Concepts

Concepts before formalism. The big ideas of many-body physics recur across very different systems and methods, so here you can follow an idea — every topic that illustrates it, wherever it lives.

14 concepts mapped · 10 with topics so far.

• Broken symmetry Ground states that choose less symmetry than their Hamiltonian — order parameters, rigidity, and Goldstone modes. 2 topics
• Competing orders Several would-be ground states close in energy — the source of rich phase diagrams and intertwined order. 1 topic
• Effective models Throwing away what does not matter at low energy — the art of writing the simplest model that still contains the physics. 1 topic
• Emergence Behaviour that belongs to the whole, not the parts — the reason many-body physics is more than a sum of one-body problems. 2 topics
• Entanglement The quantum correlations that have no classical analogue — area laws, and why tensor networks work. planned
• Geometry Band geometry, Berry curvature, and frustration — when the shape of the problem is the physics. planned
• Linear response How a system answers a weak push — susceptibilities, spectral functions, and fluctuation–dissipation. planned
• Localization When particles stop propagating — Mott (interaction-driven) and Anderson (disorder-driven) insulators. 3 topics
• Phase transitions Qualitative change with a tuning parameter — first-order vs continuous, critical points, and quantum criticality. 2 topics
• Quasiparticles Dressed excitations that behave like nearly-free particles — Landau's idea, its weight Z, and where it dies. 3 topics
• Scaling & universality Why microscopically different systems share critical behaviour — relevant couplings, exponents, and fixed points. 1 topic
• Strong correlations The regime where interactions dominate kinetic energy and independent-particle pictures fail. 2 topics
• Symmetry The transformations a system respects — they organise the spectrum, fix selection rules, and predict what can happen. 1 topic
• Topology Properties that survive smooth deformation — invariants, protected edge states, and order without a local order parameter. planned