中国物理B ›› 2019, Vol. 28 ›› Issue (10): 107103-107103.doi: 10.1088/1674-1056/ab3dfe

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇    下一篇

Benchmarking the simplest slave-particle theory with Hubbard dimer

Wei-Wei Yang(杨薇薇), Hong-Gang Luo(罗洪刚), Yin Zhong(钟寅)   

  1. 1 Center for Interdisciplinary Studies and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China;
    2 Beijing Computational Science Research Center, Beijing 100084, China
  • 收稿日期:2019-07-26 修回日期:2019-08-21 出版日期:2019-10-05 发布日期:2019-10-05
  • 通讯作者: Yin Zhong E-mail:zhongy@lzu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11704166, and 11834005), the Fundamental Research Funds for the Central Universities, China, and Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT-16R35).

Benchmarking the simplest slave-particle theory with Hubbard dimer

Wei-Wei Yang(杨薇薇)1, Hong-Gang Luo(罗洪刚)1,2, Yin Zhong(钟寅)1   

  1. 1 Center for Interdisciplinary Studies and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China;
    2 Beijing Computational Science Research Center, Beijing 100084, China
  • Received:2019-07-26 Revised:2019-08-21 Online:2019-10-05 Published:2019-10-05
  • Contact: Yin Zhong E-mail:zhongy@lzu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11674139, 11704166, and 11834005), the Fundamental Research Funds for the Central Universities, China, and Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT-16R35).

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摘要： Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal-insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods:(i) slave-spin method on mean-field level, (ii) slave-spin method with gauge constraint, and (iii) the exact solution as a benchmark. We find that, protected by the particle-hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space. These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.

关键词: slave particle theory, Hubbard dimer, strongly correlated physics

Abstract: Slave-particle method is a powerful tool to tackle the correlation effect in quantum many-body physics. Although it has been successfully used to comprehend various intriguing problems, such as Mott metal-insulator transition and Kondo effect, there is still no convincing theory so far on the availability and limitation of this method. The abuse of slave-particle method may lead to wrong physics. As the simplest slave-particle method, Z2 slave spin, which is widely applied to many strongly correlated problems, is highly accessible and researchable. In this work, we will uncover the nature of the Z2 slave-spin method by studying a two-site Hubbard model. After exploring aspects of properties of this toy model, we make a comparative analysis of the results obtained by three methods:(i) slave-spin method on mean-field level, (ii) slave-spin method with gauge constraint, and (iii) the exact solution as a benchmark. We find that, protected by the particle-hole symmetry, the slave-spin mean-field method can recover the static properties of ground state exactly at half filling. Furthermore, in the parameter space where both U and T are small enough, the slave-spin mean-field method is also reliable in calculating the dynamic and thermal dynamic properties. However, when U or T is considerably large, the mean-field approximation gives ill-defined behaviors, which result from the unphysical states in the enlarged Hilbert space. These findings lead to our conclusion that the accuracy of slave particle can be guaranteed if we can exclude all unphysical states by enforcing gauge constraints. Our work demonstrates the promising prospect of slave-particle method in studying complex strongly correlated models with specific symmetry or in certain parameter space.

Key words: slave particle theory, Hubbard dimer, strongly correlated physics

中图分类号:  (Theories and models of many-electron systems)

  • 71.10.-w
71.27.+a (Strongly correlated electron systems; heavy fermions)