scholarly journals Variational tensor network renormalization in imaginary time: Benchmark results in the Hubbard model at finite temperature

2016 ◽  
Vol 94 (23) ◽  
Author(s):  
Piotr Czarnik ◽  
Marek M. Rams ◽  
Jacek Dziarmaga
Keyword(s):  
Hubbard Model ◽  
Finite Temperature ◽  
Imaginary Time ◽  
Tensor Network

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 RKKY Interaction in Graphene at Finite Temperature

2019 ◽  
Vol 5 (2) ◽  
pp. 14 ◽  
Author(s):  
Eugene Kogan
Keyword(s):  
Perturbation Theory ◽  
Finite Temperature ◽  
Thermodynamic Potential ◽  
Short Paper ◽  
Magnetic Impurities ◽  
Zero Temperature ◽  
Rkky Interaction ◽  
Imaginary Time ◽  
Coordinate Representation

In our publication from eight years ago (Kogan, E. 2011, vol. 84, p. 115119), we calculated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities adsorbed on graphene at zero temperature. We show in this short paper that the approach based on Matsubara formalism and perturbation theory for the thermodynamic potential in the imaginary time and coordinate representation which was used then, can be easily generalized, and calculate RKKY interaction between the magnetic impurities at finite temperature.

scholarly journals Tensor-network Study of Correlation-spreading Dynamics in the Two-dimensional Bose-Hubbard Model

2021 ◽  
Author(s):  
Ryui Kaneko ◽  
Ippei Danshita
Keyword(s):  
Hubbard Model ◽  
Single Particle ◽  
Correlation Functions ◽  
Cold Atoms ◽  
Spatial Dimension ◽  
Two Dimensional ◽  
Particle Correlation ◽  
Time Dynamics ◽  
Density Correlation ◽  
Tensor Network

Abstract Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly challenging for dynamics of systems with more than one spatial dimension. Here we demonstrate that a tensor-network method running on classical computers is useful for this purpose. We specifically analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from the Mott insulator by means of the infinite projected entangled pair state algorithm. Calculated single-particle correlation functions are found to be in good agreement with a recent experiment [Y. Takasu et al., Sci. Adv. 6, eaba9255 (2020)]. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region, which serves as a quantitative benchmark for future experiments.

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