Universal Kardar-Parisi-Zhang Dynamics in Integrable Quantum Systems

Abstract

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically-driven models. Motivated by recent advances in the realization of SU(N )-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems.

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

“…Superdiffusive transport hMi ∼ t 2=3 at D = 1 is a characteristic of systems within the KPZ universality class. Moreover, numerical studies found that the spin-spin correlation function coincides with the KPZ scaling function (44,49), which has led to the conjecture that nearequilibrium spin transport in the Heisenberg model belongs to the KPZ universality class (44,50,51). This universality class is associated with the classical nonlinear stochastic KPZ equation @h=@t ¼ n∇ 2 h þ lð∇hÞ 2 þ h x; t ð Þ, which was originally introduced (52) to describe the dynamics of driven interfaces as a height field h x; t ð Þ, where v, l, and h set the strength of the smoothening diffusion, roughening nonlinear growth, and stochasticity terms, respectively.…”

Universality in coupled stochastic Burgers systems with degenerate flux Jacobian

“…More recently, revived interest has been initiated through the study of spin chains, both classical [26][27][28][29] and quantum [12,13,30]. The KPZ exponent 3/2 was theoretically established and experimentally confirmed [14,15,31,32].…”

Anomalous transport from hot quasiparticles in interacting spin chains

“…In practice, all of these truncation schemes break integrability, so it is unclear a priori that they should be able to faithfully describe transport in integrable systems. Nevertheless, promising results on the Heisenberg spin chain have been achieved with DMT as well as DAOE [164,165]. One can regard our exact results on integrable systems as providing a benchmark to test the performance of these methods against.…”