13719580150

Committed 07 Mar 2025 11:18AM UTC coverage: 86.979% (-13.0%) from 100.0%

Build # 13719580150

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Pull #93

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web-flow

Commit Message

Merge d738954ea into 17b683f9d

Pull Request Pull Request #93: Add DMFT

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10.64

/src/quant_met/dmft/utils.py

# SPDX-FileCopyrightText: 2025 Tjark Sievers
#
# SPDX-License-Identifier: MIT

"""Utility functions used in DMFT."""

import numpy as np
import numpy.typing as npt
from triqs.gf import Gf, MeshBrZone, MeshImFreq, MeshProduct, conjugate, dyson, inverse, iOmega_n


def get_gloc(
    s: Gf,
    s_an: Gf,
    h0_nambu_k: Gf,
    xmu: npt.NDArray[np.complex128],
    broadening: float,
    kmesh: MeshBrZone,
) -> tuple[Gf, Gf]:
    """Compute local GF from bare lattice Hamiltonian and self-energy.

    Parameters
    ----------
    s
    s_an
    h0_nambu_k

    Returns
    -------
    tuple[Gf, Gf]

    """
    z = Gf(mesh=s.mesh, target_shape=h0_nambu_k.target_shape)
    n_orbitals = z.target_shape[0] // 2
    if isinstance(s.mesh, MeshImFreq):
        z[:n_orbitals, :n_orbitals] << iOmega_n + xmu - s
        z[:n_orbitals, n_orbitals:] << -s_an
        z[n_orbitals:, :n_orbitals] << -s_an
        z[n_orbitals:, n_orbitals:] << iOmega_n - xmu + conjugate(s)
    else:
        z[:n_orbitals, n_orbitals:] << -s_an
        z[n_orbitals:, :n_orbitals] << -s_an
        for w in z.mesh:
            z[w][:n_orbitals, :n_orbitals] = (w + 1j * broadening + xmu) * np.eye(n_orbitals) - s[w]
            z[w][n_orbitals:, n_orbitals:] = (w + 1j * broadening - xmu) * np.eye(
                n_orbitals
            ) + conjugate(s(-w))

    g_k = Gf(mesh=MeshProduct(kmesh, z.mesh), target_shape=h0_nambu_k.target_shape)
    for k in kmesh:
        g_k[k, :] << inverse(z - h0_nambu_k[k])

    g_loc_nambu = sum(g_k[k, :] for k in kmesh) / len(kmesh)

    g_loc = s.copy()
    g_loc_an = s_an.copy()
    g_loc[:] = g_loc_nambu[:n_orbitals, :n_orbitals]
    g_loc_an[:] = g_loc_nambu[:n_orbitals, n_orbitals:]
    return g_loc, g_loc_an


def _dmft_weiss_field(g_iw: Gf, g_an_iw: Gf, s_iw: Gf, s_an_iw: Gf) -> tuple[Gf, Gf]:
    """Compute Weiss field from local GF and self-energy.

    Parameters
    ----------
    g_iw
    g_an_iw
    s_iw
    s_an_iw

    Returns
    -------
    tuple[Gf, Gf]

    """
    n_orbitals = g_iw.target_shape[0]
    nambu_shape = (2 * n_orbitals, 2 * n_orbitals)
    g_nambu_iw = Gf(mesh=g_iw.mesh, target_shape=nambu_shape)
    s_nambu_iw = Gf(mesh=s_iw.mesh, target_shape=nambu_shape)

    g_nambu_iw[:n_orbitals, :n_orbitals] = g_iw
    g_nambu_iw[:n_orbitals, n_orbitals:] = g_an_iw
    g_nambu_iw[n_orbitals:, :n_orbitals] = g_an_iw
    g_nambu_iw[n_orbitals:, n_orbitals:] = -conjugate(g_iw)

    s_nambu_iw[:n_orbitals, :n_orbitals] = s_iw
    s_nambu_iw[:n_orbitals, n_orbitals:] = s_an_iw
    s_nambu_iw[n_orbitals:, :n_orbitals] = s_an_iw
    s_nambu_iw[n_orbitals:, n_orbitals:] = -conjugate(s_iw)

    g0_nambu_iw = dyson(G_iw=g_nambu_iw, Sigma_iw=s_nambu_iw)

    g0_iw = g_iw.copy()
    g0_an_iw = g_an_iw.copy()
    g0_iw[:] = g0_nambu_iw[:n_orbitals, :n_orbitals]
    g0_an_iw[:] = g0_nambu_iw[:n_orbitals, n_orbitals:]
    return g0_iw, g0_an_iw

1	# SPDX-FileCopyrightText: 2025 Tjark Sievers
2	#
3	# SPDX-License-Identifier: MIT
4
5	"""Utility functions used in DMFT."""
6
7	import numpy as np	1✔
8	import numpy.typing as npt	1✔
9	from triqs.gf import Gf, MeshBrZone, MeshImFreq, MeshProduct, conjugate, dyson, inverse, iOmega_n	1✔
10
11
12	def get_gloc(	1✔
13	s: Gf,
14	s_an: Gf,
15	h0_nambu_k: Gf,
16	xmu: npt.NDArray[np.complex128],
17	broadening: float,
18	kmesh: MeshBrZone,
19	) -> tuple[Gf, Gf]:
20	"""Compute local GF from bare lattice Hamiltonian and self-energy.
21
22	Parameters
23	----------
24	s
25	s_an
26	h0_nambu_k
27
28	Returns
29	-------
30	tuple[Gf, Gf]
31
32	"""
NEW 33	z = Gf(mesh=s.mesh, target_shape=h0_nambu_k.target_shape)	×
NEW 34	n_orbitals = z.target_shape[0] // 2	×
NEW 35	if isinstance(s.mesh, MeshImFreq):	×
NEW 36	z[:n_orbitals, :n_orbitals] << iOmega_n + xmu - s	×
NEW 37	z[:n_orbitals, n_orbitals:] << -s_an	×
NEW 38	z[n_orbitals:, :n_orbitals] << -s_an	×
NEW 39	z[n_orbitals:, n_orbitals:] << iOmega_n - xmu + conjugate(s)	×
40	else:
NEW 41	z[:n_orbitals, n_orbitals:] << -s_an	×
NEW 42	z[n_orbitals:, :n_orbitals] << -s_an	×
NEW 43	for w in z.mesh:	×
NEW 44	z[w][:n_orbitals, :n_orbitals] = (w + 1j * broadening + xmu) * np.eye(n_orbitals) - s[w]	×
NEW 45	z[w][n_orbitals:, n_orbitals:] = (w + 1j * broadening - xmu) * np.eye(	×
46	n_orbitals
47	) + conjugate(s(-w))
48
NEW 49	g_k = Gf(mesh=MeshProduct(kmesh, z.mesh), target_shape=h0_nambu_k.target_shape)	×
NEW 50	for k in kmesh:	×
NEW 51	g_k[k, :] << inverse(z - h0_nambu_k[k])	×
52
NEW 53	g_loc_nambu = sum(g_k[k, :] for k in kmesh) / len(kmesh)	×
54
NEW 55	g_loc = s.copy()	×
NEW 56	g_loc_an = s_an.copy()	×
NEW 57	g_loc[:] = g_loc_nambu[:n_orbitals, :n_orbitals]	×
NEW 58	g_loc_an[:] = g_loc_nambu[:n_orbitals, n_orbitals:]	×
NEW 59	return g_loc, g_loc_an	×
60
61
62	def _dmft_weiss_field(g_iw: Gf, g_an_iw: Gf, s_iw: Gf, s_an_iw: Gf) -> tuple[Gf, Gf]:	1✔
63	"""Compute Weiss field from local GF and self-energy.
64
65	Parameters
66	----------
67	g_iw
68	g_an_iw
69	s_iw
70	s_an_iw
71
72	Returns
73	-------
74	tuple[Gf, Gf]
75
76	"""
NEW 77	n_orbitals = g_iw.target_shape[0]	×
NEW 78	nambu_shape = (2 * n_orbitals, 2 * n_orbitals)	×
NEW 79	g_nambu_iw = Gf(mesh=g_iw.mesh, target_shape=nambu_shape)	×
NEW 80	s_nambu_iw = Gf(mesh=s_iw.mesh, target_shape=nambu_shape)	×
81
NEW 82	g_nambu_iw[:n_orbitals, :n_orbitals] = g_iw	×
NEW 83	g_nambu_iw[:n_orbitals, n_orbitals:] = g_an_iw	×
NEW 84	g_nambu_iw[n_orbitals:, :n_orbitals] = g_an_iw	×
NEW 85	g_nambu_iw[n_orbitals:, n_orbitals:] = -conjugate(g_iw)	×
86
NEW 87	s_nambu_iw[:n_orbitals, :n_orbitals] = s_iw	×
NEW 88	s_nambu_iw[:n_orbitals, n_orbitals:] = s_an_iw	×
NEW 89	s_nambu_iw[n_orbitals:, :n_orbitals] = s_an_iw	×
NEW 90	s_nambu_iw[n_orbitals:, n_orbitals:] = -conjugate(s_iw)	×
91
NEW 92	g0_nambu_iw = dyson(G_iw=g_nambu_iw, Sigma_iw=s_nambu_iw)	×
93
NEW 94	g0_iw = g_iw.copy()	×
NEW 95	g0_an_iw = g_an_iw.copy()	×
NEW 96	g0_iw[:] = g0_nambu_iw[:n_orbitals, :n_orbitals]	×
NEW 97	g0_an_iw[:] = g0_nambu_iw[:n_orbitals, n_orbitals:]	×
NEW 98	return g0_iw, g0_an_iw	×

Ruberhauptmann / quant-met / 13719580150

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