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. 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.
- Authors:
-
[1];
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
- OSTI Identifier:
- 1828001
- Alternate Identifier(s):
- OSTI ID: 1788020
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 127; Journal Issue: 10; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; Anomalous diffusion; Antiferromagnetism; Quantum transport; Spin diffusion; Spin dynamics; 1-dimensional spin chains; Antiferromagnets; Heisenberg model; Kardar–Parisi–Zhang equation; Luttinger liquid model; Matrix product states; Nuclear magnetic resonance; Quantum spin chains; Spin chains; Tensor network methods
Citation Formats
Dupont, Maxime, Sherman, Nicholas E., and Moore, Joel E. Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet. United States: N. p., 2021.
Web. doi:10.1103/physrevlett.127.107201.
Dupont, Maxime, Sherman, Nicholas E., & Moore, Joel E. Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet. United States. https://doi.org/10.1103/physrevlett.127.107201
Dupont, Maxime, Sherman, Nicholas E., and Moore, Joel E. Tue .
"Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet". United States. https://doi.org/10.1103/physrevlett.127.107201. https://www.osti.gov/servlets/purl/1828001.
@article{osti_1828001,
title = {Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet},
author = {Dupont, Maxime and Sherman, Nicholas E. and Moore, Joel E.},
abstractNote = {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.},
doi = {10.1103/physrevlett.127.107201},
journal = {Physical Review Letters},
number = 10,
volume = 127,
place = {United States},
year = {Tue Aug 31 00:00:00 EDT 2021},
month = {Tue Aug 31 00:00:00 EDT 2021}
}
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