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

Journal Article · Tue Aug 31 00:00:00 EDT 2021 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.127.107201· OSTI ID:1788020

Dupont, Maxime ^[1]; Sherman, Nicholas E. ^[1]; Moore, Joel E. ^[1]

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1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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. In this work, as the temperature $$T$$ is reduced, we show that the onset of superdiffusion takes place at longer length and time scales $$\propto 1/T$$. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg $S=1/2$ chain compound Sr$$_2$$CuO$$_3$$ yet calls for new and dedicated experiments.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1788020
• Alternate ID(s): OSTI ID: 1828001
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 127; ISSN 0031-9007
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

1-dimensional spin chains
36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Anomalous diffusion
Antiferromagnetism
Antiferromagnets
Heisenberg model
Kardar–Parisi–Zhang equation
Luttinger liquid model
Matrix product states
Nuclear magnetic resonance
Quantum spin chains
Quantum transport
Spin chains
Spin diffusion
Spin dynamics
Tensor network methods