Quantum Many Body (QMB) Operations

Low-level helpers to assemble local, two-body, and plaquette-like operators in the full many-body Hilbert space, including optional basis projections.

Helpers to assemble lattice operators in the full many-body Hilbert space.

This module provides low-level functions used by term classes to construct local, two-body, and four-body sparse operators on a lattice, including support for site-dependent basis projections (e.g. gauge bases).

edlgt.modeling.qmb_operations.qmb_operator(ops, op_names_list, add_dagger=False, get_real=False, get_imag=False)

Build a many-body sparse operator from an ordered list of site operators.

Parameters:

• ops (dict) – Dictionary mapping operator names to single-site sparse matrices.

• op_names_list (list) – Ordered list of operator names to tensor together, one per lattice site, following the project site ordering convention.

• add_dagger (bool, optional) – If True, symmetrize by adding the Hermitian conjugate.

• get_real (bool, optional) – If True, return only the Hermitian (real) part.

• get_imag (bool, optional) – If True, return only the anti-Hermitian-derived imaginary part.

Returns:

Sparse many-body operator in the full Hilbert space.

Return type:

scipy.sparse.csr_matrix

edlgt.modeling.qmb_operations.local_op(operator, op_site, lvals, has_obc, staggered_basis=False, gauge_basis=None, loc_dims=None)

Construct a single-site operator embedded in the full lattice Hilbert space.

Parameters:

• operator (scipy.sparse.spmatrix) – Single-site operator.

• op_site (int) – Site index where the operator acts.

• lvals (list[int]) – Lattice sizes along each axis.

• has_obc (list[bool]) – Boundary-condition flags for each axis (True for OBC).

• staggered_basis (bool, optional) – Whether a staggered basis is used.

• gauge_basis (dict, optional) – Site-label-dependent basis projectors.

• loc_dims (numpy.ndarray, optional) – Per-site local dimensions used when operators are already projected and provided as 3D site-resolved arrays.

Returns:

Embedded local operator.

Return type:

scipy.sparse.csr_matrix

edlgt.modeling.qmb_operations.two_body_op(op_list, op_sites_list, lvals, has_obc, staggered_basis=False, gauge_basis=None, loc_dims=None)

Construct a two-site operator embedded in the full lattice Hilbert space.

Parameters:

• op_list (list) – Two single-site operators.

• op_sites_list (list[int]) – Two site indices where the operators act.

• lvals (list[int]) – Lattice sizes along each axis.

• has_obc (list[bool]) – Boundary-condition flags for each axis.

• staggered_basis (bool, optional) – Whether a staggered basis is used.

• gauge_basis (dict, optional) – Site-label-dependent basis projectors.

• loc_dims (numpy.ndarray, optional) – Per-site local dimensions used when operators are already projected and provided as 3D site-resolved arrays.

Returns:

Embedded two-body operator.

Return type:

scipy.sparse.csr_matrix

edlgt.modeling.qmb_operations.four_body_op(op_list, op_sites_list, lvals, has_obc, staggered_basis=False, gauge_basis=None, loc_dims=None, get_real=False)

Construct a four-site (plaquette-like) operator in the full Hilbert space.

Parameters:

• op_list (list) – Four single-site operators.

• op_sites_list (list[int]) – Four site indices where the operators act.

• lvals (list[int]) – Lattice sizes along each axis.

• has_obc (list[bool]) – Boundary-condition flags for each axis.

• staggered_basis (bool, optional) – Whether a staggered basis is used.

• gauge_basis (dict, optional) – Site-label-dependent basis projectors.

• loc_dims (numpy.ndarray, optional) – Per-site local dimensions used when operators are already projected and provided as 3D site-resolved arrays.

• get_real (bool, optional) – If True, return only the Hermitian (real) part.

Returns:

Embedded four-body operator.

Return type:

scipy.sparse.csr_matrix

edlgt.modeling.qmb_operations.construct_operator_list(op_list, op_sites_list, lvals, has_obc, staggered_basis, gauge_basis, loc_dims=None)

Create per-site operator labels/matrices for a lattice operator product.

Parameters:

• op_list (list) – Operators to place on the lattice.

• op_sites_list (list[int]) – Lattice sites where the operators in op_list act.

• lvals (list[int]) – Lattice sizes along each axis.

• has_obc (list[bool]) – Boundary-condition flags for each axis.

• staggered_basis (bool) – Whether a staggered basis is used.

• gauge_basis (dict or None) – Site-label-dependent basis projectors, or None for a uniform basis.

• loc_dims (numpy.ndarray, optional) – Per-site local dimensions. Required when op_list contains projected site-resolved operators with shape (n_sites, max_loc_dim, max_loc_dim).

Returns:

(ops_dict, op_names_list) where ops_dict is a dictionary of projected operators and op_names_list is the ordered list of names passed to qmb_operator().

Return type:

tuple

edlgt.modeling.qmb_operations.apply_basis_projection(op, op_name, basis_label, gauge_basis)

Project a single-site operator into a site-dependent basis if needed.

Parameters:

• op (scipy.sparse.spmatrix) – Operator to project.

• op_name (str) – Base operator name.

• basis_label (str) – Site label used to select the projector.

• gauge_basis (dict or None) – Dictionary of projectors keyed by basis_label.

Returns:

Projected operator and its (possibly updated) name.

Return type:

tuple