Exact time evolution formulae in the XXZ spin chain with domain wall initial state
arXiv:2112.12092 · doi:10.1088/1751-8121/ac5fe8
Abstract
We study the time evolution of the spin-1/2 XXZ chain initialized in a domain wall state, where all spins to the left of the origin are up, all spins to its right are down. The focus is on exact formulae, which hold for arbitrary finite (real or imaginary) time. In particular, we compute the amplitudes corresponding to the process where all but spins come back to their initial orientation, as a fold contour integral. These results are obtained using a correspondence with the six vertex model, and taking a somewhat complicated Hamiltonian/Trotter-type limit. Several simple applications are studied and also discussed in a broader context.
arXiv comment44 pages, 5 figures
References in corpus (56)
- Level-Spacing Distributions and the Airy Kernel
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Hydrodynamic Diffusion in Integrable Systems
- Spin diffusion from an inhomogeneous quench in an integrable system
- Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
- Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
- Families of quasi-local conservation laws and quantum spin transport
- Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
- Microscopic origin of ideal conductivity in integrable quantum models
- Full counting statistics in a propagating quantum front and random matrix spectra
- Stochastic interacting particle systems out of equilibrium
- The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
- Quantum Generalized Hydrodynamics
- Partially Asymmetric Exclusion Process with Open Boundaries
- Integral Formulas for the Asymmetric Simple Exclusion Process
- Inhomogeneous field theory inside the arctic circle
- A Fredholm Determinant Representation in ASEP
- Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
- Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
- Superdiffusion in spin chains
- Six-Vertex Model with Domain Wall Boundary Conditions and One-Matrix Model
- Logarithmic current fluctuations in non-equilibrium quantum spin chains
- Relaxation dynamics in the gapped XXZ spin-1/2 chain
- The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
- Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
- The arctic curve of the domain-wall six-vertex model
- Current operators in Bethe Ansatz and Generalized Hydrodynamics: An exact quantum/classical correspondence
- Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
- Boundary correlation functions of the six-vertex model
- Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
- Arctic curves of the six-vertex model on generic domains: the Tangent Method
- Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
- Current operators in integrable spin chains: lessons from long range deformations
- Emptiness formation probability, Toeplitz determinants, and conformal field theory
- Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
- The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime
- Free fermions at the edge of interacting systems
- Exciting Hard Spheres
- Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
- Inhomogeneous Gaussian Free Field inside the interacting arctic curve
- Quantum Crystals and Spin Chains
- On the partition function of the six-vertex model with domain wall boundary conditions
- Extreme boundary conditions and random tilings
- Droplet Excitations for the Spin-1/2 XXZ Chain with Kink Boundary Conditions
- On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions
- Arctic curves for paths with arbitrary starting points: a tangent method approach
- Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions
- Arctic curves of the twenty-vertex model with domain wall boundaries
- Analytical results on the Heisenberg spin chain in a magnetic field
- The propagator of the finite XXZ spin- chain
- Integral formulas and antisymmetrization relations for the six-vertex model
- Concavity analysis of the tangent method
- Non-probabilistic fermionic limit shapes