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Register a new userExact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
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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, $|downarrowdotsdownarrowuparrowdotsuparrowdownarrowdotsdownarrowrangle$. 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.
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In spin chains with local unitary evolution preserving the magnetization $S^{rm z}$, the domain-wall state $left| dots uparrow uparrow uparrow uparrow uparrow downarrow downarrow downarrow downarrow downarrow dots right>$ typically melts. At large times, a non-trivial magnetization profile develops in an expanding region around the initial position of the domain-wall. For non-integrable dynamics the melting is diffusive, with entropy production within a melted region of size $sqrt{t}$. In contrast, when the evolution is integrable, ballistic transport dominates and results in a melted region growing linearly in time, with no extensive entropy production: the spin chain remains locally in states of zero entropy at any time. Here we show that, for the integrable spin-$1/2$ XXZ chain, low-energy quantum fluctuations in the melted region give rise to an emergent Luttinger liquid which, remarkably, differs from the equilibrium one. The striking feature of this emergent Luttinger liquid is its quasi-particle charge (or Luttinger parameter $K$) which acquires a fractal dependence on the XXZ chain anisotropy parameter $Delta$.
We discuss the exact solution for the properties of the recently introduced ``necklace model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.
We demonstrate that the exact non-equilibrium steady state of the one-dimensional Heisenberg XXZ spin chain driven by boundary Lindblad operators can be constructed explicitly with a matrix product ansatz for the non-equilibrium density matrix where the matrices satisfy a {it quadratic algebra}. This algebra turns out to be related to the quantum algebra $U_q[SU(2)]$. Coherent state techniques are introduced for the exact solution of the isotropic Heisenberg chain with and without quantum boundary fields and Lindblad terms that correspond to two different completely polarized boundary states. We show that this boundary twist leads to non-vanishing stationary currents of all spin components. Our results suggest that the matrix product ansatz can be extended to more general quantum systems kept far from equilibrium by Lindblad boundary terms.
All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + Delta S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $Delta=0 , cos(0.3pi)$, and 1. The dynamic spin pair correlations $< S_{l+n}^{mu}(t) S_l^{mu} > , (mu=x,z)$, the dynamic structure factors $S^{mu}(q,omega)$, and the intermediate structure factors $I^{mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,omega)$ is mainly concentrated on the region $|omega| < varepsilon_2(q)$, where $varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{mu}(q,t)$ for $Delta eq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.
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