Universität zu Köln

Schmoll, Philipp, Kshetrimayum, Augustine, Eisert, Jens ORCID: 0000-0003-3033-1292, Orus, Roman and Rizzi, Matteo (2021). The classical two-dimensional Heisenberg model revisited: An SU (2)-symmetric tensor network study. SciPost Phys., 11 (5). AMSTERDAM: SCIPOST FOUNDATION. ISSN 2542-4653

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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 chi(eff)(E) similar to 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schmoll, Philipp UNSPECIFIED UNSPECIFIED UNSPECIFIED Kshetrimayum, Augustine UNSPECIFIED UNSPECIFIED UNSPECIFIED Eisert, Jens UNSPECIFIED orcid.org/0000-0003-3033-1292 UNSPECIFIED Orus, Roman UNSPECIFIED UNSPECIFIED UNSPECIFIED Rizzi, Matteo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-597146
DOI:	10.21468/SciPostPhys.11.5.098
Journal or Publication Title:	SciPost Phys.
Volume:	11
Number:	5
Date:	2021
Publisher:	SCIPOST FOUNDATION
Place of Publication:	AMSTERDAM
ISSN:	2542-4653
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NONLINEAR SIGMA-MODEL; MATRIX PRODUCT STATES; ASYMPTOTIC FREEDOM; PHASE-TRANSITION; NOBEL-LECTURE; LATTICE THEORIES; CONTINUUM-LIMIT; SPIN Multiple languages Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/59714