Finite-temperature transport in one-dimensional quantum lattice models

Simulating Hydrodynamics on Noisy Intermediate-Scale Quantum Devices with Random Circuits

“…We find that αðtÞ exhibits damped oscillations (presumably caused by the integrability of H [76]) around the mean value α ≈ 2=3, which signals superdiffusion and is consistent with a description of spin transport in terms of the Kardar-Parisi-Zhang (KPZ) universality class for the integrable and isotropic Heisenberg chain [29,[76][77][78][79][80][81]. Remarkably, αðtÞ is essentially independent of δt and α ≈ 2=3 can be readily extracted even for the largest δt ¼ 2.…”

“…Transport processes represent one of the most generic nonequilibrium situations [29]. In the quantum realm, the understanding of transport not only plays a key role to pave the way for future technologies such as spintronics [30], but is also intimately related to fundamental questions of equilibration and thermalization in many-body systems [31][32][33].…”

“…In the quantum realm, the understanding of transport not only plays a key role to pave the way for future technologies such as spintronics [30], but is also intimately related to fundamental questions of equilibration and thermalization in many-body systems [31][32][33]. While quantum transport has been experimentally studied in mesoscopic systems, solid-state quantum magnets, and cold-atom settings (see, e.g., [34][35][36][37][38]), active questions from the theory side include the quantitative calculation of transport coefficients [29,39], as well as explaining the emergence of conventional hydrodynamic transport from the underlying unitary time evolution of closed quantum systems [40].…”

“…where S z lðl 0 Þ is a spin-1=2 operator at lattice site l (l 0 ), S z l ðtÞ ¼ e iHt S l e −iHt is the time-evolved operator with respect to some Hamiltonian H, and L denotes the number of spins (qubits). The spatiotemporal correlations C l;l 0 ðtÞ are central objects for studying transport within linear response theory [29], as well as thermalization and manybody localization in quantum systems [43]. As a key ingredient, our scheme exploits the concept of quantum typicality [44][45][46], which asserts that ensemble averages can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space [47][48][49].…”

Probing the edge between integrability and quantum chaos in interacting few-atom systems

“…The interest in quantum chaos, especially when caused by the interactions between particles, has grown significantly in the last few years due to its relationship with several questions of current experimental and theoretical research that arise in atomic, molecular, optical, condensed matter, and high energy physics, as well as in quantum information science. In interacting many-body quantum systems, quantum chaos ensures thermalization and the validity of the eigenstate thermalization hypothesis (ETH) [17,28,114], hinders localization [74,79,98], facilitates the phenomenon of many-body quantum scarring [8,107], leads to diffusive transport [12,55] and causes the fast spread of quantum information [75,91].…”