Condensed Matter References

Condensed-matter references use quantum mechanics in a many-particle and materials-facing setting. The main risks for readers trained only in one-particle quantum mechanics are uncontrolled notation changes, thermodynamic-limit assumptions, second-quantized language, and field-theory shorthand.

Use Quantum Matter Reference and Data to attach source locators, version, convention, and reuse-license metadata to a material-facing lookup record; use this page with the Condensed Matter Roadmap, Quantum Matter Formulas, and the QFT Bridge.

Solid-State Entry Points

Ashcroft and Mermin, Solid State Physics.

Best for: crystal structure, electrons in solids, phonons, transport, magnetism, and a durable physical introduction.

Watch for: it predates modern topological band theory and much of the language of strongly correlated systems.

Kittel, Introduction to Solid State Physics.

Best for: compact coverage of standard solid-state topics and quick orientation.

Watch for: it is not a modern research map; use newer sources for topology, correlations, and many-body methods.

Marder, Condensed Matter Physics.

Best for: a broad and modern textbook route through solids, statistical mechanics, and materials phenomena.

Watch for: it is extensive; choose chapters by problem rather than reading linearly.

Simon, The Oxford Solid State Basics.

Best for: a gentler conceptual bridge into solids, band structure, phonons, and basic many-body language.

Watch for: it is an entry point, not a replacement for advanced many-body references.

Many-Body and Field-Theory Style

Altland and Simons, Condensed Matter Field Theory.

Best for: path integrals, Green functions, symmetry breaking, disorder, and field-theory methods in condensed matter.

Watch for: it assumes comfort with second quantization and field-theory notation.

Coleman, Introduction to Many-Body Physics.

Best for: Green functions, response, Fermi liquids, magnetism, and physical reasoning in interacting systems.

Watch for: it is conceptually rich and sometimes informal; check technical details against method-specific references.

Fetter and Walecka, Quantum Theory of Many-Particle Systems.

Best for: many-body perturbation theory, Green functions, linear response, and classic formalism.

Watch for: notation is older and dense; translate conventions before cross-linking formulas.

Auerbach, Interacting Electrons and Quantum Magnetism.

Best for: quantum magnetism, spin systems, path integrals for spins, and correlated-electron models.

Watch for: it is specialized; use it after the basic angular-momentum and spin-model foundations are secure.

Topological and Correlated Matter

Wen, Quantum Field Theory of Many-Body Systems.

Best for: topological order, emergent gauge fields, and strongly correlated systems.

Watch for: it is advanced and field-theory-facing; do not use it as a first introduction to quantum mechanics.

Fradkin, Field Theories of Condensed Matter Physics.

Best for: field-theory methods, critical phenomena, topology, and correlated matter.

Watch for: it assumes prior field-theory fluency.

Hasan and Kane, “Colloquium: Topological insulators.”

Best for: early topological-insulator vocabulary, band topology, and experimental context.

Watch for: current topological materials and classification schemes require newer specialized literature.

Convention Checks

• Decide whether momentum sums are normalized by $1/V$, $1/N$, or absorbed into integration measures.
• Track whether $\hbar=1$ and lattice spacing $a=1$ have been set.
• Distinguish first-quantized many-particle wavefunctions from second-quantized Fock-space states.
• Check Green-function sign conventions before comparing formulas.
• Separate single-particle band topology from many-body topological order.

Cross-Links

• Condensed Matter Roadmap
• Second Quantization
• Bloch Theorem
• Chern Number
• QFT Bridge References

References

• N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston, 1976.
• C. Kittel, Introduction to Solid State Physics, 8th ed., Wiley, 2004.
• M. P. Marder, Condensed Matter Physics, 2nd ed., Wiley, 2010.
• S. H. Simon, The Oxford Solid State Basics, Oxford University Press, 2013.
• A. Altland and B. D. Simons, Condensed Matter Field Theory, 2nd ed., Cambridge University Press, 2010.
• P. Coleman, Introduction to Many-Body Physics, Cambridge University Press, 2015.
• A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, Dover, 2003.
• A. Auerbach, Interacting Electrons and Quantum Magnetism, Springer, 1994.
• X.-G. Wen, Quantum Field Theory of Many-Body Systems, Oxford University Press, 2004.
• E. Fradkin, Field Theories of Condensed Matter Physics, 2nd ed., Cambridge University Press, 2013.
• M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Reviews of Modern Physics 82, 3045-3067 (2010), DOI: 10.1103/RevModPhys.82.3045.
• X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Reviews of Modern Physics 83, 1057-1110 (2011), DOI: 10.1103/RevModPhys.83.1057.