Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model

Abstract

We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|\Delta |<1$, initially prepared in a product state with two domain walls i.e, $|\downarrow \cdots \downarrow \uparrow \cdots \uparrow \downarrow \cdots \downarrow ⟩$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $\Delta =0$, we derive exact asymptotic results for the magnetization and the spin current by using a semi-classical Wigner function approach, and we exactly determine the spreading of entanglement entropy exploiting the recently developed tools of quantum fluctuating hydrodynamics. In the interacting case, we analytically solve the Generalized Hydrodynamics equation providing exact expressions for the conserved quantities. We display some numerical results for the entanglement entropy also in the interacting case and we propose a conjecture for its asymptotic value.

27 pages, 10 figures; v3: corrected authors' information; fixed typos

References in corpus (25)

• Bosonizing one-dimensional cold atomic gases
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Entanglement evolution and generalised hydrodynamics: interacting integrable systems
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Relaxation in the XX quantum chain
• Stationary states in a free fermionic chain from the Quench Action Method
• Algebraic construction of current operators in integrable spin chains
• Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Front dynamics and entanglement in the XXZ chain with a gradient
• Current operators in integrable models: A review
• Magnetization and entanglement after a geometric quench in the XXZ chain
• Free fermions at the edge of interacting systems
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Wigner function for a particle in an infinite lattice
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• Wigner function for noninteracting fermions in hard wall potentials
• Domain Wall Dynamics near a Quantum Critical Point
• Nonequilibrium dynamics of noninteracting fermions in a trap
• Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy

Cited by in corpus (19)

• Domain wall melting across a defect
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Interface dynamics in the two-dimensional quantum Ising model
• Scaling of fronts and entanglement spreading during a domain wall melting
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$
• Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing
• Navier-Stokes Equations for Low-Temperature One-Dimensional Fluids
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Experimental Investigation of a Bipartite Quench in a 1D Bose gas
• A hydrodynamic approach to Stark localization
• Quantum fluctuating theory for one-dimensional shock waves
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Enhanced correlations due to ballistic transport
• Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Analytical solution of a free-fermion chain with time-dependent ramps
• Electrostatic solution of massless quenches in Luttinger liquids
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model