Coexistence of energy diffusion and local thermalization in nonequilibriumXXZspin chains with integrability breaking

Abstract

In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit. We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.

Energy transport in a disordered spin chain with broken U(1) symmetry: Diffusion, subdiffusion, and many-body localization

“…In the limit of no disorder (W = 0), we find that the energy current j E is independent of the length of the system, which signals that the energy transport is ballistic; this is consistent with previous work on the XYZ model [36]. Ballistic energy transport has been linked to the integrability of quantum systems [48], a characteristic which is also visible in the Poissonian statistics of the Hamiltonian's eigenenergy spectrum [49]. For 0 < ∆ ≤ 2 and 0 < η ≤ 1 we find that the average of r falls close to the Poissonian value r P = ln 4 − 1 over the entire spectrum.…”

Non-equilibrium conformal field theories with impurities

“…This suggestion has later received further support by the work [30], where an exact bound on the so-called Drude weight was derived for integrable systems driven by Lindblad operators. Numerical confirmations, although limited to XXZ spin chains, have also been found in [24,25] and the very recent [26]. Since a CFT is integrable, this would imply a non-negligible ballistic component even for non-integrable microscopic 1D systems if their low-temperature regimes were described by non-equilibrium CFTs.…”

Thermalization with detailed-balanced two-site Lindblad dissipators

“…2(a). We have run various tests using also the ρ T described in [23,25], and we found that using Eq. 11 was consistently resulting in ratios of effective inverse temperatures closest to 1.…”