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Merge pull request #896 from zerothi/873-bdg-final
fixed and finalized BdG spin configuration
2 parents af036e0 + 7afbefb commit cfde869

23 files changed

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‎changes/896.change.rst‎

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Changed ``hermitian => conjugate``
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Now one should use ``H.transpose(conjugate=True, ...)``
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instead. The Hermitian argument did not make sense, since
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the transpose was implicit of the function name.
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It is now also more obvious how ``conjugate=..., spin=...``
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works together.
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Also, all arguments to this method are forced keywords.
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A ``len(H) == H.no * 4`` for Nambu spin configuration.
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The diagonalization of the Hamiltonian will return
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an eigenvalue symmetric spectrum (about E=0).
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Hence this one will be dependent on the shift of the
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spectrum.

‎changes/896.feat.rst‎

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Added Nambu spin configuration
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Allowed `sisl` to operate with the Nambu spin-configuration.
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This spin-configuration is made for spin-orbit +
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super-conductivity.
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Nearly all functionality that is available for SOC is also
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availiable for BdG (Nambu) spin configuration.
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This goes in line with the recent additions to the Siesta
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code with superconductivity.

‎changes/896.fix.rst‎

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Non-collinear transposing was buggy
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The code for transposing + conjugating (adjoint operator)
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was wrong for non-collinear matrices.
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This is now finally fixed, and checked for.
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Fixed documentation in ``trs`` method for matrices.
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Fixed overlap conjugation for transpose when complex
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numbers are used.

‎changes/orphan.14.change.rst‎

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This file was deleted.

‎developments/spin.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "158426a6-f7f2-40b4-96fc-087a3035af30",
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy import *\n",
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"\n",
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"init_printing(use_unicode=False, use_latex=False)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e15cb269-f88e-4055-b714-bf8b48269d79",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Create the Pauli matrices\n",
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"\n",
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"sigma_x = Matrix([[0, 1], [1, 0]])\n",
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"sigma_y = Matrix([[0, -I], [I, 0]])\n",
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"sigma_z = Matrix([[1, 0], [0, -1]])\n",
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"\n",
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"assert sigma_x**2 == eye(2)\n",
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"assert sigma_y**2 == eye(2)\n",
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"assert sigma_z**2 == eye(2)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "606b36c4-83b6-4188-a5fe-76555d258a3c",
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"metadata": {},
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"source": [
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"## Spin configurations\n",
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"\n",
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"Here we'll show different spin-configurations, and do various operations. First we'll define some generic operators that we'll apply.\n",
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"Then comes the different spin sections."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ac6a0b74-47e9-49b4-bafa-44b82753a652",
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"metadata": {},
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"outputs": [],
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"source": [
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"def equal(M1, M2):\n",
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" return Eq(M1, M2).doit()\n",
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"\n",
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"\n",
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"def trs(H):\n",
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" return sympify(sigma_y * H.conjugate() * sigma_y)\n",
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"\n",
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"\n",
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"def make_trs(H):\n",
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" H_trs = sympify(H + trs(H))\n",
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" return MatMul(H_trs, \"1/2\", evaluate=False)\n",
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"\n",
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"\n",
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"def do_trs(H):\n",
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" H_trs = make_trs(H)\n",
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" assert equal(H_trs, trs(H_trs))\n",
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" return trs(H)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "89f80956-a8d3-4b6c-9340-334c76d092a7",
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"metadata": {},
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"source": [
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"### Non-collinear"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e3b2d4e9-f8e4-4c50-b409-057926887d5b",
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"metadata": {},
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"outputs": [],
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"source": [
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"uu, dd, ud = symbols(\"m0 m1 m2\")\n",
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"H_nc = Matrix([[uu, ud], [ud.conjugate(), dd]])\n",
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"do_trs(H_nc)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "82080cf9-bf53-4b4d-af96-7ae53c0b3079",
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"metadata": {},
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"source": [
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"### Spin-orbit"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8bcf161a-0be1-493f-b6d5-806a0a00360f",
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"metadata": {},
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"outputs": [],
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"source": [
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"uu, dd, ud, du = symbols(\"m0 m1 m2 m3\")\n",
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"H_soc = Matrix([[uu, ud], [du, dd]])\n",
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"do_trs(H_soc)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e762a0d9-98f8-4c35-b2d3-8fd7053b74bc",
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"metadata": {},
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"source": [
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"### Nambu (Delta matrix)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d12089c2-7b11-41bc-92f1-b8cbbc4137b9",
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"metadata": {},
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"outputs": [],
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"source": [
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"S, T0, Tu, Td = symbols(\"S T0 Tu Td\")\n",
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"Delta = Matrix([[Tu, S + T0], [-S + T0, Td]])\n",
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"do_trs(Delta)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "fc6fb8bf-44b6-4a7f-ab8d-f76e0cfe4f21",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎src/sisl/_core/sparse.py‎

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return csr
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def transpose(self, sort=True):
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def transpose(self, sort: bool = True):
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"""Create the transposed sparse matrix
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Parameters

‎src/sisl/conftest.py‎

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""" Global sisl fixtures """
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import logging
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import os
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from functools import partial
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from pathlib import Path
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import numpy as np
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def sisl_tolerance():
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r32 = (1e-6, 1e-11)
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r64 = (1e-9, 1e-15)
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return {np.float32: r32, np.float64: r64, np.complex64: r32, np.complex128: r64}
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return {
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np.float32: r32,
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np.float32(0).dtype: r32,
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np.float64: r64,
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np.float64(0).dtype: r64,
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np.complex64: r32,
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np.complex64(0).dtype: r32,
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np.complex128: r64,
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np.complex128(0).dtype: r64,
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None: r64,
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}
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@pytest.fixture(scope="session")
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def sisl_allclose(sisl_tolerance):
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def factory(dtype):
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atol, rtol = sisl_tolerance[dtype]
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return partial(np.allclose, atol=atol, rtol=rtol)
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return {key: factory(key) for key in sisl_tolerance.keys()}
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@pytest.fixture(scope="session")
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def sisl_isclose(sisl_tolerance):
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def factory(dtype):
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atol, rtol = sisl_tolerance[dtype]
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return partial(np.isclose, atol=atol, rtol=rtol)
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return {key: factory(key) for key in sisl_tolerance.keys()}
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@pytest.fixture(scope="session", params=[np.float32, np.float64])

‎src/sisl/io/ham.py‎

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if hermitian:
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herm_acc = kwargs.get("herm_acc", 1e-6)
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h_ht = H - H.transpose(hermitian=True)
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h_ht = H - H.transpose(conjugate=True, spin=True)
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amax = np.abs(h_ht._csr._D).max()
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if amax > herm_acc:
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warn(

‎src/sisl/io/siesta/_help.py‎

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def _mat_siesta2sisl(M) -> None:
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"""Conversion of Siesta spin matrices to sisl spin matrices
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The matrices from Siesta are given in a format adheering to the following
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The matrices from Siesta are given in a format adhering to the following
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concept.
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There are two cases:
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1. A non-colinear calculation:
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1. A non-collinear calculation:
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Siesta uses this convention:
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H12 == H[:, 2] + 1j H[:, 3] # spin-box Hermitian
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H21 == H[:, 2] - 1j H[:, 3]
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2. A spin-orbit calculation:
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2. A spin-orbit calculation + Nambu:
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Siesta uses this convention:
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‎src/sisl/physics/_matrix_ddk.pyx‎

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from ._matrix_phase3 import *
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from ._phase import *
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__all__ = ["matrix_ddk", "matrix_ddk_nc", "matrix_ddk_diag",
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__all__ = [
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"matrix_ddk",
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"matrix_ddk_nc",
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"matrix_ddk_diag",
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"matrix_ddk_so",
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"matrix_ddk_nambu"
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]

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