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Norbert Schuch
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Qmechanic ♦
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Truncation Problem of Density Matrix Renormalisation Group  (DMRG)

I am wondering that is there any restrictions for the truncation in DMRG algorithm. Currently I am using DMRG to calculate ground state energy per site of a many-body system described by on-site potential term only($H_{i} = -\mu c^{\dagger}_{i}c_{i}$). However, I got a diverging answer. This is not physical since the ground state energy per site is an intensive quantity, which is independent of the size of the system. Therefore, I re-examine my code and I found something strange there. I print out the eigenvalues of the reduced density matrix of system: \begin{equation} \text{Eigenvalues of $\rho_{sys}$} = [1.000, 6.988\text{E-31}, 8.362\text{E-32}, 6.398\text{E-33},...,0.000] \end{equation} Despite $\text{tr}(\rho_{sys}) \simeq 1$, I think that this set of eigenvalues is strange. The first element is already equal 1 and the difference between the first and second element is $10^{-30}$. This means that only the first eigenstate is most probable and other states are not. Therefore, we can truncate other states out. When I set the number of maximum states for truncation to some number(e.g. 16), I got a diverging answer. This means that I have set a wrong condition for truncation. Therefore, based on the above discussion, what truncation condition should I use if the eigenvalues of $\rho_{sys}$ like that? Besides, is there any restriction for the truncation in DMRG which I have not discussed above? Thank you.

Truncation Problem of Density Matrix Renormalisation Group(DMRG)

I am wondering that is there any restrictions for the truncation in DMRG algorithm. Currently I am using DMRG to calculate ground state energy per site of a many-body system described by on-site potential term only($H_{i} = -\mu c^{\dagger}_{i}c_{i}$). However, I got a diverging answer. This is not physical since the ground state energy per site is an intensive quantity, which is independent of the size of the system. Therefore, I re-examine my code and I found something strange there. I print out the eigenvalues of the reduced density matrix of system: \begin{equation} \text{Eigenvalues of $\rho_{sys}$} = [1.000, 6.988\text{E-31}, 8.362\text{E-32}, 6.398\text{E-33},...,0.000] \end{equation} Despite $\text{tr}(\rho_{sys}) \simeq 1$, I think that this set of eigenvalues is strange. The first element is already equal 1 and the difference between the first and second element is $10^{-30}$. This means that only the first eigenstate is most probable and other states are not. Therefore, we can truncate other states out. When I set the number of maximum states for truncation to some number(e.g. 16), I got a diverging answer. This means that I have set a wrong condition for truncation. Therefore, based on the above discussion, what truncation condition should I use if the eigenvalues of $\rho_{sys}$ like that? Besides, is there any restriction for the truncation in DMRG which I have not discussed above? Thank you.

Truncation Problem of Density Matrix Renormalisation Group  (DMRG)

I am wondering that is there any restrictions for the truncation in DMRG algorithm. Currently I am using DMRG to calculate ground state energy per site of a many-body system described by on-site potential term only($H_{i} = -\mu c^{\dagger}_{i}c_{i}$). However, I got a diverging answer. This is not physical since the ground state energy per site is an intensive quantity, which is independent of the size of the system. Therefore, I re-examine my code and I found something strange there. I print out the eigenvalues of the reduced density matrix of system: \begin{equation} \text{Eigenvalues of $\rho_{sys}$} = [1.000, 6.988\text{E-31}, 8.362\text{E-32}, 6.398\text{E-33},...,0.000] \end{equation} Despite $\text{tr}(\rho_{sys}) \simeq 1$, I think that this set of eigenvalues is strange. The first element is already equal 1 and the difference between the first and second element is $10^{-30}$. This means that only the first eigenstate is most probable and other states are not. Therefore, we can truncate other states out. When I set the number of maximum states for truncation to some number(e.g. 16), I got a diverging answer. This means that I have set a wrong condition for truncation. Therefore, based on the above discussion, what truncation condition should I use if the eigenvalues of $\rho_{sys}$ like that? Besides, is there any restriction for the truncation in DMRG which I have not discussed above?

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Ricky Pang
Ricky Pang
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Truncation Problem of Density Matrix Renormalisation Group(DMRG)

I am wondering that is there any restrictions for the truncation in DMRG algorithm. Currently I am using DMRG to calculate ground state energy per site of a many-body system described by on-site potential term only($H_{i} = -\mu c^{\dagger}_{i}c_{i}$). However, I got a diverging answer. This is not physical since the ground state energy per site is an intensive quantity, which is independent of the size of the system. Therefore, I re-examine my code and I found something strange there. I print out the eigenvalues of the reduced density matrix of system: \begin{equation} \text{Eigenvalues of $\rho_{sys}$} = [1.000, 6.988\text{E-31}, 8.362\text{E-32}, 6.398\text{E-33},...,0.000] \end{equation} Despite $\text{tr}(\rho_{sys}) \simeq 1$, I think that this set of eigenvalues is strange. The first element is already equal 1 and the difference between the first and second element is $10^{-30}$. This means that only the first eigenstate is most probable and other states are not. Therefore, we can truncate other states out. When I set the number of maximum states for truncation to some number(e.g. 16), I got a diverging answer. This means that I have set a wrong condition for truncation. Therefore, based on the above discussion, what truncation condition should I use if the eigenvalues of $\rho_{sys}$ like that? Besides, is there any restriction for the truncation in DMRG which I have not discussed above? Thank you.