Suppression of transport in nondisordered quantum spin chains due to confined excitations

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here, we show that the confinement of quasiparticles can also suppress transport even if the dynamics are generated by nondisordered Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields, prepared in a paradigmatic state with a domain wall and thus with a spatially varying energy density. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from “hot” to “cold” regions of the chain is suppressed for all accessible times. We argue that this phenomenon is general, as it relies solely on the emergence of confinement of excitations.

Figure 1

Evolution of the energy density $\langle {\mathcal{H}}_i\left(t\right)\rangle$ (left panel) and of the energy current density $\langle {\mathcal{J}}_i\left(t\right)\rangle$ (right panel) profiles, governed by the Hamiltonian (1) starting from the inhomogeneous domain-wall state (2), obtained from TEBD simulations, for a range of increasing field values $h_z=0.2$ ($L=50$), 0.4 ($L=100$), and $h_x=0.15$, 0.3, 0.6, varying as indicated by the axes. (Units are fixed such that $J=1$.) The same qualitative behavior as that illustrated here persists up to long times $t={10}^3$. Note the oscillations of the profiles around the junction, with spatial amplitude $\propto h_z/h_x$ and frequency $\propto h_x$, while there is no evidence for the activation of transport.

Figure 2

Comparison between the numerical results $\langle {\sigma }_{L/2}^x\left(t\right)\rangle , \langle {\mathcal{H}}_{L/2}\left(t\right)\rangle , \langle {\mathcal{J}}_{L/2}\left(t\right)\rangle$ (symbols), and the analytical predictions $m_{L/2}\left(t\right), e_{L/2}\left(t\right), j_{L/2}\left(t\right)$ (solid lines) for the magnetization (left panel), energy density (central panel), and energy density current (right panel), respectively, at the junction $j=L/2$, as obtained from ED (with $L=16$) or TEBD (with $L=50$ or 100), and from the effective single-particle model, respectively. These curves refer to $h_x=0.45, h_z=0.2$ (top row), and $h_x=0.3, h_z=0.4$ (bottom row). (Units are fixed such that $J=1$.) Note that discrepancies between symbols and solid lines appear as time increases, due to the neglected multikink processes. The associated timescale, however, increases upon decreasing $h_z$.