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.

Dynamics and level statistics of interacting fermions in the lowest Landau level

“…In the 'tight-binding chain' picture, this would mean unit filling for the first third or last third of the chain, and zero filling for the rest of the chain. This would then be analogous to the dynamics considered in, e.g. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], for spin or tight-binding systems, when the initial state has all fermions or all -spins on one side of the chain. In such cases, the single-particle hopping leads to transport of particles from the filled side to the empty side, with a current-carrying non-equilibrium steady state arising dynamically within the light cone region.…”

“…This has an obvious analogy in fermionic tight-binding chains, and is also analogous to a spin chain where some contiguous block start in a spin-up state and the rest start in a spin-down state, e.g.the 'domain wall' state        ñ | . For tight-binding fermionic chains and spin chains, this type of dynamics by now has been studied in some detail [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Related situations, e.g.when one/both of the regions are not completely full/empty, are also of interest and sometimes involve similar physics [23,[32][33][34][35][36][37][38][39][40][41].…”

Front dynamics and entanglement in the XXZ chain with a gradient

“…when two parts of a system are prepared initially in their (otherwise homogeneous) ground states with different magnetizations. The resulting front structures have been widely studied for the XX [22][23][24][25][26][27][28][29], the transverse Ising [30][31][32][33][34] and the XXZ chains [11,27,31,35,36]. In the latter case, a remarkable analytical solution has been found very recently [37], using the method of generalized hydrodynamics (GHD).…”

Front dynamics in the XY chain after local excitations

“…Recently, however, domain walls created upon the symmetry-broken ferromagnetic ground states of TI or XY chains have been considered [23][24][25]. The ordering in these chains occurs in the longitudinal component of the magnetization, which is a highly nonlocal string operator in the fermionic picture, being nontrivially related to the local conserved densities.…”

“…Hence, even though one has a free-fermion model at hand, it is a priori unclear whether a hydrodynamic description still holds for this observable. Nevertheless, in [24,25] it has been shown that, for domain walls excited by a single local fermion operator, the longitudinal magnetization profile has the usual hydrodynamic scaling limit one would naively expect. Namely, the profile is determined by noninteracting quasiparticles carrying the fraction of a spin-flip and traveling at the corresponding group velocity.…”