scholarly journals Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

2016 ◽  
Vol 93 (18) ◽  
Author(s):  
Piotr Czarnik ◽  
Jacek Dziarmaga ◽  
Andrzej M. Oleś
Keyword(s):  
Finite Temperature ◽  
Two Dimensional ◽  
Imaginary Time ◽  
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 RKKY Interaction in Graphene at Finite Temperature

2019 ◽  
Author(s):  
Eugene Kogan
Keyword(s):  
Finite Temperature ◽  
Thermodynamic Potential ◽  
Real Space ◽  
Magnetic Impurities ◽  
Zero Temperature ◽  
Rkky Interaction ◽  
Imaginary Time ◽  
Direct Evaluation ◽  
Time Representation ◽  
Short Notice

In our publication from 8 years ago1 we calculated RKKY interaction between two magnetic impurities in graphene. The consideration was based on the perturbation theory for the thermodynamic potential in the imaginary time representation and direct evaluation of real space spin susceptibility. Only the case of zero temperature was considered. We show in this short notice that the approach can be easily generalized to the case of finite temperature.

scholarly journals Tensor network study of two dimensional lattice $\phi^{4}$ theory

2019 ◽  
Author(s):  
Ryo Sakai ◽  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Yoshifumi Nakamura ◽  
Shinji Takeda ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Network
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