Introduction to the statistical physics of integrable many-body systems

Introduction to the statistical physics of integrable many-body systems /

"Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied."--

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Bibliographic Details
Online Access: Full text (MCPHS users only)
Main Authors: Šamaj, Ladislav, 1959- (Author), Bajnok, Zoltán (Author)
Format: Electronic eBook
Language:English
Published: Cambridge : Cambridge University Press, 2013
Subjects:
Quantum theory > Statistical methods.
Many-body problem.
Local Note:ProQuest Ebook Central

MARC

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100 1 |a Šamaj, Ladislav,  |d 1959-  |e author.  |1 https://id.oclc.org/worldcat/entity/E39PCjC9djyfmMy9QWPh669jBX 
245 1 0 |a Introduction to the statistical physics of integrable many-body systems /  |c Ladislav Šamaj, Zoltán Bajnok. 
264 1 |a Cambridge :  |b Cambridge University Press,  |c 2013. 
300 |a 1 online resource (504 pages) 
336 |a text  |b txt  |2 rdacontent 
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504 |a Includes bibliographical references (pages 596-501) and index. 
505 0 |a Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index. 
520 |a "Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied."--  |c Provided by publisher 
546 |a Text in English. 
588 0 |a Print version record. 
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650 0 |a Quantum theory  |x Statistical methods. 
650 0 |a Many-body problem. 
700 1 |a Bajnok, Zoltán,  |e author. 
776 0 8 |i Print version:  |a Šamaj, Ladislav, 1959-  |t Introduction to the statistical physics of integrable many-body systems.  |d Cambridge : Cambridge University Press, 2013  |z 9781107030435  |w (DLC) 2012051080  |w (OCoLC)830674559 
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880 0 |6 505-00/(S  |a Cover -- Contents -- Preface -- Part I Spinless Bose and Fermi gases -- 1 Particles with nearest-neighbor interactions: Bethe ansatz and the ground state -- 1.1 General formalism -- 1.2 Point interactions -- 1.3 Bosons with δ-potential: Bethe ansatz equations -- 1.4 Bound states for attractive bosons -- 1.5 Repulsive bosons -- 1.6 Particles with finite hard-core interactions -- Exercises -- 2 Bethe ansatz: Zero-temperature thermodynamics and excitations -- 2.1 Response of the ground state -- 2.2 Zero-temperature thermodynamics -- 2.3 Low-lying excitations -- Exercises -- 3 Bethe ansatz: Finite-temperature thermodynamics -- 3.1 The concept of holes -- 3.2 Thermodynamic equilibrium -- Exercises -- 4 Particles with inverse-square interactions -- 4.1 The two-body scattering problem -- 4.2 The ground-state wavefunction of a product form -- 4.3 Excited states for the trigonometric case -- Exercises -- Part II Quantum inverse-scattering method -- 5 QISM: Yang--Baxter equation -- 5.1 Generalized Bethe ansatz -- 5.2 Derivation of the Yang--Baxter equation -- 5.3 Lax operators, monodromy and transfer matrices -- 5.4 Two-state solutions of the YBE -- 5.5 Braid-group solution -- 5.6 Quantum groups -- Exercises -- 6 QISM: Transfer matrix and its diagonalization -- 6.1 Vertex models on the square lattice -- 6.2 Connection with quantum models on a chain -- 6.3 Diagonalization of the trigonometric transfer matrix -- Exercises -- 7 QISM: Treatment of boundary conditions -- 7.1 Formulation of boundary conditions -- 7.2 Boundary conditions and the inhomogeneous transfer matrix -- 7.3 Diagonalization of the inhomogeneous transfer matrix -- 8 Nested Bethe ansatz for spin-½ fermions with δ-interactions -- 8.1 The scattering problem -- 8.2 Nested Bethe equations for spin-½ fermions -- 8.3 Ground state and low-lying excitations -- Exercises. 
880 8 |6 505-00/(S  |a 9 Thermodynamics of spin-½ fermions with δ-interactions -- 9.1 Repulsive regime c>0 -- 9.2 Attractive regime c<0 -- Exercises -- Part III Quantum spin chains -- 10 Quantum Ising chain in a transverse field -- 10.1 Jordan-Wigner transformation -- 10.2 Diagonalization of the quadratic form -- 10.3 Ground-state properties and thermodynamics -- 10.4 Thermodynamics of the classical 2D Ising model -- Exercises -- 11 XXZ Heisenberg chain: Bethe ansatz and the ground state -- 11.1 Symmetries of the Hamiltonian -- 11.2 Schrödinger equation -- 11.3 Coordinate Bethe ansatz -- 11.4 Orbach parameterization -- 11.5 The ground state -- 11.6 The absolute ground state for Δ<1 -- Exercises -- 12 XXZ Heisenberg chain: Ground state in the presence of a magnetic field -- 12.1 Fundamental integral equation for the λ-density -- 12.2 Formula for the magnetic field -- 12.3 Ground-state energy near half-filling -- Exercises -- 13 XXZ Heisenberg chain: Excited states -- 13.1 Strings -- 13.2 Response of the ground state to a perturbation -- 13.3 Low-lying excitations -- Exercises -- 14 XXX Heisenberg chain: Thermodynamics with strings -- 14.1 Thermodynamic Bethe ansatz -- 14.2 High-temperature expansion -- 14.3 Low-temperature expansion -- Exercises -- 15 XXZ Heisenberg chain: Thermodynamics without strings -- 15.1 Quantum transfer matrix -- 15.2 Bethe ansatz equations -- 15.3 Nonlinear integral equations for eigenvalues -- 15.4 Representations of the free energy -- Exercises -- 16 XYZ Heisenberg chain -- 16.1 Diagonalization of the transfer matrix for the eight-vertex model -- 16.2 Restricted models and the ϕ parameter -- 16.3 XYZ chain: Bethe ansatz equations -- 16.4 XYZ chain: Ground-state energy -- 16.5 XYZ chain: Critical ground-state properties -- Exercises -- 17 Integrable isotropic chains with arbitrary spin -- 17.1 Construction of the spin-s scattering matrix. 
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