Dynamics of one-dimensional quantum systems: inverse-square interaction models
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2009
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XII, 474 S. graph. Darst. |
| ISBN: | 9780521815987 9781107424722 |
Internformat
MARC
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| 100 | 1 | |a Kuramoto, Yoshio |e Verfasser |0 (DE-588)141422165 |4 aut | |
| 245 | 1 | 0 | |a Dynamics of one-dimensional quantum systems |b inverse-square interaction models |c Yoshio Kuramoto ; Yusuke Kato |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2009 | |
| 300 | |a XII, 474 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Matrix inversion | |
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Datensatz im Suchindex
| _version_ | 1804139406767947776 |
|---|---|
| adam_text | Contents
Preface page
xi
1
Introduction
1
1.1
Motivation
1
1.2
One-dimensional
interaction as a disguise
3
1.3
Two-body problem with 1/r2 interaction
4
1.4
Freezing spatial motion
10
1.5
Prom spin permutation to graded permutation
11
1.6
Variants of 1/r2 systems
13
1.7
Contents of the book
16
Part I Physical properties
19
2
Single-component Sutherland model
21
2.1
Preliminary approach
22
2.1.1
Jastrow-type wave functions
22
2.1.2
Triangular matrix for Hamiltonian
24
2.1.3
Ordering of basis functions
30
2.2
Descriptions of energy spectrum
32
2.2.1
Interacting boson description
32
2.2.2
Interacting fermion description
34
2.2.3
Exclusion statistics
34
2.3
Elementary excitations
36
2.3.1
Partitions
37
2.3.2
Quasi-particles
40
2.3.3
Quasi-holes
43
2.3.4
Neutral excitations
45
Contents
2.4
Thermodynamics
47
2.4.1
Interacting boson picture
48
2.4.2
Free anyon picture
50
2.4.3
Exclusion statistics and duality
51
2.4.4
Elementary excitation picture
54
2.5
Introduction to Jack polynomials
55
2.6
Dynamics in thermodynamic limit
61
2.6.1
Hole propagator
ψ(χ,ί)φ(0,0))
62
2.6.2
Particle propagator
{φ{χ,ήφΐ
(0,0)) 65
2.6.3
Density correlation function
67
2.7
Derivation of dynamics for finite-sized systems
70
2.7.1
Hole propagator
71
2.7.2
*Particle propagator
77
2.7.3
Density correlation function
86
2.8
*Reduction to Tomonaga-Luttinger liquid
90
2.8.1
Asymptotic behavior of correlation functions
91
2.8.2
Finite-size corrections
93
Multi-component Sutherland model
98
3.1
Triangular form of Hamiltonian
99
3.2
Energy spectrum of multi-component fermionic model
104
3.2.1
Eigenstates of identical particles
104
3.2.2
Wave function of ground state
107
3.2.3
Eigenstates with bosonic Fock condition
109
3.3
Energy spectrum with most general internal symmetry 111
3.4
Elementary excitations
114
3.4.1
Quasi-particles
114
3.4.2
Quasi-holes
115
3.5
Thermodynamics
120
3.5.1
Multi-component bosons and
fermions
120
3.5.2
Explicit results for U(2) anyons
123
3.5.3
Generalization to V(K) symmetry
127
3.6
Eigenfunctions
129
3.6.1
Non-symmetric Jack polynomials
129
3.6.2
Jack polynomials with U(2) symmetry
133
3.7
Dynamics of U(2) Sutherland model
135
3.7.1
Hole propagator
(φ {χ,ί)φι
(0,0)) 136
3.7.2
Unified description of correlation functions
138
3.8
Derivation of dynamics for finite-sized systems
142
3.8.1
Hole propagator
142
3.8.2
Density correlation function
146
Contents
vii
Spin chain with 1/r2 interactions
150
4.1
Mapping to hard-core bosons
151
4.2
Gutzwiller—Jastrow wave function
152
4.2.1
Hole representation of lattice
fermions
152
4.2.2
Gutzwiller wave function in Jastrow form
155
4.3
Projection to the Sutherland model
156
4.4
Static structure factors
157
4.5
*Derivation of static correlation functions
163
4.6
Spectrum of
magnons
171
4.7
Spinons
173
4.7.1
Localized spinons
173
4.7.2
Spectrum of spinons
175
4.7.3
Polarized ground state
178
4.8
Energy levels and their degeneracy
180
4.8.1
Degeneracy beyond SU(2) symmetry
180
4.8.2
Local current operators
183
4.8.3
Freezing trick
185
4.9
From Young diagrams to ribbons
188
4.9.1
Removal of phonons
188
4.9.2
Completeness of spinon basis
190
4.9.3
Semionic statistics of spinons
193
4.9.4
Variants of Young diagrams
194
4.10
Thermodynamics
196
4.10.1
Energy functional of spinons
196
4.10.2
Thermodynamic potential of spinons
200
4.10.3
Susceptibility and specific heat
203
4.10.4
Thermodynamics by freezing trick
205
4.11
Dynamical structure factor
208
4.11.1
Brief survey on dynamical theory
208
4.11.2
Exact analytic results
211
4.11.3
Dynamics in magnetic field
215
4.11.4
Comments on experimental results
219
SU(Jf) spin chain
220
5.1
Coordinate representation of ground state
221
5.2
Spectrum and motif
223
5.3
Statistical parameters via freezing trick
229
5.4
Dynamical structure factor
231
viii Contents
6 Supersymmetric t-J
model with
l/r2
interaction
233
6.1
Global
supersymmetry in
í-J model
234
6.2
Mapping to
11(1,1)
Sutherland model
235
6.3
Static structure factors
239
6.4
Spectrum of elementary excitations
245
6.4.1
Energy of polynomial wave functions
245
6.4.2
Spinons and antispinons
250
6.4.3
Holons and antiholons
253
6.5
Yangian supersymmetry
256
6.5.1
Yangian generators
256
6.5.2
Ribbon diagrams and
supermultiplets
259
6.5.3
Motif as representation of
supermultiplets
261
6.6
Thermodynamics
262
6.6.1
Parameters for exclusion statistics
262
6.6.2
Energy and thermodynamic potential
265
6.6.3
Fully polarized limit
267
6.6.4
Distribution functions at low temperature
268
6.6.5
Magnetic susceptibility
270
6.6.6
Charge susceptibility
272
6.6.7
Entropy and specific heat
274
6.7
Dynamics of supersymmetric t—J model
278
6.7.1
Coupling of external fields to quasi-particles
278
6.7.2
Dynamical spin structure factor
280
6.7.3
Dynamical structure factor in magnetic fields
287
6.7.4
Dynamical charge structure factor
290
6.7.5
Electron addition spectrum
293
6.7.6
Electron removal spectrum
295
6.7.7
Momentum distribution
300
6.8
Derivation of dynamics for finite-sized t-J model
302
6.8.1
Electron addition spectrum
303
6.8.2
Dynamical spin structure factor
306
Part II Mathematics related to 1/r2 systems
309
7
Jack polynomials
311
7.1
Non-symmetric Jack polynomials
312
7.1.1
Composition
312
7.1.2
Cherednik-Dunkl operators
314
7.1.3
Definition of non-symmetric Jack polynomials
319
7.1.4
Orthogonality
319
Contents ix
7.1.5
Generating operators
324
7.1.6
Arms and legs of compositions
329
7.1.7
Evaluation formula
333
7.2
Antisymmetrization of Jack polynomials
334
7.2.1
Antisymmetric Jack polynomials
334
7.2.2
Integral norm
338
7.2.3
Binomial formula
341
7.2.4
Combinatorial norm
342
7.3
Symmetric Jack polynomials
346
7.3.1
Relation to non-symmetric Jack polynomials
346
7.3.2
Evaluation formula
351
7.3.3
Symmetry-changing operator
352
7.3.4
Bosonic description of partitions
355
7.3.5
Integral norm
359
7.3.6
Combinatorial norm
360
7.3.7
Binomial formula
364
7.3.8
Power-sum decomposition
364
7.3.9
Duality
365
7.3.10
Skew Jack functions and
Pieri
formula
368
7.4
U(2) Jack polynomials
371
7.4.1
Relation to non-symmetric Jack polynomials
371
7.4.2
Integral norm
372
7.4.3
Cauchy product expansion formula
373
7.4.4
UB(2) Jack polynomials
373
7.4.5
Evaluation formula
375
7.4.6
Binomial formula
377
7.4.7
Power-sum decomposition
381
7.5
U(l,l) Jack polynomials
382
7.5.1
Relation to non-symmetric Jack polynomials
382
7.5.2
Evaluation formula
384
7.5.3
Bosonization for separated states
385
7.5.4
Factorization for separated states
386
7.5.5
Binomial formula for separated states
388
7.5.6
Integral norm
389
8
Yang—Baxter relations and orthogonal eigenbasis
391
8.1
Fock condition and R-matrix
392
8.2
R-matrix and monodromy matrix
397
8.3
Yangian gl2
401
8.4
Relation to U(2) Sutherland model
403
x
Contents
8.5
Construction
of
orthogonal
set of eigenbasis
406
8.5.1
Examples for small systems
406
8.5.2
Orthogonal eigenbasis for TV-particle systems
416
8.6
Norm of Yangian Gelfand-Zetlin basis
419
9
SU(íí)
and supersymmetric Yangians
422
9.1
Construction of monodromy matrix
423
9.2
Quantum determinant vs. ordinary determinant
426
9.3
Capelli
determinant
427
9.4
Quantum determinant of
SU(-ří)
Yangian
430
9.5
Alternative construction of monodromy matrix
431
9.6
Drinfeld polynomials
435
9.7
Extension to supersymmetry
438
10
Uglov s theory
441
10.1
Macdonald
symmetric polynomials
441
10.2
Uglov polynomials
444
10.3
Reduction to single-component bosons
445
10.4
From Yangian Gelfand-Zetlin basis to Uglov polynomials
449
10.5
Dynamical correlation functions
450
Afterword
455
References
458
Index of symbols
464
Index
471
|
| any_adam_object | 1 |
| author | Kuramoto, Yoshio Kato, Yusuke 1929- |
| author_GND | (DE-588)141422165 (DE-588)141422203 |
| author_facet | Kuramoto, Yoshio Kato, Yusuke 1929- |
| author_role | aut aut |
| author_sort | Kuramoto, Yoshio |
| author_variant | y k yk y k yk |
| building | Verbundindex |
| bvnumber | BV035694026 |
| callnumber-first | Q - Science |
| callnumber-label | QC176 |
| callnumber-raw | QC176.8.E4 |
| callnumber-search | QC176.8.E4 |
| callnumber-sort | QC 3176.8 E4 |
| callnumber-subject | QC - Physics |
| classification_rvk | UK 1200 UL 2000 |
| classification_tum | PHY 602f PHY 026f |
| ctrlnum | (OCoLC)699146495 (DE-599)BVBBV035694026 |
| dewey-full | 530.4/11015118 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/11015118 |
| dewey-search | 530.4/11015118 |
| dewey-sort | 3530.4 811015118 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035694026 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:43:35Z |
| institution | BVB |
| isbn | 9780521815987 9781107424722 |
| language | English |
| lccn | 2009023529 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017748056 |
| oclc_num | 699146495 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-384 DE-11 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-384 DE-11 |
| physical | XII, 474 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Kuramoto, Yoshio Verfasser (DE-588)141422165 aut Dynamics of one-dimensional quantum systems inverse-square interaction models Yoshio Kuramoto ; Yusuke Kato 1. publ. Cambridge Cambridge University Press 2009 XII, 474 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathematisches Modell Electronic structure Mathematical models Matrix inversion Many-body problem Elektronenstruktur (DE-588)4129531-6 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Vielkörperproblem (DE-588)4078900-7 gnd rswk-swf Dimension 1 (DE-588)4323094-5 gnd rswk-swf Vielkörperproblem (DE-588)4078900-7 s Elektronenstruktur (DE-588)4129531-6 s Quantenmechanisches System (DE-588)4300046-0 s Dimension 1 (DE-588)4323094-5 s DE-604 Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Kato, Yusuke 1929- Verfasser (DE-588)141422203 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017748056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kuramoto, Yoshio Kato, Yusuke 1929- Dynamics of one-dimensional quantum systems inverse-square interaction models Mathematisches Modell Electronic structure Mathematical models Matrix inversion Many-body problem Elektronenstruktur (DE-588)4129531-6 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Mathematische Physik (DE-588)4037952-8 gnd Vielkörperproblem (DE-588)4078900-7 gnd Dimension 1 (DE-588)4323094-5 gnd |
| subject_GND | (DE-588)4129531-6 (DE-588)4300046-0 (DE-588)4037952-8 (DE-588)4078900-7 (DE-588)4323094-5 |
| title | Dynamics of one-dimensional quantum systems inverse-square interaction models |
| title_auth | Dynamics of one-dimensional quantum systems inverse-square interaction models |
| title_exact_search | Dynamics of one-dimensional quantum systems inverse-square interaction models |
| title_full | Dynamics of one-dimensional quantum systems inverse-square interaction models Yoshio Kuramoto ; Yusuke Kato |
| title_fullStr | Dynamics of one-dimensional quantum systems inverse-square interaction models Yoshio Kuramoto ; Yusuke Kato |
| title_full_unstemmed | Dynamics of one-dimensional quantum systems inverse-square interaction models Yoshio Kuramoto ; Yusuke Kato |
| title_short | Dynamics of one-dimensional quantum systems |
| title_sort | dynamics of one dimensional quantum systems inverse square interaction models |
| title_sub | inverse-square interaction models |
| topic | Mathematisches Modell Electronic structure Mathematical models Matrix inversion Many-body problem Elektronenstruktur (DE-588)4129531-6 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Mathematische Physik (DE-588)4037952-8 gnd Vielkörperproblem (DE-588)4078900-7 gnd Dimension 1 (DE-588)4323094-5 gnd |
| topic_facet | Mathematisches Modell Electronic structure Mathematical models Matrix inversion Many-body problem Elektronenstruktur Quantenmechanisches System Mathematische Physik Vielkörperproblem Dimension 1 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017748056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kuramotoyoshio dynamicsofonedimensionalquantumsystemsinversesquareinteractionmodels AT katoyusuke dynamicsofonedimensionalquantumsystemsinversesquareinteractionmodels |