notes add kkr mala research

notes/hzdr-casus-talk-notes.org

@@ -23,6 +23,9 @@
 - [[#outline][Outline]]
 - [[#journal][Journal]]
 - [[#research][Research]]
+  - [[#kkr-and-ldos][KKR and LDOS]]
+  - [[#kkr-and-cpa][KKR and CPA]]
+  - [[#jukkr-and-temperature][JuKKR and temperature]]
 
 * Project management
 :PROPERTIES:
@@ -82,3 +85,312 @@ KKR-JLCDM.
 :PROPERTIES:
 :CUSTOM_ID: h-766FE7B8-FDF7-4492-832D-5FE5FC98D35E
 :END:
+** KKR and LDOS
+:PROPERTIES:
+:CUSTOM_ID: h-4D83C24A-9390-438D-9746-6B94D902436D
+:END:
+Question: Can, and if so, how can KKR-GF, an JuKKR in particular, calculate
+local density of states (LDOS)?
+
+*** JuKKR and LDOS - online search
+:PROPERTIES:
+:CUSTOM_ID: h-46848893-F465-462B-B1A8-CB59C6860254
+:END:
+- Google search. jukkr AND "local density of states". [[https://www.google.com/search?q=jukkr+AND+%22local+density+of+states%22][URL]].
+  - Rüßmann et al. Density functional Bogoliubov-de Gennes analysis of
+    superconducting Nb and Nb(110) surfaces. [[https://juser.fz-juelich.de/record/907131/files/PhysRevB.105.125143.pdf?version=1][JUSER]].
+    #+begin_quote
+    FIG. 4. Electronic band structure and local density of states (DOS) [...]
+    #+end_quote
+  - Reho et al. Density functional Bogoliubov-de Gennes theory for
+    superconductors implemented in the SIESTA code.
+    #+begin_quote
+    In SIESTA-BdG, [...] one can perform a self-consistent calculation of both
+    normal and superconducting (anomalous) charge densities to compute the
+    pairing potential and superconducting properties, such as local density of
+    states (directly comparable with scanning tunneling microscopy experiments),
+    [...]
+
+    We computed the superconducting state DOS using the full SCF-BdG method and
+    compared the SIESTA-BdG result with the JuKKR code and experimental data
+    from STM measurements [...]
+    #+end_quote
+  - Rüßmann et al. Ab Initio Theory of Fourier-Transformed Quasiparticle
+    Interference Maps and Application to the Topological Insulator Bi2Te3.
+    [[https://juser.fz-juelich.de/record/877498/files/pssb.202000031.pdf][JUSER]].
+    #+begin_quote
+    The difference in the local density of states is connected to the
+    one-electron Green function of the system with impurity, \(G^{\text {imp
+    }}(\boldsymbol{r}, \boldsymbol{r} ; E)\), and to the one of the pristine
+    host, \(G^{\text {host }}(\boldsymbol{r}, \boldsymbol{r} ; E)\), by the
+    well-known identity
+
+    \[
+    \Delta n(\boldsymbol{r} ; E)=-\frac{1}{\pi} \operatorname{Im} \operatorname{Tr}\left[G^{\mathrm{imp}}(\boldsymbol{r}, \boldsymbol{r} ; E)-G^{\text {host }}(\boldsymbol{r}, \boldsymbol{r} ; E)\right]
+    \]
+    #+end_quote
+  - AiiDA KKR manual - Workflows - Density of states. [[https://aiida-kkr.readthedocs.io/en/latest/module_guide/workflows.html#module-aiida_kkr.workflows.dos][URL]].
+    - No mention of LDOS.
+*** KKR and LDOS - AI conversations
+:PROPERTIES:
+:CUSTOM_ID: h-FAB9D358-F504-4299-A231-9D874238B112
+:END:
+**** Claude AI - KKR, MALA and LDOS
+:PROPERTIES:
+:CUSTOM_ID: h-85D4A3E4-24F0-4F6B-94CD-1799A0327C58
+:END:
+Claude AI. KKR, MALA and LDOS. [[https://claude.ai/chat/028e19f3-4343-4660-a841-605e68031444][URL]].
+
+About LDOS in KKR and MALA.
+
+#+begin_quote
+The LDOS n(r,E) at position r and energy E is given by:
+
+n(r,E) = -(1/π) Im[G(r,r,E)]
+
+[...]
+
+Density of States (DOS) n(E) by integrating over all space:
+
+n(E) = ∫ n(r,E) dr
+
+Electron density n(r) by integrating over all energies up to the Fermi level EF:
+
+n(r) = ∫^EF n(r,E) dE
+
+In KKR-GF formalism, these quantities can be calculated directly from the Green's function:
+
+For the DOS:
+
+n(E) = -(1/π) Im[Tr G(E)] = -(1/π) ∫ Im[G(r,r,E)] dr
+
+For the electron density:
+
+n(r) = -(1/π) ∫^EF Im[G(r,r,E)] dE
+#+end_quote
+
+On advantages of integrating JuKKR with MALA.
+
+#+begin_quote
+USER
+
+Okay. I am wondering. The MALA framework by Fiedler and Cangi (I hope you are
+familiar with it?), as I said, relies on the idea that ML predicting the LDOS
+can completely bypass DFT calculations, since all relevant info can be
+calculated from the LDOS. The training data for MALA can currently only be
+generated with Quantum Espresso (pp.x module for LDOS). I wonder if there is any
+merit of making MALA compatible with a KKR-GF code, such as the JuKKR codes.
+What do you think?
+
+ASSISTANT
+
+While I aim to be accurate, I should note that I have a knowledge cutoff date
+and may not be fully up-to-date on the latest developments in MALA. That said, I
+can analyze the merits of making MALA compatible with KKR-GF codes.
+
+Potential advantages of integrating MALA with KKR-GF codes like JuKKR:
+
+1. Multiple Scattering Theory Benefits:
+- KKR-GF is particularly good at handling disordered systems and alloys through
+  CPA
+- Better treatment of relativistic effects
+- Natural inclusion of finite temperature effects
+- More realistic description of spectral properties due to lifetime effects
+
+2. Training Data Quality:
+- More realistic LDOS training data that includes broadening effects
+- Better representation of metallic systems where lifetime effects are important
+- Could potentially improve ML predictions for disordered/alloyed systems
+
+3. Complementary Strengths:
+- While QE provides clean band structures, KKR-GF gives spectral functions with
+  lifetime effects
+- This could allow MALA to learn different aspects of electronic structure
+- Could potentially lead to a more robust ML model
+
+Challenges to consider:
+
+1. Implementation Complexity:
+- Need to handle complex energy contour integration
+- Need to properly account for the broadened nature of spectral features
+- May need to modify MALA's architecture to handle complex-valued functions
+
+2. Training Data Processing:
+- Would need to develop methods to handle the additional information in KKR-GF
+  LDOS (broadening, lifetime effects)
+- Might require modification of MALA's data processing pipeline
+
+Given these considerations, I think there could be significant merit in making
+MALA compatible with KKR-GF codes, particularly for applications involving:
+- Disordered systems and alloys
+- Metallic systems where lifetime effects are important
+- Systems where relativistic effects are significant
+
+Would you like me to elaborate on any of these points or discuss specific
+technical aspects of how such an integration might be achieved?
+#+end_quote
+
+On selecting another prediction target than LDOS for MALA-JuKKR.
+
+#+begin_quote
+USER
+
+In your assessment here, it seems to me that you assumed for the approach to
+integrate MALA with a KKR-GF code (like JuKKR) that we pursue the same
+prediction target, the LDOS. Could there be other potential first-principles
+prediction targets, that given that we do this for a KKR-GF method, would be
+equally or perhaps even more suitable than the LDOS? For instance, the GF
+itself, or the electron density or the electron potential (the SCF convergence
+quantity in JuKKR), or something else.
+
+ASSISTANT
+
+That's an excellent point - we shouldn't automatically assume LDOS as the
+prediction target just because that's what MALA currently uses. Let's analyze
+alternative prediction targets specific to KKR-GF:
+
+1. Green's Function G(r,r',E):
+Advantages:
+- Contains complete information (LDOS can be derived from it)
+- Natural quantity in KKR-GF formalism
+- Directly relates to many physical observables
+
+Disadvantages:
+- Complex-valued function
+- Two spatial variables (r,r') plus energy
+- Larger dimensionality could make ML more challenging
+
+2. Electron Density n(r):
+Advantages:
+- Real-valued scalar field
+- Direct physical interpretation
+- Central quantity for SCF convergence
+- Smaller dimensionality than LDOS or GF
+- Already proven successful target in other ML frameworks
+
+Disadvantages:
+- Less information than LDOS or GF
+- Might need additional predictions for energy-dependent properties
+
+3. Effective Potential V_eff(r):
+Advantages:
+- Direct SCF convergence quantity
+- Real-valued scalar field
+- Natural control quantity for KKR-GF
+- Could potentially accelerate SCF convergence
+
+Disadvantages:
+- Less direct physical interpretation than density
+- May require careful handling of core regions
+
+4. Scattering Path Operator τ:
+Advantages:
+- Central quantity in multiple scattering theory
+- Computationally expensive to calculate conventionally
+- Contains key information about electronic structure
+
+Disadvantages:
+- Complex matrix structure
+- Angular momentum expansion makes it more complicated
+- May require significant architectural changes to ML model
+
+Given KKR-GF's specific strengths, I think either the effective potential or the
+scattering path operator might actually be more suitable prediction targets than
+the LDOS. The effective potential could be particularly promising as it's:
+- Directly useful for SCF acceleration
+- Simpler dimensionality than LDOS
+- Natural quantity for the method
+
+Would you like me to elaborate on any of these alternatives or discuss specific
+aspects of implementing ML predictions for any of them?
+#+end_quote
+
+The following from [[#h-F1E6525B-39E3-46F1-B112-4C8633376D03][Claude AI - KKR, temperature, MALA, transport properties]].
+
+#+begin_quote
+USER
+
+So, if we trained an ML model to predict the JuKKR (or, more generally, KKR-GF)
+LDOS rather than the Quantum Espresso LDOS, what advantage might that have in
+terms of additional information possibly contained in the former vs. the latter
+LDOS?
+
+ASSISTANT
+
+Interesting question! Training an ML model on KKR-GF LDOS rather than Quantum
+Espresso LDOS could potentially capture richer physical information because the
+Green's function method naturally includes lifetime/broadening effects in the
+electronic states. This means:
+
+1. The KKR-GF LDOS inherently contains information about the finite lifetimes of
+   electronic states, which reflects their interaction with the environment and
+   potential decay channels
+2. The spectral representation gives insight into the "robustness" or
+   "stability" of electronic states - sharp peaks indicate well-defined,
+   long-lived states while broader features suggest states that interact more
+   strongly with their environment
+3. If disorder effects are included through CPA or similar methods, the LDOS
+   would contain information about how electronic states are affected by
+   chemical or structural disorder
+
+In contrast, the Quantum Espresso LDOS shows sharper, more idealized states that
+might miss some of these real-world effects. While this makes for cleaner, more
+easily interpretable results, an ML model trained on such data might not learn
+to predict these important lifetime and interaction effects.
+
+So if the goal is to predict electronic properties of real materials where these
+broadening effects matter (like in transport properties or excited state
+dynamics), training on KKR-GF LDOS could provide a more complete physical
+picture.
+
+Would you like me to elaborate on any of these aspects or discuss specific
+applications where these differences might be particularly important?
+
+
+#+end_quote
+** KKR and CPA
+:PROPERTIES:
+:CUSTOM_ID: h-252AD278-5A9F-434B-A91F-2A1FCE17572A
+:END:
+*** KKR and LDOS - AI conversations
+:PROPERTIES:
+:CUSTOM_ID: h-C6C0A7AE-5B97-4F44-9AA4-225F9B8A0F8C
+:END:
+**** Claude AI - KKR, CPA and VCA
+:PROPERTIES:
+:CUSTOM_ID: h-C88C2508-87EA-482B-AC09-4F18EFC2866F
+:END:
+Claude AI. KKR, CPA and VCA. [[https://claude.ai/chat/dd3d5aee-4cf4-4e34-a02e-aea1549c7df8][URL]].
+
+Explanation of CPA method in KKR formalism and comparison to similar methods in
+other codes, like virtual crystal approxmiation (VCA).
+** JuKKR and temperature
+:PROPERTIES:
+:CUSTOM_ID: h-95C7B45E-6ADE-421D-A286-13F9282E057E
+:END:
+Question. Can JuKKR do finite-temperature calculations?
+
+Answers.
+
+- Only artificial or "electronic temperature" for "energy broadening". At least
+  in default mode. Maybe "real temperature" in CPA / DLM calcs. See JuKKR Wiki.
+*** JuKKR and temperature - online search
+:PROPERTIES:
+:CUSTOM_ID: h-BED6169C-31E1-4BFF-8A72-3E947AB629E9
+:END:
+- Google search. jukkr and "finite temperature". [[https://www.google.com/search?q=jukkr+AND+%22finite+temperature%22&client=firefox-b-d&sca_esv=c9ba1905e1b36b97&sxsrf=AHTn8zoENn4nidYZ88VyyROJcaaquNbyLA%3A1739236800382&ei=wKWqZ_z8FqGqi-gPhp_NkQw&ved=0ahUKEwj83Kr9ubqLAxUh1QIHHYZPM8IQ4dUDCBA&uact=5&oq=jukkr+AND+%22finite+temperature%22&gs_lp=Egxnd3Mtd2l6LXNlcnAiHmp1a2tyIEFORCAiZmluaXRlIHRlbXBlcmF0dXJlIjIHECEYoAEYCjIHECEYoAEYCjIHECEYoAEYCkj9P1ChD1jmPXAEeACQAQCYAb0CoAGQK6oBCDIuMTkuOC4zuAEDyAEA-AEBmAIkoAL_K8ICCBAAGLADGO8FwgILEAAYgAQYsAMYogTCAgQQIxgnwgIKEAAYgAQYQxiKBcICCxAAGIAEGLEDGIMBwgILEC4YgAQYsQMYgwHCAg4QLhiABBixAxiDARjUAsICDhAuGIAEGLEDGIMBGIoFwgIIEC4YgAQYsQPCAgUQLhiABMICChAAGIAEGBQYhwLCAgUQABiABMICCxAuGIAEGMcBGK8BwgIIEAAYgAQYsQPCAgcQLhiABBgKwgIKEAAYgAQYsQMYCsICBxAAGIAEGArCAggQABiABBjLAcICBxAAGIAEGA3CAgcQLhiABBgNwgIJEC4YgAQYChgNwgINEC4YgAQYxwEYDRivAcICBhAAGA0YHsICCBAAGAgYDRgewgIFEAAY7wXCAggQABiABBiiBMICBBAhGBXCAgUQIRigAZgDAIgGAZAGBZIHCDYuMTkuOC4zoAfj4AE&sclient=gws-wiz-serp][URL]].
+- JuKKR Wiki search. temperature. [[https://iffgit.fz-juelich.de/search?search=temperature&nav_source=navbar&project_id=403&group_id=3&scope=wiki_blobs][URL]].
+  - inputcard
+*** JuKKR and temperature - AI conversations
+:PROPERTIES:
+:CUSTOM_ID: h-11B4F6B2-9D46-4943-ABF8-EDA3D6F6D05C
+:END:
+**** Claude AI - KKR, temperature, MALA, transport properties
+:PROPERTIES:
+:CUSTOM_ID: h-F1E6525B-39E3-46F1-B112-4C8633376D03
+:END:
+Claude AI. KKR, temperature, MALA, transport properties. [[https://claude.ai/chat/af7349a0-daf7-4ca6-8dc2-d31ee2109aae][URL]].
+
+- Explains the KKR "electronic temperature" as a numerical parameter for energy
+  broadening.
+- For things related to MALA, see [[#h-85D4A3E4-24F0-4F6B-94CD-1799A0327C58][Claude AI - KKR, MALA and LDOS]].