][17][18]. This provides an opportunity to gain new insights about the coherent dynamics of many-particle quantum systems. One intriguing question one may ask is how order melts, or forms, when an isolated many-particle system is driven across a phase transition. Related questions have been studied in solids, but there one essentially deals with open quantum systems and has access to very different observables, see e.g. [19,20]. The basic setup we have in mind is as follows. Let us consider a system of quantum spins with Hamiltonian H that is initially prepared in a state with density matrix ρ(0). In this state there is long-range order characterized by a local order parameter O =

Relaxation of the order-parameter statistics in the Ising quantum chain

“…Moreover, we definitively stress a very appealing relation between the stationary PDF and the properties of the ground state of the post-quench Hamiltonian, in close analogy to what has been put forward in Ref. [33], undoubtedly confirming the great generality of such relationship which may be applied to other models. Indeed, it turns out that, when the initial ordered state is quenched into the unbroken symmetry phase, the local order quickly disappear and the PDF acquire a simple Gaussian shape which dynamically depends only on the first two cumulants of the local order parameter.…”

“…However, depending on the phase of matter the post-quench Hamiltonian belongs within, some remnants of the original order may locally survives. Local remnants of the original order have been recently observed by the author in a similar setup for the antiferromagnetic XXZ spin-1/2 chain [33].…”

“…In the following discussion indeed, although we will be referring to the specific case of the Ising quantum chain, we argue that the general arguments should be valid for any quantum system which exhibits similar characteristics, as it has been already put forward in Ref. [33].…”

“…However, in spite of a generous literature regarding PDFs of various observables (mainly conserved quantities, transverse magnetisation in the Ising spin chain, particle number in the Bose(Fermi)-Hubbard model, etc.) in different quantum models, both non-interacting and interacting, either at the equilibrium [34][35][36][37][38][39][40][41][42][43][44][45] or out-of-equilibrium [46][47][48][49][50][51], the results on the order-parameter statistics are very few [33,52,53]. In particular analytical finding on the PDF of the longitudinal magnetisation in the Ising quantum chain are only limited to some universal scaling behaviour in the ground state at the critical point [54].…”

Full counting statistics in the gapped XXZ spin chain

“…The FCS generating function is directly measured in iTEBD simulations [45], as explained in details, e.g., in Refs. [27,37]. The results in the thermodynamic limit for three values of ∆ > 1 and for = 200 are shown in Figure 2.…”