nLab solid state physics

Idea

The physics of solid condensed matter (made of fermions, due to the Pauli exclusion principle), also continuum mechanics.

Properties

Topological phases of matter

See at K-theory classification of topological phases of matter.

Related concepts

• quantum many-body physics

• Bloch's theorem

• degeneracy pressure

• Bose-Einstein condensate

• Levin-Wen model

• quantum material

  • superconductivity

  • topological phases of matter

  • topological order

  • symmetry protected trivial order

• AdS-CFT in condensed matter physics

• phase of matter

• Josephson effect

• mesoscopic physics

• high energy physics, nuclear physics

References

General

Textbook accounts:

• Charles Kittel, Introduction to Solid State Physics, Wiley (1953-) $[$ISBN:978-0-471-41526-8, pdf, Wikipedia entry$]$

• Ulrich Rößler, Solid State Theory: An Introduction, Springer (2004, 2009) $[$doi:10.1007/978-3-540-92762-4$]$

Lecture notes:

• David Tong, Lectures on solid state physics (2017) $[$pdf, webpage$]$

Specifically on Bloch-Floquet theory:

• Michael Reed, Barry Simon, Sec. XIII.16 Schrödinger operators with periodic potentials, of: Methods of Modern Mathematical Physics – IV: Analysis of Operators, Academic Press (1978)

  (ISBN:9780080570457)

With focus on semiconductor-theory:

• Karlheinz Seeger, Semiconductor Physics, Advanced texts in physics, Springer (2004) $[$doi:10.1007/978-3-662-09855-4$]$

• Sheng San Li, Semiconductor Physical Electronics, Springer (2006) 61-104 $[$doi:10.1007/0-387-37766-2$]$

See also:

• Wikipedia, Solid state physics

and maybe also

• Lev Landau, Evgeny Lifshitz, Theory of Elasticity, part VII of Course of Theoretical Physics, 1959, 1970

Examples and applications

Discussion of possible realization of the SYK-model in condensed matter physics:

• D. I. Pikulin, M. Franz, Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system, Phys. Rev. X 7, 031006 (2017) (arXiv:1702.04426)

AdS/CMT correspondence

On AdS/CFT in condensed matter physics:

• Sean Hartnoll, Andrew Lucas, Subir Sachdev, Holographic quantum matter, MIT Press 2018 (arXiv:1612.07324, publisher)

Proposed realization of aspects of p-adic AdS/CFT correspondence in solid state physics:

• Gregory Bentsen, Tomohiro Hashizume, Anton S. Buyskikh, Emily J. Davis, Andrew J. Daley, Steven Gubser, Monika Schleier-Smith, Treelike interactions and fast scrambling with cold atoms, Phys. Rev. Lett. 123, 130601 (2019) (arXiv:1905.11430)

K-Theory classification of gapped topological phases of matter

Classification of condensed matter with gapped Hamiltonians (topological insulators, topological phases of matter) by twisted equivariant topological K-theory:

• Alexei Kitaev, Periodic table for topological insulators and superconductors, talk at: L.D.Landau Memorial Conference “Advances in Theoretical Physics”, June 22-26, 2008, In:AIP Conference Proceedings 1134, 22 (2009) (arXiv:0901.2686, doi:10.1063/1.3149495)

• Daniel Freed, Gregory Moore, Twisted equivariant matter, Ann. Henri Poincaré (2013) 14: 1927 (arXiv:1208.5055)

• Guo Chuan Thiang, On the K-theoretic classification of topological phases of matter, Annales Henri Poincare 17(4) 757-794 (2016) (arXiv:1406.7366)

• Ralph M. Kaufmann, Dan Li, Birgit Wehefritz-Kaufmann, Topological insulators and K-theory (arXiv:1510.08001, spire:1401095/)

• Daniel Freed, Michael Hopkins, Reflection positivity and invertible topological phases (arXiv:1604.06527)

• Daniel Freed, Lectures on field theory and topology (cds:2699265)

• Charles Zhaoxi Xiong, Classification and Construction of Topological Phases of Quantum Matter (arXiv:1906.02892)

Tensor networks in solid state physics

Discussion of exotic phases of matter via tensor network states:

General:

• Roman Orus, A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States, Annals of Physics 349 (2014) 117-158 (arXiv:1306.2164)

• Jens Eisert, Entanglement and tensor network states, Modeling and Simulation 3, 520 (2013) (arXiv:1308.3318)

• Thorsten B. Wahl, Tensor network states for the description of quantum many-body systems (arXiv:1509.05984)

Specifically tree tensor networks:

• Valentin Murg, Örs Legeza, Reinhard M. Noack, Frank Verstraete, Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks, Phys. Rev. B 82, 205105 (2010) (arXiv:1006.3095)

Concrete materials:

• A. Kshetrimayum, C. Balz, B. Lake, Jens Eisert, Tensor network investigation of the double layer Kagome compound $Ca_{10} Cr_{7} O_{28}$ (arXiv:1904.00028)