Quantum quenches in anXXZspin chain from a spatially inhomogeneous initial state

Abstract

Results are presented for the nonequilibrium dynamics of a quantum XXZ -spin chain whose spins are initially arranged in a domain wall profile via the application of a magnetic field in the z direction, which is spatially varying along the chain. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time evolution of the domain wall profile as well as various two-point spin correlation functions are studied by the exact solution of the fermionic problem for the XX chain and via a bosonization approach and a mean-field approach for the XXZ chain. At long times the magnetization is found to equilibrate (reach the ground state value), while the two-point correlation functions in general do not. In particular, for quenches within the gapless XX phase, the spin correlation function transverse to the z direction acquires a spatially inhomogeneous structure at long times whose details depend on the initial domain wall profile. The spatial inhomogeneity is also recovered for the case of classical spins initially arranged in a domain wall profile and shows that the inhomogeneities arise due to the dephasing of transverse spin components as the domain wall broadens. A generalized Gibbs ensemble approach is found to be inadequate in capturing this spatially inhomogeneous state.

Random phase approximation study of one-dimensional fermions after a quantum quench

“…These effectively non-interacting theories, including those considered in this paper, allow for exact analytical treatment of the non-trivial dynamics. [5][6][7][8][9][10] In 1D, efficient numerical studies are also possible with the time-dependent density matrix renormalization group (tDMRG), 11,12 and exact diagonalization studies of finite systems. 13,14 Some of the analytical and numerical studies have revealed that 1D systems after a quantum quench often reach athermal steady states which can be characterized by a generalized Gibbs ensemble (GGE) constructed from identifying the conserved quantities of the system.…”

“…6,7,10,15,16 There are also many counter-examples where such a description fails, as not all physical quantities can be described using the GGE. 5,7,[17][18][19][20] One important question concerns the stability of these athermal steady states generated after a quantum quench to other perturbations such as non-trivial interactions that introduce mode-coupling and/or the breaking of integrability. Precisely this question was addressed recently in Ref 21.…”

Universal front propagation in the quantum Ising chain with domain-wall initial states

“…While the overall shape of the front is simple to obtain from a hydrodynamic (semiclassical) picture in terms of the fermionic excitations [9], the fine structure is more involved and shows universal features around the edge of the front [10,11] The melting of domain walls has been considered in various different lattice models, such as the transverse Ising [12,13], the XY [14] and XXZ chains [15][16][17][18], hard-core bosons [19][20][21], as well as in the continuum for a Luttinger model [22], the Lieb-Liniger gas [23] or within conformal field theory [24,25]. Instead of a sharp domain wall, the melting of inhomogeneous interfaces can also be studied by applying a magnetic field gradient, which is then suddenly quenched to zero [26][27][28]. Mappings from the time-evolved state of an initial domain wall to the ground state of a specific Hamiltonian have also been established [26,29].…”

Inhomogeneous quenches in a free fermionic chain: Exact results

“…The large-time behavior for fixed x and y is then determined [21] from the points where the phase is stationary, as well as possible singularities in f (k, q). For this type of protocol, it is for example known that a NESS develops in the middle [14][15][16]. Here we are interested in a different regime at large time where x/t is kept finite.…”

“…In the gapless phase (0 ≤ V ≤ 1), the stationary state supporting a ballistic particle current has been numerically investigated in [16,31,32]. Correlation functions in the NESS are those of the ground-state at half-filling multiplied by a space-dependent phase [15]. In the gapped phase, the presence of heavy-mass Hamiltonian eigenstates having dominant overlap with the DW initial state [34] prevents the formation of a light-cone and leads eventually to absence of particle transport for large times [31].…”