Parameters

Please note that throughout this documentation we use the older short syntax for the lattice_builder input. We recommend to use the the newer, explicit syntax as described in the lattice_validator documentation, see Schema definitions.

Unit-Cell and System Parameters

A unit cell is the smallest building block of a Bravais lattice. It is composed of sites and bonds, which represent the physical system. The complete Bravais lattice is generated by repeating the unit cell along integer multiples of the lattice vectors.

For the site type spins, the representation of the spin operators can be controlled using the spin_representation input variable. spin_representation has to be a positive integer \(n\), which determines the spin quantum number \(s = n/2\).

NOTE: In presence of transverse magnetic fields (\(B_x \neq 0\) and/or \(B_y \neq 0\)) \(S_z\) is no longer a good quantum number. In order to allow for states to break this symmetry please specify the input parameter mod_Sz to be non-zero. mod_Sz has to be a positive even integer. For example, mod_Sz: 2 allows eigenstates to be a superposition of states differing by single or multiple spin flips.

Spinless Fermion System

• N:

  Fixes the number of fermions in the system. For spinless fermions it must be less or equal to the total number of sites.

• mod_N:

  In the presence of anomalous pairing, N is no longer a good quantum number. In order to allow for states to break this symmetry please specify the input parameter mod N to be non-zero, usually mod_N = 2. mod_N has to be a positive even integer.

Spinful Fermion System

• N:

  Fixes the number of fermions in the system. For spinful fermions it must be less or equal to twice the total number of sites.

• mod_N:

  In the presence of anomalous pairing, N is no longer a good quantum number. In order to allow for states to break this symmetry please specify the input parameter mod N to be non-zero, usually mod_N = 2. mod_N has to be a positive even integer.

• Sz:

  Fixes the z-component of the total spin where -N <= Sz <= N and ** 0 <= N <= M**, where "M" is the number of sites and "N" the number of fermions, and Sz <= 2 * M - N for for N > M. Note that the Sz component is twice the physical Sz expectation number in order to classify the quantum numbers with integers.

• mod_Sz:

  In the presence of a transverse magnetic field (\(B_x \neq 0\) and/or \(B_y \neq 0\)) or spin-orbit coupling (non-zero t-Values for ↑↓, ↓↑ channel) \(S_z\) is no longer a good quantum number. In order to allow for breaking this symmetry mod Sz to be a positive even integer.

Spin System

• Sz:

  The spin polarization fixes the z-component of the total spin where -M <= Sz <= M, where "M" is the number of sites. Note that the Sz component is twice the physical Sz expectation number in order to classify the quantum numbers with integers.

• mod_Sz:

  In the presence of a transverse magnetic field (\(B_x \neq 0\) and/or \(B_y \neq 0\)) \(S_z\) is no longer a good quantum number. In order to allow for states to break this symmetry mod_Sz has to be a positive even integer. For example, mod_Sz: 2 allows eigenstates to be a superposition of states differing by single or multiple spin flips.