Spectroscopic Probes of Electronic States in Strongly Correlated Materials and Unconventional Superconductors Restricted; Files Only

Abstract

Understanding the behavior of strongly correlated electron systems remains a central challenge in modern condensed matter physics, particularly in nonequilibrium regimes. This thesis presents a comprehensive investigation into electronic, spin, charge, and lattice dynamics probed by X-ray spectroscopies. Focusing on cuprate materials, prototypical platforms for exploring high-temperature superconductivity, entanglement, and emergent phases, this work develops the theoretical and computational framework necessary to simulate and interpret nonequilibrium phenomena. Starting from first principles, realistic models such as the single-band, multi-band, Hubbard and extended Hubbard models are derived and solved numerically using the exact diagonalization method based on Krylov subspace techniques as detailed in Chapters 1, 3, and 4. Chapters 2 and 5 apply these tools to quantum entanglement in strongly correlated systems, introducing entanglement witnesses and demonstrating their connection to experimentally accessible observables in equilibrium. We further show that quantum Fisher information can be extracted from nonequilibrium spectra and validate this with simulations on a simple cuprate chain. Chapters 6 and 7 shift the focus to the mechanisms underlying unconventional superconductivity. Time-resolved RIXS experiments on electron-doped cuprates reveal the generation of paramagnons and a momentum-dependent redistribution of spectral weight, consistent with signatures of spin scrambling. Additionally, we show that the charge-transfer energy, closely linked to Tc, undergoes photo-induced renormalization. Motivated by this, Floquet theory is applied to model light-driven modifications of superconducting states. These results collectively highlight the potential of X-ray spectroscopies not only as diagnostic tools for probing complex phenomena, but also as avenues for controlling material properties in nonequilibrium settings.

Table of Contents

1 Foundations of Many-Body Quantum Models

1 1.1 Quantum Mechanical Background . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Hilbert Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 First Quantization: Operators . . . . . . . . . . . . . . . . . . 6

1.1.3 Expectation Values . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2 Second Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.1 One-Body Operators . . . . . . . . . . . . . . . . . . . . . . . 13

1.2.2 Two-Body Operators . . . . . . . . . . . . . . . . . . . . . . . 14

1.3 System of Non-interacting Particles . . . . . . . . . . . . . . . . . . . 14

1.3.1 Bloch’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.3.2 Band theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3.3 Molecular Orbitals and Wannier Functions . . . . . . . . . . . 17

1.3.4 Tight-Binding Model . . . . . . . . . . . . . . . . . . . . . . . 18

1.3.5 Peierls Substitution . . . . . . . . . . . . . . . . . . . . . . . . 19

1.4 Many-Body Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.4.1 Single Band Hubbard Model . . . . . . . . . . . . . . . . . . . 22

1.4.2 Extended Hubbard Model . . . . . . . . . . . . . . . . . . . . 23

1.4.3 The Emery Model . . . . . . . . . . . . . . . . . . . . . . . . 24

1.5 Material Platforms for Correlated Electrons . . . . . . . . . . . . . . 25

1.5.1 Choosing Appropriate Hubbard Model Parameters . . . . . . 26

1.5.2 Doping and Particle-Hole Representations . . . . . . . . . . . 27

1.5.3 Entangled Cuprate Chain . . . . . . . . . . . . . . . . . . . . 28

1.5.4 High-Temperature Superconductivity . . . . . . . . . . . . . . 28

1.5.5 Nickelates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

2 Detecting Entanglement 31

2.1 Entanglement Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.1.1 Entangled and Separable States . . . . . . . . . . . . . . . . . 32

2.1.2 Multipartite Entanglement . . . . . . . . . . . . . . . . . . . . 34

2.1.3 Pure and Mixed States . . . . . . . . . . . . . . . . . . . . . . 35

2.2 Characterizing Entanglement . . . . . . . . . . . . . . . . . . . . . . 36

2.2.1 Entanglement Entropy . . . . . . . . . . . . . . . . . . . . . . 36

2.2.2 Many-Body Systems . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.3 Entanglement Witnesses . . . . . . . . . . . . . . . . . . . . . 39

2.2.4 One- and Two-Tangle . . . . . . . . . . . . . . . . . . . . . . . 40

2.2.5 Quantum Fisher Information . . . . . . . . . . . . . . . . . . . 43

2.2.6 2CRDM Entanglement Witness . . . . . . . . . . . . . . . . . 45

2.3 Experimental Observables and QFI . . . . . . . . . . . . . . . . . . . 46

2.3.1 Linear Response Theory . . . . . . . . . . . . . . . . . . . . . 47

2.3.2 Dynamical Structure Factor . . . . . . . . . . . . . . . . . . . 48

2.3.3 Linking QFI to the Dynamical Structure Factor . . . . . . . . 49 

3 X-Ray Spectroscopy 51

3.1 Theory of X-ray Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 52

3.1.1 Absorption Edges . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.1.2 Matrix Elements . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2 XAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2.1 Fermi’s Golden Rule . . . . . . . . . . . . . . . . . . . . . . . 56

3.2.2 Application: Zhang-Rice Peak . . . . . . . . . . . . . . . . . . 57

3.3 RIXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.3.1 Direct RIXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3.2 Polarization Dependence . . . . . . . . . . . . . . . . . . . . . 60

3.3.3 Indirect RIXS . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.3.4 Kramers-Heisenberg Cross-section . . . . . . . . . . . . . . . . 62

3.3.5 Ultrashort Core Hole Lifetime Limit . . . . . . . . . . . . . . 63

3.3.6 RIXS Accessible Excitations . . . . . . . . . . . . . . . . . . . 65

3.4 Time-Resolved X-Ray Spectroscopy . . . . . . . . . . . . . . . . . . . 66

3.4.1 trXAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.4.2 trRIXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4 Numerical Methods 70

4.1 ED Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.1 Binary Basis Representation . . . . . . . . . . . . . . . . . . . 72

4.1.2 Compressed Sparse Row Simplification . . . . . . . . . . . . . 74

4.1.3 Krylov Iterative Methods . . . . . . . . . . . . . . . . . . . . . 76

4.2 Pump-Probe Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.2.1 Time-Dependent ED . . . . . . . . . . . . . . . . . . . . . . . 79

4.2.2 Floquet Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

5 Witnessing Entanglement with trRIXS 83

5.1 Controlling Entanglement . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2 Self-consistent Method for Instantaneous QFI . . . . . . . . . . . . . 85

5.2.1 Snapshot QFI: Direct Integral . . . . . . . . . . . . . . . . . . 86

5.2.2 Evaluating QFI by Self-consistent Iteration . . . . . . . . . . . 88

5.3 Entanglement in a Cuprate Chain . . . . . . . . . . . . . . . . . . . . 90

5.3.1 Boundary of the QFI Entanglement Witness . . . . . . . . . . 90

5.3.2 Witnessing Light-Driven Entanglement . . . . . . . . . . . . . 92

5.4 Imperfection of RIXS Measurements . . . . . . . . . . . . . . . . . . 94

5.4.1 Normalizing Equilibrium RIXS . . . . . . . . . . . . . . . . . 95

6 Paramagnons and Acoustic Plasmons in a Photo-excited Cuprate 97

6.1 Light-engineered Paramagnon and Plasmon . . . . . . . . . . . . . . 98

6.2 NCCO Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.2.1 Spin Scramble . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 

7 Floquet Renormalization of Charge-transfer Energy 104

7.1 Charge Transfer Energy as a Control of Tc . . . . . . . . . . . . . . . 105

7.1.1 Cuprate Material LSCO . . . . . . . . . . . . . . . . . . . . . 105

7.2 Pump-Induced Renormalization of the Charge-Transfer Energy . . . . 107

7.2.1 Floquet Corrected Charge-Transfer Energy . . . . . . . . . . . 109

7.2.2 Simulated trRIXS and Experimental Verification of Peak Renormalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.2.3 Control of the Charge-Transfer Energy . . . . . . . . . . . . . 112 

8 Conclusion 114 

Appendix A Full Derivations 118

A.1 Spin-1/2 Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

A.2 Purity Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

A.3 Von Neumann Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 121

A.4 Kubo Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

A.5 Floquet Calculation for LSCO . . . . . . . . . . . . . . . . . . . . . . 123

Bibliography 126

About this Dissertation

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School	Laney Graduate School
Department	Chemistry
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Chemistry, Physical Physics, Quantum Physics, Condensed Matter
Keyword	X-ray Spectroscopy Entanglement Exact Diagonalization Many-Body Physics Unconventional Superconductivity
Committee Chair / Thesis Advisor	Yao Wang, Emory University
Committee Members	Katherine M. Davis, Emory University Francesco Evangelista, Emory University

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