isqham.lattice package¶
Submodules¶
isqham.lattice.fermion module¶
- exception FermionHamiltonianError¶
Bases:
Exception
- class SpinfulHamiltonian¶
Bases:
objectset a general Hamiltonian: \(H=H_0+H_1\) where
\(H_0=\sum_{ij}\sum_{\sigma\sigma'} c^\dagger_{i\sigma} c_{j\sigma'}\) and \(H_1=\sum_{ijkl}\sum_{\alpha\beta\gamma\delta} c^\dagger_{i\alpha} c^\dagger_{j\beta} c_{k\gamma}c_{l\delta}\)
This Hamiltonian is made of SpinlessHamiltonian with mapping spin-up (spin-down) into even (odd) site.
- exportPauliOperator(encoding)¶
- setCoulombU(i, U)¶
\(U n_{i\uparrow} n_{i\downarrow}\)
- Parameters:
i (int) – site index
U (float) – U
- Return type:
self
- setCoulombV1(i, j, V)¶
\(V n_i n_j\), where \(n_i = n_{i\uparrow} + n_{i\downarrow}\)
- Parameters:
i (int) – site index
j (int) – site index
V (float) – V
- setHopping(i, j, tij)¶
\(t_{ij} \sum_{i,j,\sigma} c^+_{i\sigma} c_{j\sigma} + h.c.\)
- Parameters:
i (int) – site index.
j (int) – site index.
tij (complex) – _description_
- setOnSiteEnergy(i, m)¶
\(m \sum_{\sigma} c^+_{i\sigma}c_{i\sigma}\)
- Parameters:
i (_type_) – site index
m (_type_) – energy
- Return type:
self
- class SpinlessHamiltonian¶
Bases:
objectset a general Hamiltonian: \(H=\sum_{ij} c^\dagger_i c_j +\sum_{ijkl} c^\dagger_i c^\dagger_j c_k c_l\)
- exportPauliOperator(encoding)¶
- getCountN()¶
count total number of sites
- setCoulomb(i, j, U)¶
\(U n_i n_j\)
- Parameters:
i (int) – site index
j (int) – site index
U (float) – U
- setHopping(i, j, tij)¶
\(t_{ij} c^+_i c_j + h.c.\)
- Parameters:
i (int) – site index
j (int) – site index
tij (complex) – hopping energy
- setOnSiteEnergy(i, m)¶
\(m * n_i\)
- Parameters:
i (int) – site index
m (float) – onsite energy
- set_CC(i, j, val)¶
- term:
v C_i C_j + h.c.
- Parameters:
i (int) – site index
j (int) – site index
val (complex) – coefficient
- set_CdC(i, j, val)¶
- term:
v C^+_i C_j + h.c.
- Parameters:
i (int) – site index
j (int) – site index
val (complex) – coefficient
- set_CdCCdC(i, j, k, l, val)¶
- term:
v C^+_i C_j C^+_k C_l + h.c.
- Parameters:
i (int) – site index
j (int) – site index
k (int) – site index
l (int) – site index
val (complex) – coefficient
- set_CdCdCC(i, j, k, l, val)¶
- term:
v C^+_i C^+_j C_k C_l + h.c.
- Parameters:
i (int) – site index
j (int) – site index
k (int) – site index
l (int) – site index
val (complex) – coefficient
isqham.lattice.fermionLattice module¶
- exception FermionLatticeError¶
Bases:
Exception
- class IntegerMesh¶
Bases:
object- static get_all_inside_parallelepiped(a1, a2, a3)¶
reture all integer points inside a parallelepiped which has one vertex at the origin and arms defined by a1,a2,a3. For 2D case, set a3=[0,0,1]. And for 1D case also set a2=[0,1,0].
- Parameters:
a1 (int) – arms of parallelepiped
a2 (int) – arms of parallelepiped
a3 (int) – arms of parallelepiped
- static iterateAround(pos)¶
- static posInList(pos, posList)¶
- class PrimaryLattice_HubbardModel(basis)¶
Bases:
PrimaryLattice_SpinlessHamiltonianPrimaryLattice of Hubbard model. Contains t,mu,U
- setCoulombU(orbit_i, U)¶
\(U n_{R_0 i} n_{R_0 j}\)
- Parameters:
orbit_i (int) – orbit index
U (float) – U
- setHopping(R, orbit_i, orbit_j, tij)¶
- setInterV(R, orbit_i, orbit_j, V)¶
\(V n_i n_j = V ( n_{i\uparrow} + n_{i\downarrow} ) ( n_{j\uparrow} + n_{j\downarrow} )\) where orbit_i is in current cluster and orbit_j is R
- Parameters:
R (int) – R_j
orbit_i (int) – index of site
orbit_j (int) – index of site
V (float) – strength
- Returns:
_description_
- Return type:
_type_
- Yields:
_type_ – _description_
- setOnSide(orbit_i, m)¶
- setOrbitPosition(idx, pos)¶
- class PrimaryLattice_SpinlessHamiltonian(basis)¶
Bases:
objectSet Hamiltonian of a lattice model. This class: * use lest effort to define the toplogy of a lattice Hamiltonian. * contains only connection topology, need not position information. BUT, we contains position information here. This class is a basic one for spinless fermion system.
- exportLocalHamiltonian()¶
return a cluster Hamiltonian, will ignore non-local part
- Return type:
- getInteraction()¶
- getNumOfSpinlessOrbit()¶
- getOrbitPosition(idx)¶
- getPositionOnLattice(index)¶
- getPrimaryBasis()¶
- getTmatrix(nOrbit=None)¶
return hopping terms
- setCdC(R, i, j, tij)¶
\(t_{R_i i, R_j j} c^\dagger_{R_i i} c_{R_j j} + h.c.\) By default, \({R_i}\) is [0]*d. So one need only to give \(R_j\) by R.
- Parameters:
R (int) – list of int. represent index of primary cell.
i (int) – index of orbit in current ([0]*d) cell.
j (int) – index of orbit in Rj
tij (complex) – hopping strength
- setCdCCdC(R, i1, i2, j1, j2, v)¶
\(v c^\dagger_{R_i i_1} c_{R_i i_2} c^\dagger_{R_j j_1} c_{R_j j_2} + h.c.\) By default, \({R_i}\) is [0]*d. So one need only to give \(R_j\) by R.
- Parameters:
R (int) – list, \({R_j}\): [int]*d
i1 (int) – index of orbit in current ([0]*d) cell.
i2 (int) – index of orbit in current ([0]*d) cell.
j1 (int) – index of orbit in Rj
j2 (int) – index of orbit in Rj
v (complex) – energy value
- setCdCdCC(R, i1, i2, j1, j2, v)¶
\(v c^\dagger_{R_i i_1} c^\dagger_{R_i i_2} c_{R_j j_1} c_{R_j j_2} + h.c.\) By default, \({R_i}\) is [0]*d. So one need only to give \(R_j\) by R.
- Parameters:
R (int) – list, \({R_j}\): [int]*d
i1 (int) – index of orbit in current ([0]*d) cell.
i2 (int) – index of orbit in current ([0]*d) cell.
j1 (int) – index of orbit in Rj
j2 (int) – index of orbit in Rj
v (complex) – energy value
- setOrbitPosition(idx, pos)¶
- class SuperLatticeHamiltonian(priHam, superLatticeIndex)¶
Bases:
objectMake super-lattice Hamiltonian by PrimaryHamiltonian 只能计算14类格子中的7类: 简单(x5)，三角(x1)和六角(x1)。拓扑上等价于简单立方。
- Parameters:
priHam (
PrimaryLattice_SpinlessHamiltonian)
- abstractT_from_primaryH()¶
- getAbsPositionOfOrbit(pid, oid)¶
_summary_
- Parameters:
pid (int) – index of primary cell
oid (int) – index of orbit in primary cell
- Returns:
absolute position of a given orbit in real space
- Return type:
Vector
- getCLusterSize()¶
\(V_{lattic}/V_{cell}\)
- getNumOrbitInCell()¶
Total numer of (spinless) orbits in a primary cell (or say basis cell)
- Returns:
number of orbits
- Return type:
int
- getOrbitIndexInSuperCell(pid, oid)¶
- Parameters:
pid (int) – index of primary-cell
oid (int) – index of orbit in primary-cell
- Returns:
orbit index in super-cell.
- Return type:
int
- getTq(q, index=None)¶
\(T_q=\sum_{\Delta}e^{i \boldsymbol{q} \cdot \boldsymbol{\Delta} } t(\Delta)\), where \(\Delta=\boldsymbol{R}-\boldsymbol{0}\)
- Parameters:
q (list[int]) – k vector
index (list[int] | None, optional) – _description_. Defaults to None.
- get_ClusterH()¶
- Return type:
- getDirectHam(U)¶
- getHam(latticeHam)¶
- getLatticeHam(U)¶
- getSupH(U)¶