Hello, there seems to be a slight error in sample 2.1

[shuailiu199966]

Hello, I have three questions. Based on the code in sample 2.1, the entropy value that I obtained is negative and it is the same for all models. Can the Python script you provided be used for calculations on all models？ How should I calculate the average bond density（W_p）?

[shuailiu199966]

[tmisawa]

This problem is caused by the fact that the entropy has degrees of freedom in constant shifts. In this calculation, the high-temperature limit of entropy is set to zero and the zero-temperature limit of the entropy is -log(d_H), where d_H is the dimensions of the Hilbert space. For example, if you take the 12-site spin 1/2 model, d_H is given by 2^{12}. In that case, the entropy converges to -log(2^12)~ -8.3177 at the zero-temperature limit. If you want to set S(T=0)=0, please add log(d_H) to the calculation results.

[shuailiu199966]

 If I set L=2 and W=3 for the 2D kaitev model under the standard model, then should d_H be 2 ^ {6} or 2 ^ {12}? What other parameters should I change   ------------------ Original ------------------ From: @.>; Date:  Tue, May 14, 2024 03:36 PM To: @.>; Cc: @.>; @.>; Subject:  Re: [issp-center-dev/HPhi] Hello, there seems to be a slight error in sample 2.1 (Issue #163)

 

This problem is caused by the fact that the entropy has degrees of freedom in constant shifts. In this calculation, the high-temperature limit of entropy is set to zero and the zero-temperature limit of the entropy is -log(d_H), where d_H is the dimensions of the Hilbert space. For example, if you take the 12-site spin 1/2 model, d_H is given by 2^{12}. In that case, the entropy converges to -log(2^12)~ -8.3177. If you want to set S(T=0)=0, please add log(d_H) to the calculation results.

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[tmisawa]

In that case, d_H=2^12. You can find the information of d_H in standard output by HPhi. For example, MAX DIMENSION idim_max=4096. Here, idim_max means d_H.

[tmisawa]

You can also find information of idim_max in output/CHECK_Memory.dat.

[tmisawa]

How should I calculate the average bond density（W_p）?

Does W_p mean the flux of the Kitaev model? If so, it is possible to calculate W_p. Since W_p is defined by the product of six spin operators, i.e., W_p=Sx*Sy*Sz*Sx*Sy*Sz, it is necessary to an input file for calculating six-body Green functions.
Please note that SixBodyG is the keyword for specifying the six-body Green functions in calmod.def .

[shuailiu199966]

This problem is caused by the fact that the entropy has degrees of freedom in constant shifts. In this calculation, the high-temperature limit of entropy is set to zero and the zero-temperature limit of the entropy is -log(d_H), where d_H is the dimensions of the Hilbert space. For example, if you take the 12-site spin 1/2 model, d_H is given by 2^{12}. In that case, the entropy converges to -log(2^12)~ -8.3177 at the zero-temperature limit. If you want to set S(T=0)=0, please add log(d_H) to the calculation results.

 如果我在标准模型下为 2D kaitev 模型设置 L=2 和 W=3，那么d_H应该是 2 ^ {6} 还是 2 ^ {12}？我还应该更改哪些其他参数   ------------------ 原版 ------------------ 发件人： @.>; 日期：  周二， 2024年5月14日 03：36 PM 收件人：@.>; 抄送：@.>;@.>; 主题：  回复：[issp-center-dev/HPhi] 您好，示例 2.1（问题 #163）中似乎存在轻微错误   这个问题是由熵在恒定位移中具有自由度这一事实引起的。在此计算中，熵的高温极限设置为零 熵的零温度极限是 -log（d_H），其中 d_H 是希尔伯特空间的维数。例如，如果采用 12 位自旋 1/2 模型，则d_H由 2^{12} 给出。在这种情况下，熵收敛到 -log（2^12）~ -8.3177。如果要设置 S（T=0）=0，请在计算结果中添加 log（d_H）。 — 直接回复此电子邮件，在 GitHub 上查看或取消订阅。 您收到此消息是因为您创作了线程。消息 ID：@.>

Hello,In your example, this formula { (log (Z)+/T)/log (dH)} was used to calculate the entropy of the Heisenberg model. Can this formula be used for other models, such as kitaev. It is very sweet of you!!!

[tmisawa]

Yes. This formula can be used for any other model, such as the Kitaev model. This factor comes from the normalization of wave functions and does not relate to lattice geometry.