In:
SciPost Physics, Stichting SciPost, Vol. 11, No. 5 ( 2021-11-29)
Abstract:
The classical Heisenberg model in two spatial dimensions constitutes
one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still,
despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether
the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of
the O(3) O ( 3 ) non-linear sigma model in 1+1 1 + 1 dimensions, one of the simplest quantum field theories encompassing
crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in 3+1 3 + 1 dimensions), namely the phenomenon of asymptotic freedom. This should
also exclude finite-temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this
work, we make use of state-of-the-art tensor network approaches, representing the classical partition function in the thermodynamic limit
over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an SU(2) S U ( 2 ) symmetry in our two-dimensional tensor network contraction scheme, we
are able to handle very large effective bond dimensions of the environment up to \chi_E^\text{eff} \sim 1500 χ E eff ∼ 1500 ,
a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length,
whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a
finite- T T transition and asymptotic freedom, though with a slight preference for
the second.
Type of Medium:
Online Resource
ISSN:
2542-4653
DOI:
10.21468/SciPostPhys
DOI:
10.21468/SciPostPhys.11.5.098
Language:
Unknown
Publisher:
Stichting SciPost
Publication Date:
2021
detail.hit.zdb_id:
2886659-9
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