Condensed Matter Field Theory

By A. Altland, Ben D. Simons. 2006

1,331 citations recorded by the source corpus.

The methods of quantum field theory underpin many conceptual advances in contemporary condensed matter physics and neighbouring fields. This book provides a praxis-oriented and pedagogical introduction to quantum field theory in many-particle physics, emphasizing the application of theory to real physical systems. This third edition is organized into two parts: the first half of the text presents a streamlined introduction, elevating readers to a level where they can engage with contemporary research literature, from the introduction of many-body techniques and functional integration to renormalization group methods, and the second half addresses a range of advanced topics including modern aspects of gauge theory, topological and relativistic quantum matter, and condensed matter physics out of thermal equilibrium. At all stages, the text seeks a balance between methodological aspects of quantum field theory and practical applications. Extended problems with worked solutions provide a bridge between formal theory and a research-oriented approach.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8d47009e2dc29c5f90a8654a64bea1bf42d9d773

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Citations in the corpus

Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials (2010, background): “Away from the quantum system, the chain becomes effectively translationally invariant and it is a standard exercise in condensed matter physics to diagonalize such a chain in terms of plane waves [17].”
Momentum-space entanglement and renormalization in quantum field theory (2011, background): “This type of Wilsonian action is more commonly discussed in field theories without Lorentz invariance, such as those describing condensed matter systems (see, for example, [9]).”
Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep (2013, background): “In di-mensionless units, the equation of motion becomes Using the nonequilibrium path integral approach 32 , the probability of ﬁnding the skyrmion at r (cid:48) at t (cid:48) starting from the initial position r 0 at t 0 is p ( r (cid:48) , t (cid:48) | r 0 , t 0 ) = D [ r , ˜ r ] exp dt L , (B3)…”
Geometry of quantum phase transitions (2019, background): “By means of the fluctuation-dissipation theorem [338], one can further derive an expression for Eq.”
Anderson Transitions (2007, background): “10 A pedagogical introduction of topological concepts in the context of condensed matter theory can be found in the recent monograph by Altland and Simons (2006).”
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States (2013, background): “ased on proposing simplied models that are believed to reproduce the relevant interactions responsible for the observed physics, e.g. the Hubbard and t Jmodels in the case of high-T csuperconductors [7]. Once a model is proposed, and with the exception of some lucky cases where these models are exac”
Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities (2012, methodology): “[20, 21] for more details.)”
Impure AdS/CFT correspondence (2008, positive): “Instead the system is best described by a finite temperature 2+1 dimensional conformal field theory (CFT) [1, 2].”
Statistical models for spatial patterns of heavy particles in turbulence (2014, background): “formula which expresses an average over a product of Gaussian random functions as a sum over products of their covariances [184].”