Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet

Abstract

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-1/2 chain falls at low-temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in 1 + 1 dimensions. This work aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. As the temperature is reduced, we show that the onset of superdiffusion takes place at longer length and time scales ∝ 1/ . This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg = 1/2 chain compound Sr 2 CuO 3 yet calls for new and dedicated experiments.

Creating quantum spin chains through edge reconstruction in pure graphene armchair nanoribbons towards ballistic spin transport

“…The spins make quantum Heisenberg antiferromagnetic spin- 1 2 chains described by Hamiltonian (1), where the exchange constant J is equivalent to ∆E. In the thermodynamic limit, there is no long-range magnetic order in them because of the Mermin-Wagner theorem 40 , but such quantum spin chains can host diffusive, super-diffusive, or ballistic spin transport, depending on the temperature and magnetization [29][30][31][32] . More importantly, if the chain length becomes finite, such as l = 30, or the magnetization is nonzero, there are nonzero spin Drude weights at finite temperature, and thus ballistic quantum spin transport can be achieved along the reconstructed edges [29][30][31][32][41][42][43] .…”

“…The reconstructed edges consist of carbon pentagons or a hybrid of hexagons and pentagons, and host quantum Heisenberg antiferromag-netic spin-1 2 chains. These quantum spin chains, with finite lengthes or nonzero magnetization, can be used to transfer spin information due to their super-diffusive and ballistic spin transport [29][30][31][32] . More detailed result will be presented in the following.…”

Anomalous transport from hot quasiparticles in interacting spin chains

“…Assuming that nuclear spins decay by coupling to magnetic fluctuations, the rate at which nuclear spins depolarize (i.e. the T 1 time) is related as follows to the local autocorrelation function of the nearby electron spins [167,168]:…”

Efficient separation of quantum from classical correlations for mixed states with a fixed charge

“…Thus, we have shown that the configuration coherence can be efficiently computed for 1D systems with a suitable low-rank MPDO representation. Such systems include infinite size dissipative quantum chains [74], open many-body localized systems [75][76][77], strongly thermalizing systems [78], exciton dynamics [79], the quantum Heisenberg magnet [80], and temporal entanglement in many-body Floquet dynamics [81,82]. Experimentally, the configuration coherence can be obtained by estimating the purity of the mixed state [83,84] and subtracting the values encoding classical correlations; the latter are constructed out of local density measurements.…”