scholarly journals Tensor network simulation of the Kitaev-Heisenberg model at finite temperature

2019 ◽  
Vol 100 (16) ◽  
Author(s):  
Piotr Czarnik ◽  
Anna Francuz ◽  
Jacek Dziarmaga
Keyword(s):  
Finite Temperature ◽  
Heisenberg Model ◽  
Network Simulation ◽  
Tensor Network

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

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Philipp Schmoll ◽  
Augustine Kshetrimayum ◽  
Jens Eisert ◽  
Román Orús ◽  
Matteo Rizzi
Keyword(s):  
Finite Temperature ◽  
Heisenberg Model ◽  
Symmetric Tensor ◽  
Linear Sigma Model ◽  
Asymptotic Freedom ◽  
Quantum Field Theories ◽  
Two Dimensional ◽  
Tensor Network ◽  
Spatial Dimensions ◽  
Contraction Scheme

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+11+1 dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in 3+13+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)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_E^\text{eff} \sim 1500χEeff∼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-TT transition and asymptotic freedom, though with a slight preference for the second.

scholarly journals Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

2004 ◽  
Vol 38 (4) ◽  
pp. 599-616 ◽  
Author(s):  
N. Shannon ◽  
B. Schmidt ◽  
K. Penc ◽  
P. Thalmeier
Keyword(s):  
Finite Temperature ◽  
Heisenberg Model ◽  
Square Lattice

scholarly journals Tensor network simulation of polaron-polaritons in organic microcavities

2018 ◽  
Vol 98 (16) ◽  
Author(s):  
Javier del Pino ◽  
Florian A. Y. N. Schröder ◽  
Alex W. Chin ◽  
Johannes Feist ◽  
Francisco J. Garcia-Vidal
Keyword(s):  
Network Simulation ◽  
Tensor Network

Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Ai-Yuan Hu ◽  
Lin Wen ◽  
Guo-Pin Qin ◽  
Zhi-Min Wu ◽  
Peng Yu ◽  
...  
Keyword(s):  
Phase Transition ◽  
Finite Temperature ◽  
Heisenberg Model
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