Connected correlations in partitioning protocols: a case study and beyond
arXiv:2212.07151 · doi:10.21468/SciPostPhys.15.1.027
Abstract
The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is ``local enough'' to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.
arXiv comment38+14 pages, 6+3 figures; typos corrected
References in corpus (62)
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Finite-temperature transport in one-dimensional quantum lattice models
- Generalized HydroDynamics on an Atom Chip
- Hydrodynamic Diffusion in Integrable Systems
- Spin diffusion from an inhomogeneous quench in an integrable system
- Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
- Soliton gases and generalized hydrodynamics
- Diffusion in generalized hydrodynamics and quasiparticle scattering
- The Quench Action
- Microscopic origin of ideal conductivity in integrable quantum models
- Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
- Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
- Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
- Analytic solution of the Domain Wall non-equilibrium stationary state
- Full counting statistics in a propagating quantum front and random matrix spectra
- Generalized hydrodynamics in strongly interacting 1D Bose gases
- A note on generalized hydrodynamics: inhomogeneous fields and other concepts
- Quantum Generalized Hydrodynamics
- Generalized hydrodynamics with space-time inhomogeneous interactions
- Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
- Entanglement evolution and generalised hydrodynamics: noninteracting systems
- On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
- Correlation functions and transport coefficients in generalised hydrodynamics
- Universality in the full counting statistics of trapped fermions
- Determination of the Nonequilibrium Steady State Emerging from a Defect
- Inhomogeneous quenches in a fermionic chain: exact results
- Extension of the Generalized Hydrodynamics to the Dimensional Crossover Regime
- Non-equilibrium thermal transport in the quantum Ising chain
- Generalised hydrodynamics of the classical Toda system
- Exact large-scale correlations in integrable systems out of equilibrium
- Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
- Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model
- Entanglement evolution and generalised hydrodynamics: interacting integrable systems
- Finite temperature free fermions and the Kardar-Parisi-Zhang equation at finite time
- Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
- Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
- Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics
- Universal front propagation in the quantum Ising chain with domain-wall initial states
- Spin-charge separation effects in the low-temperature transport of 1D Fermi gases
- Quantum ripples over a semi-classical shock
- Scaling and front dynamics in Ising quantum chains
- Energy transport in an integrable parafermionic chain via generalized hydrodynamics
- Domain-wall melting in the spin- XXZ spin chain: emergent Luttinger liquid with fractal quasi-particle charge
- Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
- Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
- Universal broadening of the light cone in low-temperature transport
- Scaling behaviour of the relaxation in quantum chains
- Locally quasi-stationary states in noninteracting spin chains
- Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
- Charges and currents in quantum spin chains: late-time dynamics and spontaneous currents
- Universal ground state properties of free fermions in a -dimensional trap
- Low-Temperature Transport in Out-of-Equilibrium XXZ Chains
- Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
- Equilibration towards generalized Gibbs ensembles in non-interacting theories
- Kinetic theory of quantum and classical Toda lattices
- Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians
- Prethermalization at Low Temperature: the Scent of Long-Range Order
- Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains
- Front dynamics in the XY chain after local excitations
- Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics
- Non-probabilistic fermionic limit shapes
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- Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
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- Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
- Asymptotic behaviour of determinants through the expansion of the Moyal star product
- Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State