Direct support of different problems

In addition to the algebraic rules, more domain specific knowledge can be added to drudge subclasses for the convenience of working on specific problems. In these Drudge subclasses, we have not only the general mathematical knowledge like commutation rules, but more detailed information about the problem as well, like some commonly used ranges, dummies.

class drudge.GenMBDrudge(*args, exch=-1, op_label='c', orb=((Range('L'), 'abcdefghijklmnopq'), ), spin=(), one_body=t, two_body=u, dbbar=False, **kwargs)

Drudge for general many-body problems.

In a general many-body problem, a state for the particle is given by a symbolic orbital quantum numbers for the external degrees of freedom and optionally a concrete spin quantum numbers for the internal states of the particles. Normally, there is just one orbital quantum number and one or no spin quantum number.

In this model, a default Hamiltonian of the model is constructed from a one-body and two-body interaction, both of them are assumed to be spin conserving.

Also Einstein summation convention is assumed for this drudge in drudge scripts.

op

The vector base for the field operators.

cr

The base for the creation operator.

an

The base for the annihilation operator.

orb_ranges

A list of all the ranges for the orbital quantum number.

spin_vals

A list of all the explicit spin values. None if spin values are not given.

spin_range

The symbolic range for spin values. None if it is not given.

orig_ham

The original form of the Hamiltonian without any simplification.

ham

The simplified form of the Hamiltonian.

__init__(*args, exch=-1, op_label='c', orb=((Range('L'), 'abcdefghijklmnopq'), ), spin=(), one_body=t, two_body=u, dbbar=False, **kwargs)

Initialize the drudge object.

Parameters:

• exch – The exchange symmetry of the identical particle.
• op_label – The label for the field operators. The creation operator will be registered in the names archive by name of this label with _dag appended. And the annihilation operator will be registered with a single trailing underscore.
• orb – An iterable of range and dummies pairs for the orbital quantum number, which is considered to be over the direct sum of all the ranges given. All the ranges and dummies will be registered to the names archive by Drudge.set_dumms().
• spin – The explicit spin quantum number. It can be an empty sequence to disable explicit spin. Or it can be a sequence of SymPy expressions to give explicit spin values, or a range and dummies pair for symbolic spin.
• one_body – The indexed base for the amplitude in the one-body part of the Hamiltonian. It will also be added to the name archive.
• two_body – The indexed base for the two-body part of the Hamiltonian. It will also be added to the name archive.
• dbbar (bool) – If the two-body part of the Hamiltonian is double-bared.

class drudge.PartHoleDrudge(*args, op_label='c', part_orb=(Range('V', 0, nv), (a, b, c, d, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, a35, a36, a37, a38, a39, a40, a41, a42, a43, a44, a45, a46, a47, a48, a49)), hole_orb=(Range('O', 0, no), (i, j, k, l, i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20, i21, i22, i23, i24, i25, i26, i27, i28, i29, i30, i31, i32, i33, i34, i35, i36, i37, i38, i39, i40, i41, i42, i43, i44, i45, i46, i47, i48, i49)), spin=(), one_body=t, two_body=u, fock=f, dbbar=True, **kwargs)

Drudge for the particle-hole problems.

This is a shallow subclass of GenMBDrudge for the particle-hole problems. It contains different forms of the Hamiltonian.

orig_ham

The original form of the Hamiltonian, written in terms of bare one-body and two-body interaction tensors without normal-ordering with respect to the Fermion vacuum.

full_ham

The full form of the Hamiltonian in terms of the bare interaction tensors, normal-ordered with respect to the Fermi vacuum.

ham_energy

The zero energy inside the full Hamiltonian.

one_body_ham

The one-body part of the full Hamiltonian, written in terms of the bare interaction tensors.

ham

The most frequently used form of the Hamiltonian, written in terms of Fock matrix and the two-body interaction tensor.

__init__(*args, op_label='c', part_orb=(Range('V', 0, nv), (a, b, c, d, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, a35, a36, a37, a38, a39, a40, a41, a42, a43, a44, a45, a46, a47, a48, a49)), hole_orb=(Range('O', 0, no), (i, j, k, l, i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20, i21, i22, i23, i24, i25, i26, i27, i28, i29, i30, i31, i32, i33, i34, i35, i36, i37, i38, i39, i40, i41, i42, i43, i44, i45, i46, i47, i48, i49)), spin=(), one_body=t, two_body=u, fock=f, dbbar=True, **kwargs)

Initialize the particle-hole drudge.

op_parser

Get the special operator parser for particle-hole problems.

Here when the first index to the operator is resolved to be a hole state, the creation/annihilation character of the operator will be flipped.

eval_fermi_vev(tensor: drudge.drudge.Tensor)

Evaluate expectation value with respect to Fermi vacuum.

This is just an alias to the actual FockDrudge.eval_phys_vev() method to avoid confusion about the terminology in particle-hole problems. And it is set as a tensor method by the same name.

parse_tce(tce_out: str, cc_bases: typing.Mapping[int, sympy.tensor.indexed.IndexedBase])

Parse TCE output into a tensor.

The CC amplitude bases should be given as a dictionary mapping from the excitation order to the actual base.

drudge.UP

The symbol for spin up.

drudge.DOWN

The symbolic value for spin down.

class drudge.SpinOneHalfGenDrudge(*args, **kwargs)

Drudge for many-body problems of particles with explicit 1/2 spin.

This is just a shallow subclass of the drudge for general many-body problems, with exchange set to fermi and has explicit spin values of UP and DOWN.

__init__(*args, **kwargs)

Initialize the drudge object.

class drudge.SpinOneHalfPartHoleDrudge(*args, part_orb=(Range('V', 0, nv), (a, b, c, d, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, a35, a36, a37, a38, a39, a40, a41, a42, a43, a44, a45, a46, a47, a48, a49, beta, gamma)), hole_orb=(Range('O', 0, no), (i, j, k, l, i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20, i21, i22, i23, i24, i25, i26, i27, i28, i29, i30, i31, i32, i33, i34, i35, i36, i37, i38, i39, i40, i41, i42, i43, i44, i45, i46, i47, i48, i49, u, v)), spin=(SpinOneHalf.UP, SpinOneHalf.DOWN), **kwargs)

Drudge for the particle-hole problems with explicit one-half spin.

This is a shallow subclass over the general particle-hole drudge without explicit spin. The spin values are given explicitly, which are set to UP and DOWN by default. And the double-bar of the two-body interaction is disabled. And some additional dummies traditional in the field are also added.

__init__(*args, part_orb=(Range('V', 0, nv), (a, b, c, d, a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16, a17, a18, a19, a20, a21, a22, a23, a24, a25, a26, a27, a28, a29, a30, a31, a32, a33, a34, a35, a36, a37, a38, a39, a40, a41, a42, a43, a44, a45, a46, a47, a48, a49, beta, gamma)), hole_orb=(Range('O', 0, no), (i, j, k, l, i0, i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20, i21, i22, i23, i24, i25, i26, i27, i28, i29, i30, i31, i32, i33, i34, i35, i36, i37, i38, i39, i40, i41, i42, i43, i44, i45, i46, i47, i48, i49, u, v)), spin=(SpinOneHalf.UP, SpinOneHalf.DOWN), **kwargs)

Initialize the particle-hole drudge.