# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 48: Poster Session: Many Body Systems, Quantum Critical Phenomena

### TT 48.4: Poster

### Mittwoch, 18. März 2020, 15:00–19:00, P2/4OG

Quantitative analysis of the energy constant’s effect on the performance of directed loop quantum Monte Carlo Algorithm — •Dong-Xu Liu and Xue-Feng Zhang — Department of Physics, Chongqing University, Chongqing, 401331, China

The efficiency and performance of the stochastic series expansion (SSE) with directed loop quantum Monte Carlo algorithm is not only related to the specific Hamiltonian, but also the implementation of the algorithm. As one tunable parameter of SSE, the shifted constant of the energy is demonstrated to affect the autocorrelation time and also the performance of the algorithm. In order to quantitatively analyze the effect of the energy constant, we defined the cost-function as τ_{int} × T_{CPU}, where τ_{int} is auto-correction time and T_{CPU} is the CPU time costed by loop-updating process. The CPU time T_{CPU} has a good linear relationship with energy constant, because it will linearly increase the length of imaginary time. However, we discovered that auto-correction time shows a power-law decay and exponential decay behaviour with energy constant increased in one-dimensional spin-1/2 XY model and Heisenberg model, respectively. Then, we turn to analyze the effect of energy constant on the average length of loops. We demonstrated the average loop length is linearly related to the energy constant, however not proportional to the total energy. Finally, we discussed how to improve performance and also the accuracy of the correlation function by adjusting the energy constant.