Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory: Proceedings, International Institute of Physics, Natal, Rn, ... Proceedings in Physics (239), Band 239)

Preface
Contents
Contributors
1 Effective Field Theories for Topological States of Matter
	1.1 Introduction
	1.2 The Quantized Hall Conductance
		1.2.1 The Hall Conductance as a Chern Number
		1.2.2 The Chern–Simons Response Action
		1.2.3 The Topological Field Theory
		1.2.4 The Bulk-Boundary Correspondence
	1.3 Physical Systems with Quantized Hall Conductance
		1.3.1 The Integer Quantum Hall Effect
		1.3.2 The Hall Conductance in a Periodic Potential
		1.3.3 The Chern Insulator
	1.4 Generalizing to Other Dimensions
		1.4.1 The 1d Case
		1.4.2 Realization with Dirac Fermions
		1.4.3 Higher Dimensions
	1.5 Systems Characterized Only by Edge Modes
		1.5.1 The Time-Reversal Invariant Topological Insulator
		1.5.2 The Kitaev Chain
	1.6 Superconductors Are Topologically Ordered
		1.6.1 BF Theory of s-Wave Superconductors—Heuristic Approach
		1.6.2 The 3+1 Dimensional BF Theory
		1.6.3 Microscopic Derivation of the BF Theory
		1.6.4 The Two Dimensional p-Wave Superconductor
	1.7 Fractional Quantum Hall Liquids
		1.7.1 The Chern–Simons–Ginzburg–Landau Theory
		1.7.2 From the CSGL Theory to the Effective Topological Theory
		1.7.3 The Abelian Hierarchy
	1.8 Mathematical Background and Proofs
		1.8.1 Vector Bundles and Chern Numbers in Quantum Mechanics
		1.8.2 How to Normalize the Current
		1.8.3 The Relation Between the Chern Number and the Pontryagin Index
		1.8.4 The Parity Anomaly in 2+1 Dimensions
	References
2 An Introduction to Entanglement Measures in Conformal Field Theories  and AdS/CFT
	2.1 Introduction
	2.2 Bipartite Entanglement
		2.2.1 Entanglement Entropies
	2.3 Geometric Entanglement Entropies in QFT
		2.3.1 Intervals in 2D CFT
		2.3.2 Higher Dimensional CFT
	2.4 Entanglement Negativity
		2.4.1 Intervals in 2D CFT
	2.5 Holographic Entanglement Entropy
	References
3 Entanglement Content of Many-Body States via Concurrence, Negativity  and Schmidt Gap
	3.1 Quantum Entanglement and Its Quantification
	3.2 Concurrence Between Two Spins of a Many-Body System
	3.3 Entanglement Negativity in a Many-Body System: Case Study with the Kondo Model
	3.4 Schmidt Gap for Signalling Quantum Criticality: Case Study with an Impurity Phase Transition
	3.5 Entanglement Negativity as a Measurable Entity
	3.6 Conclusions
	References
4 Generalized Entanglement Entropy  in New Spin Chains
	4.1 Introduction
	4.2 Motzkin and Fredkin Spin Chains
		4.2.1 Fredkin Spin Chain
		4.2.2 Motzkin Spin Chain
	4.3 Rényi Entropy of Colorless Fredkin Spin Chain
	4.4 Rényi Entropy of Colorless Motzkin Spin Chain
	4.5 Rényi Entropy of s-Color Fredkin Spin Chain
		4.5.1 0<α<1 Case
		4.5.2 α>1 Case
		4.5.3 EE of s-Color Fredkin Spin Chain
		4.5.4 Phase Transition
	4.6 Rényi Entropy of s-Color Motzkin Spin Chain
		4.6.1 0<α<1 Case
		4.6.2 α>1 Case
		4.6.3 EE of s-Color Motzkin Spin Chain
		4.6.4 Phase Transition
	4.7 Discussion
	References
5 Topological Kondo Effect
	5.1 Introduction
	5.2 TKE Basics
	5.3 Superconducting Leads: The Josephson Current-Phase Relation
		5.3.1 Renormalization Group (RG) Analysis
		5.3.2 Physics at Low Temperatures: The Topological Kondo Effect
	5.4 Parafermionic Version
		5.4.1 The Hamiltonian
		5.4.2 RG Equations
	5.5 Conclusions
	References
6 Holographic Kondo Models
	6.1 Introduction
	6.2 AdS/CFT Correspondence
		6.2.1 Statement of the Correspondence
		6.2.2 Prerequisites for AdS/CFT
		6.2.3 String Theory Origin of the AdS/CFT Correspondence
		6.2.4 Finite Temperature
	6.3 Kondo Model Within Field Theory and Condensed Matter Physics
	6.4 Large N Kondo Model
	6.5 Gravity Dual of the Kondo Model
		6.5.1 Brane Construction for a Holographic Kondo Model
	6.6 Applications of the Holographic Kondo Model
		6.6.1 Entanglement Entropy
		6.6.2 Quantum Quenches
		6.6.3 Correlation Functions
	6.7 Conclusion and Outlook
	References
7 Local Probe of the Kondo Length at a Y-Junction of Critical Quantum Ising Chains
	7.1 Introduction
	7.2 Y-Junction of Quantum Ising Chains: Jordan–Wigner Transformation and Effective Kondo-Like Hamiltonian
	7.3 The Kondo Regime and the Kondo Temperature
	7.4 Modified Scaling of the Kondo Coupling at Finite-ell
	7.5 Probing the Onset of Kondo Regime
	7.6 Concluding Remarks
	References
8 Gauge Theories with Ultracold Atoms
	8.1 Introduction
	8.2 Gauge Theories
		8.2.1 Gauge Symmetry on the Lattice
	8.3 Simulation of Gauge Potentials
		8.3.1 Adiabatic Change of External Parameters
		8.3.2 Effective Hamiltonian in Periodic Driven System
	8.4 Simulation of Gauge Fields
		8.4.1 Gauge Invariance from Energy Punishment
		8.4.2 Gauge Invariance from Many Body Interaction Symmetries
		8.4.3 Encoding in 1+1 Fermions
	References
9 The Remarkable BEC Dimer
	9.1 Introduction
	9.2 Modeling Bose Einstein Condensates (BEC)
		9.2.1 BECs in Optical Lattices
		9.2.2 The BEC Dimer or ``Bose Josephson Junction\'\'
	9.3 The Global Phase Space Approach
	9.4 Full Quantum Dynamics in the BJJ: The Bose Hubbard Hamitonian
		9.4.1 Quantum ``Orbits\'\' Near Fixed Points: Dissipationless Case
		9.4.2 Quantum ``Orbits\'\' Near Fixed Point: The Dissipative Case
		9.4.3 Quantum Tunneling Between Self-trapped Fixed Points
	9.5 Conclusions
	References
10 Quantized Vortex Lines in BECs with a Generalized Equation of State
	10.1 Introduction
	10.2 Vortex Line in a Three Dimensional BEC
	10.3 Vortex Line in a Trapped Three Dimensional BEC
	10.4 Conclusions
	References
11 Topological View on Entanglement and Complexity
	11.1 Introduction
	11.2 Topological Quantum Field Theory
		11.2.1 Chern–Simons Theory. A Definition
		11.2.2 Axiomatic Definition
		11.2.3 Connecting Two Definitions
	11.3 Examples of TQFT
		11.3.1 Hilbert Spaces of Punctured Spheres
		11.3.2 Hilbert Space of T2
	11.4 Entanglement in TQFT
		11.4.1 General Idea
		11.4.2 Back to the Aravind\'s Conjecture
		11.4.3 Reinforcing Entanglement with Wilson Lines
	11.5 Complexity
		11.5.1 Complexity in Quantum Mechanics
		11.5.2 Complexity of Torus Knot States
	11.6 Conclusions
	References
12 Finite Size Effects in Topological Quantum Phase Transitions
	12.1 Topological Phase Transitions
	12.2 The Su–Schrieffer–Heeger Model
	12.3 The Bernevig–Hugues–Zhang (BHZ) Model
	12.4 Finite Size Effects at Topological Transitions
		12.4.1 Multi-band Topological Insulator
		12.4.2 Casimir Effects in Topological Insulators
	12.5 Conclusions
	References
13 From Quantum Spin Chains to Chiral Spin Liquids
	13.1 Introduction
	13.2 Effective Field Theory for the Spin-1/2 Heisenberg Chain
	13.3 Coupling Parallel Chains: The Kalmeyer–Laughlin State
	13.4 Coupling Crossed Chains with Staggered Chirality: Gapless Chiral Spin Liquid
	13.5 Conclusion
	References
14 Majorana Zero-Energy Modes in a Magnetic Field-Free Quantum Wire
	14.1 Introduction
	14.2 General Picture
	14.3 Low-Energy Bosonized Theory and Renormalization Group Treatment
	14.4 Phase Diagram
	14.5 Summary
	References
15 From Graphene to Quantum Computation: An Expedition  to the Dirac Sea
	15.1 Introduction
	15.2 Dirac Fermions in Two-Dimensional Systems
		15.2.1 Massless Dirac Fermions in Graphene
		15.2.2 Massive Dirac Fermions in Transition Metal Dichalcogenides
		15.2.3 Electromagnetic Interaction of Two-Dimensional Dirac Fermions: DC Conductivity in Graphene
		15.2.4 The Quantum Valley Hall Effect in Graphene
	15.3 Dirac Fermions in One-Dimensional Systems: Non-Abelian Statistics
		15.3.1 Interacting Massless Dirac Fermions
		15.3.2 Majorana Spinors with Non-Abelian Statistics
		15.3.3 Majorana Qubits
		15.3.4 Superselecting Sectors and Coherence Protection
	References
16 Quantum Dynamics from a Domain Wall Initial State, in Real and Imaginary Time
	16.1 The Domain Wall Initial State: Free Fermions
	16.2 A Quick Look at Generalized Hydrodynamics
	16.3 Imaginary Time Evolution
	References
17 Quantum Thermodynamics at Impurity Quantum Phase Transitions
	17.1 Introduction
	17.2 Two Impurity Kondo Model
	17.3 Thermodynamic Properties: Work Distribution
	17.4 Scaling of the Irreversible Work
	17.5 Variance Analysis of Work
	17.6 Out-of-Equilibrium Features
	17.7 Summary
	References
18 Information Delocalization in Many Body Systems: From MBL Phases  to Black Holes
	18.1 Introduction
	18.2 Information Delocalization Through Mutual Information
		18.2.1 Random States
		18.2.2 Single Particle States
		18.2.3 Irreversible Growth of the CV in Chaotic Models
		18.2.4 Many-Body-Localized Phases
	18.3 Large-N Models and Black Holes
		18.3.1 Random Free Fermions
		18.3.2 K-Body Ensembles, SYK and de Finetti Theorems
		18.3.3 Black Holes
	18.4 Summary and Discussion
	References
19 Breaking the Area Law: The Rainbow State
	19.1 Introduction
	19.2 Concentric Valence Bond States
	19.3 Results
	References
Appendix  Index
Index