5.1. tnpy.model.Thirring#

class tnpy.model.Thirring(n, delta, ma, penalty, s_target)[source]#

Bases: tnpy.model.model_1d.Model1D

The Hamiltonian

\[H = -\frac{1}{2} \sum_{n=0}^{N-1}(S_n^+ S_{n+1}^- + S_{n+1}^+ S_n^-) + \tilde{m}_0 a \sum_{n=0}^{N-1} (-1)^n \left(S_n^z + \frac{1}{2}\right) + \Delta(g) \sum_{n=0}^{N-1} \left(S_n^z + \frac{1}{2}\right) \left(S_{n+1}^z + \frac{1}{2}\right)\]

If the penalty strength \(\lambda \neq 0\), a penalty term will be taken into account

\[H \rightarrow H + \lambda \left(\sum_{n=0}^{N-1} S_n^z - S_{target}\right)^2\]
Parameters

  • n (int) – System size.

  • delta (float) – Wavefunction-renormalized bare coupling, Delta(g).

  • ma (float) – Wavefunction-renormalized bare mass.

  • penalty (float) – Penalty strength (of Lagrangian multiplier).

  • s_target (int) – The targeting total Sz charge sector.

Return type

None

__init__(n, delta, ma, penalty, s_target)[source]#

The Hamiltonian

\[H = -\frac{1}{2} \sum_{n=0}^{N-1}(S_n^+ S_{n+1}^- + S_{n+1}^+ S_n^-) + \tilde{m}_0 a \sum_{n=0}^{N-1} (-1)^n \left(S_n^z + \frac{1}{2}\right) + \Delta(g) \sum_{n=0}^{N-1} \left(S_n^z + \frac{1}{2}\right) \left(S_{n+1}^z + \frac{1}{2}\right)\]

If the penalty strength \(\lambda \neq 0\), a penalty term will be taken into account

\[H \rightarrow H + \lambda \left(\sum_{n=0}^{N-1} S_n^z - S_{target}\right)^2\]
Parameters

  • n (int) – System size.

  • delta (float) – Wavefunction-renormalized bare coupling, Delta(g).

  • ma (float) – Wavefunction-renormalized bare mass.

  • penalty (float) – Penalty strength (of Lagrangian multiplier).

  • s_target (int) – The targeting total Sz charge sector.

Return type

None

Methods

__init__(n, delta, ma, penalty, s_target)

The Hamiltonian

Attributes

mpo

Return matrix product operator (mpo) as a property of the model.

n

__init__(n, delta, ma, penalty, s_target)[source]#

The Hamiltonian

\[H = -\frac{1}{2} \sum_{n=0}^{N-1}(S_n^+ S_{n+1}^- + S_{n+1}^+ S_n^-) + \tilde{m}_0 a \sum_{n=0}^{N-1} (-1)^n \left(S_n^z + \frac{1}{2}\right) + \Delta(g) \sum_{n=0}^{N-1} \left(S_n^z + \frac{1}{2}\right) \left(S_{n+1}^z + \frac{1}{2}\right)\]

If the penalty strength \(\lambda \neq 0\), a penalty term will be taken into account

\[H \rightarrow H + \lambda \left(\sum_{n=0}^{N-1} S_n^z - S_{target}\right)^2\]
Parameters

  • n (int) – System size.

  • delta (float) – Wavefunction-renormalized bare coupling, Delta(g).

  • ma (float) – Wavefunction-renormalized bare mass.

  • penalty (float) – Penalty strength (of Lagrangian multiplier).

  • s_target (int) – The targeting total Sz charge sector.

Return type

None