Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

Abstract

We study the dynamics of a spin-1 2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schrödinger equation is used to construct a variational solution capturing several aspects of the problem.

Domain wall melting in spin-1 XXZ chains

“…This behavior is reminiscent of scarred quantum states [55], where in particular, periodic orbits in the semi-classical TDVP time evolution can be identified [56]. While in the classical model the absence of transport is related to the presence of static soliton solutions [31,32] and their "breathing" modes, our analysis suggests that even the non-integrable spin-1 quantum chains posses eigenstates which have a large overlap with semi-classical localized states. On the other hand the case with θ = π/4 shows linear growth of entanglement, see Fig.…”

“…Remarkably in the easy-plane regime ∆ < 1 the spin transport is ballistic up to a crossover time, which appears to diverge as ∆ approaches 1 − . In the isotropic case ∆ = 1 the spin dynamics has the same qualitative behaviour as in the continuous classical integrable Landau-Lifshitz (LL) partial differential equation (4) [39,40], which indeed displays anomalous spin diffusion for non-twisted domain wall initial state [31,32]. In the easy-axis regime ∆ > 1 we find insulating spin dynamics for any value of the twist.…”

“…This scenario was questioned in [22], showing the necessity of probing the interplay between charge transport and global symmetries in a more controlled set-up.In this letter, we consider the transport properties of the non-integrable anisotropic spin-1 chain far from equilibrium. In particular we focus on two setups, the socalled domain wall and twisted initial conditions [23][24][25][26][27][28][29][30][31][32][33], which are experimentally relevant, and widely used for probing the transport and non-equilibrium dynamics in many-body systems [34][35][36][37]. We compute the time evolution using the TDVP algorithm at fixed bond dimension up to times ∼ 10 3 , in units of spin coupling and compare it with the results obtained by a standard tDMRG algorithm.…”

Kardar-Parisi-Zhang universality from soft gauge modes

“…By separation of scales, the microscopic quasiparticle degrees of freedom couple to Ω as a local bath. This class of hydrodynamic states includes the tunable z-polarized domain walls ρ ∝ (1 + µσ z ) N/2 ⊗ (1 − µσ z ) N/2 that have frequently been considered in the literature 12,18,[39][40][41][42][43][44][45] . In the continuum limit N → ∞, the hydrodynamic state is determined as above, leading to a uniform initial condition for the quasiparticle mode occupancies and a domain wall initial condition for the pseudovacuum gauge field.…”

“…Obtaining the conserved modes of the Landau-Lifshitz evolution in a gauge-invariant manner is subtle, and standard parameterizations of the spin direction Ω are ineffective. An elegant solution is to regard Ω as the tangent vector of a space curve, with arc-length parameterized by position 45,50 . Then the two gauge-invariant conserved modes are found to be energy density E = κ 2 /2 and torsion τ (geometrically, κ and τ denote the curvature and torsion in the Frenet-Serret frame of the curve traced out by Ω).…”