The classical two-dimensional Heisenberg model revisited: An SU(2)-symmetric tensor network study

Schmoll P, Kshetrimayum A, Eisert J, Orus R, Rizzi M (2021)

Publication Type: Journal article

Publication year: 2021

Journal

SciPost Physics SciPost

Book Volume: 11

Article Number: 098

Journal Issue: 5

DOI: 10.21468/SciPostPhys.11.5.098

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) non-linear sigma model in 1 + 1 dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in 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) symmetry in our two-dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to χEeff ∼ 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 transition and asymptotic freedom, though with a slight preference for the second.

Involved external institutions

Johannes Gutenberg-Universität Mainz (JGU) DE Germany (DE) Freie Universität Berlin DE Germany (DE) Donostia International Physics Center (DIPC) ES Spain (ES) Forschungszentrum Jülich / Research Centre Jülich (FZJ) DE Germany (DE)

How to cite

APA:

Schmoll, P., Kshetrimayum, A., Eisert, J., Orus, R., & Rizzi, M. (2021). The classical two-dimensional Heisenberg model revisited: An SU(2)-symmetric tensor network study. SciPost Physics, 11(5). https://doi.org/10.21468/SciPostPhys.11.5.098

MLA:

Schmoll, Philipp, et al. "The classical two-dimensional Heisenberg model revisited: An SU(2)-symmetric tensor network study." SciPost Physics 11.5 (2021).

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