Bound-state confinement after trap-expansion dynamics in integrable systems

Abstract

Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin-$1/2$ anisotropic Heisenberg chain ($XXZ$ chain). Specifically, we consider the sudden vacuum expansion of a finite region $A$ prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of $A$. Since region $A$ is finite, at asymptotically long times bound states are "liberated" after the "evaporation" of all the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the $p$-Néel states, which are obtained by repetition of a unit cell with $p$ up spins followed by $p$ down spins. Upon increasing $p$, the bound-state content is enhanced. In the limit $p\to \infty$ one obtains the domain-wall initial state. We show that for $p<4$, only bound states with $n>p$ are confined at large chain anisotropy. For $p\gtrsim 4$, also bound states with $n=p$ are confined, consistent with the absence of transport in the limit $p\to \infty$. The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.

29 pages, 11 figures

References in corpus (38)

• Evolution of Entanglement Entropy in One-Dimensional Systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Time-evolution methods for matrix-product states
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• Entanglement and thermodynamics after a quantum quench in integrable systems
• Microscopic observation of magnon bound states and their dynamics
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Generalized HydroDynamics on an Atom Chip
• Quasilocal charges in integrable lattice systems
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
• Entanglement dynamics after quantum quenches in generic integrable systems
• "Light-cone" dynamics after quantum quenches in spin chains
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Super-diffusion in one-dimensional quantum lattice models
• A Shortcut to the Q-Operator
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Experimental Observation of Bethe Strings
• Ballistic spin transport in a periodically driven integrable quantum system
• Observing complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Entanglement and quantum transport in integrable systems
• Superuniversality of superdiffusion
• String-charge duality in integrable lattice models
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
• Formation of robust bound states of interacting microwave photons
• Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Dispersions of Many-Body Bethe strings
• Out-of-equilibrium dynamics in a quantum impurity model: numerics for particle transport and entanglement entropy
• Correlations and commuting transfer matrices in integrable unitary circuits
• Quantum distillation and confinement of vacancies in a doublon sea
• Observation of magnon bound states in the long-range, anisotropic Heisenberg model
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• Robustness and eventual slow decay of bound states of interacting microwave photons in the Google Quantum AI experiment