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."--
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2013.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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."-- |
| Beschreibung: | 1 online resource (504 pages) |
| Bibliographie: | Includes bibliographical references (pages 596-501) and index. |
| ISBN: | 9781139343480 9781107055872 1139343483 1107055873 9781299634466 129963446X 9781107059405 1107059402 9781107058095 1107058090 1139889613 9781139889612 1107056942 9781107056947 1107054796 9781107054790 |
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| 100 | 1 | |a Šamaj, Ladislav, |d 1959- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjC9djyfmMy9QWPh669jBX |0 http://id.loc.gov/authorities/names/n2013014652 | |
| 245 | 1 | 0 | |a Introduction to the statistical physics of integrable many-body systems / |c Ladislav Šamaj, Zoltán Bajnok. |
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| 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. | |
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 596-501) and index. | ||
| 650 | 0 | |a Quantum theory |x Statistical methods. | |
| 650 | 0 | |a Many-body problem. |0 http://id.loc.gov/authorities/subjects/sh85080793 | |
| 650 | 6 | |a Théorie quantique |x Méthodes statistiques. | |
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| 650 | 7 | |a Many-body problem |2 fast | |
| 650 | 7 | |a Quantum theory |x Statistical methods |2 fast | |
| 700 | 1 | |a Bajnok, Zoltán, |e author. |0 http://id.loc.gov/authorities/names/n2013014655 | |
| 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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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn842932618 |
|---|---|
| _version_ | 1816882232258723840 |
| adam_text | |
| any_adam_object | |
| author | Šamaj, Ladislav, 1959- Bajnok, Zoltán |
| author_GND | http://id.loc.gov/authorities/names/n2013014652 http://id.loc.gov/authorities/names/n2013014655 |
| author_facet | Šamaj, Ladislav, 1959- Bajnok, Zoltán |
| author_role | aut aut |
| author_sort | Šamaj, Ladislav, 1959- |
| author_variant | l s ls z b zb |
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| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.P7 S26 2013eb |
| callnumber-search | QC174.17.P7 S26 2013eb |
| callnumber-sort | QC 3174.17 P7 S26 42013EB |
| callnumber-subject | QC - Physics |
| collection | ZDB-4-EBA |
| contents | 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. |
| ctrlnum | (OCoLC)842932618 |
| dewey-full | 530.12015195 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12015195 |
| dewey-search | 530.12015195 |
| dewey-sort | 3530.12015195 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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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.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 596-501) and index.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Quantum theory</subfield><subfield code="x">Statistical methods.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Many-body problem.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85080793</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie quantique</subfield><subfield code="x">Méthodes statistiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Problème des N corps.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Mathematical Physics.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Physics</subfield><subfield code="x">Quantum Theory.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Many-body problem</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Quantum theory</subfield><subfield code="x">Statistical methods</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bajnok, Zoltán,</subfield><subfield code="e">author.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2013014655</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Šamaj, Ladislav, 1959-</subfield><subfield code="t">Introduction to the statistical physics of integrable many-body systems.</subfield><subfield code="d">Cambridge : Cambridge University Press, 2013</subfield><subfield code="z">9781107030435</subfield><subfield code="w">(DLC) 2012051080</subfield><subfield code="w">(OCoLC)830674559</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569229</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="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.</subfield></datafield><datafield tag="880" ind1="8" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="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.</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH34848888</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH34206679</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts 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| id | ZDB-4-EBA-ocn842932618 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:20Z |
| institution | BVB |
| isbn | 9781139343480 9781107055872 1139343483 1107055873 9781299634466 129963446X 9781107059405 1107059402 9781107058095 1107058090 1139889613 9781139889612 1107056942 9781107056947 1107054796 9781107054790 |
| language | English |
| oclc_num | 842932618 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (504 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge University Press, |
| record_format | marc |
| spelling | Šamaj, Ladislav, 1959- author. https://id.oclc.org/worldcat/entity/E39PCjC9djyfmMy9QWPh669jBX http://id.loc.gov/authorities/names/n2013014652 Introduction to the statistical physics of integrable many-body systems / Ladislav Šamaj, Zoltán Bajnok. Cambridge : Cambridge University Press, 2013. 1 online resource (504 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Text in English. "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."-- Provided by publisher 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. Print version record. Includes bibliographical references (pages 596-501) and index. Quantum theory Statistical methods. Many-body problem. http://id.loc.gov/authorities/subjects/sh85080793 Théorie quantique Méthodes statistiques. Problème des N corps. SCIENCE Mathematical Physics. bisacsh SCIENCE Physics Quantum Theory. bisacsh Many-body problem fast Quantum theory Statistical methods fast Bajnok, Zoltán, author. http://id.loc.gov/authorities/names/n2013014655 Print version: Šamaj, Ladislav, 1959- Introduction to the statistical physics of integrable many-body systems. Cambridge : Cambridge University Press, 2013 9781107030435 (DLC) 2012051080 (OCoLC)830674559 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569229 Volltext 505-00/(S 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. 505-00/(S 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. |
| spellingShingle | Šamaj, Ladislav, 1959- Bajnok, Zoltán Introduction to the statistical physics of integrable many-body systems / 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. Quantum theory Statistical methods. Many-body problem. http://id.loc.gov/authorities/subjects/sh85080793 Théorie quantique Méthodes statistiques. Problème des N corps. SCIENCE Mathematical Physics. bisacsh SCIENCE Physics Quantum Theory. bisacsh Many-body problem fast Quantum theory Statistical methods fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85080793 |
| title | Introduction to the statistical physics of integrable many-body systems / |
| title_auth | Introduction to the statistical physics of integrable many-body systems / |
| title_exact_search | Introduction to the statistical physics of integrable many-body systems / |
| title_full | Introduction to the statistical physics of integrable many-body systems / Ladislav Šamaj, Zoltán Bajnok. |
| title_fullStr | Introduction to the statistical physics of integrable many-body systems / Ladislav Šamaj, Zoltán Bajnok. |
| title_full_unstemmed | Introduction to the statistical physics of integrable many-body systems / Ladislav Šamaj, Zoltán Bajnok. |
| title_short | Introduction to the statistical physics of integrable many-body systems / |
| title_sort | introduction to the statistical physics of integrable many body systems |
| topic | Quantum theory Statistical methods. Many-body problem. http://id.loc.gov/authorities/subjects/sh85080793 Théorie quantique Méthodes statistiques. Problème des N corps. SCIENCE Mathematical Physics. bisacsh SCIENCE Physics Quantum Theory. bisacsh Many-body problem fast Quantum theory Statistical methods fast |
| topic_facet | Quantum theory Statistical methods. Many-body problem. Théorie quantique Méthodes statistiques. Problème des N corps. SCIENCE Mathematical Physics. SCIENCE Physics Quantum Theory. Many-body problem Quantum theory Statistical methods |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569229 |
| work_keys_str_mv | AT samajladislav introductiontothestatisticalphysicsofintegrablemanybodysystems AT bajnokzoltan introductiontothestatisticalphysicsofintegrablemanybodysystems |