Exact methods in low-dimensional statistical physics and quantum computing : École d'été de physique des Houches, session LXXXIX, 30 June-1 August 2008, École thématique du CNRS / edited by Jesper Jacobsen [and others].

Includes bibliographical references.

Print version record.

Contents -- List of participants -- PART I: LONG LECTURES -- 1 Quantum impurity problems in condensed matter physics -- 1.1 Quantum impurity problems and the renormalization group -- 1.2 Multichannel Kondo model -- 1.3 Quantum dots: Experimental realizations of one- and two-channel Kondo models -- 1.4 Quantum impurity problems in Luttinger liquids -- 1.5 Quantum impurity entanglement entropy -- 1.6 Y-junctions of quantum wires -- 1.7 Boundary-condition-changing operators and the X-ray edge singularity -- 1.8 Conclusions -- References

2 Conformal field theory and statistical mechanics2.1 Introduction -- 2.2 Scale invariance and conformal invariance in critical behavior -- 2.3 The role of the stress tensor -- 2.4 Radial quantization and the Virasoro algebra -- 2.5 CFT on the cylinder and torus -- 2.6 Height models, loop models, and Coulomb gas methods -- 2.7 Boundary conformal field theory -- 2.8 Further reading -- 3 The quantum Hall effect -- 4 Topological phases and quantum computation -- 4.1 Introduction: The quest for protected qubits

4.2 Topological phenomena in 1D: Boundary modes in the Majorana chain4.3 The two-dimensional toric code -- 4.4 Abelian anyons and quasiparticle statistics -- 4.5 The honeycomb lattice model -- References -- 5 Four lectures on computational statistical physics -- 5.1 Sampling -- 5.2 Classical hard-sphere systems -- 5.3 Quantum Monte Carlo simulations -- 5.4 Spin systems: Samples and exact solutions -- References -- 6 Loop models -- 6.1 Historical perspective -- 6.2 Brief summary of renormalization theory -- 6.3 Loop models -- 6.4 The Coulomb gas

6.5 Summary and perspectiveReferences -- 7 Lectures on the integrability of the six-vertex model -- 7.1 Introduction -- 7.2 Classical integrable spin chains -- 7.3 Quantization of local integrable spin chains -- 7.4 The spectrum of transfer matrices -- 7.5 The thermodynamic limit -- 7.6 The six-vertex model -- 7.7 The six-vertex model on a torus in the thermodynamic limit -- 7.8 The six-vertex model at the free-fermionic point -- 7.9 The free energy of the six-vertex model -- 7.10 Some asymptotics of the free energy

7.11 The Legendre transform of the free energy7.12 The limit shape phenomenon -- 7.13 Semiclassical limits -- 7.14 The free-fermionic point and dimer models -- 7.A Appendix -- References -- 8 Mathematical aspects of 2D phase transitions -- PART II: SHORT LECTURES -- 9 Numerical simulations of quantum statistical mechanical models -- 9.1 Introduction -- 9.2 A rapid survey of methods -- 9.3 Path integral and related methods -- 9.4 Classical worm algorithm -- 9.5 Projection methods -- 9.6 Valence bond projection method -- References

English.

"Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics."--Publisher's description.

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