Universal front propagation in the quantum Ising chain with domain-wall initial states

Abstract

We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

20 pages, 6 figures, v2: references added, v3: minor revision

References in corpus (10)

• The density-matrix renormalization group in the age of matrix product states
• Full counting statistics in a propagating quantum front and random matrix spectra
• Fermionization in an expanding 1D gas of hard-core bosons
• Emergence of quasi-condensates of hard-core bosons at finite momentum
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Entanglement evolution after connecting finite to infinite quantum chains
• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Entanglement in spin chains with gradients
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Domain Wall Dynamics near a Quantum Critical Point

Cited by in corpus (7)

• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Front dynamics and entanglement in the XXZ chain with a gradient
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
• Quantum adiabatic protocols using emergent local Hamiltonians
• Entanglement spreading after local and extended excitations in a free-fermion chain