Field theories in condensed matter physics:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Bristol [u.a.]
IoP
2002
|
| Series: | Series in condensed matter physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 408 S. Ill., graph. Darst. |
| ISBN: | 0750308761 |
Staff View
MARC
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| 245 | 1 | 0 | |a Field theories in condensed matter physics |c ed. by Sumathi Rao |
| 264 | 1 | |a Bristol [u.a.] |b IoP |c 2002 | |
| 300 | |a XIV, 408 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Series in condensed matter physics | |
| 650 | 4 | |a Condensed matter |v Congresses | |
| 650 | 4 | |a Field theory (Physics) |v Congresses | |
| 650 | 4 | |a Statistical mechanics |v Congresses | |
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| 700 | 1 | |a Rao, Sumathi |e Sonstige |4 oth | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-010350368 | ||
Record in the Search Index
| _version_ | 1804130031650209792 |
|---|---|
| adam_text | Contents
Preface
xiii
Introduction
1
1
Quantum
Many Particle Physics
7
Pinaki Majumdar
1.1
Preamble
....................... 8
1.2
Introduction
...................... 8
1.3
Introduction to many particle physics
....... 10
1.3.1
Phases of many particle systems
...... 10
1.3.2
Quantities of physical interest
........ 12
1.3.3
Fermi and
Bose
liquids
............ 14
1.4
Phase transitions and broken symmetry
...... 22
1.4.1
Phase transitions and symmetry breaking
. 22
1.4.2
Symmetry breaking and interactions in
ВБС
25
1.5
Normal Fermi systems: model problems
...... 31
1.5.1
Neutral
fermions:
dilute hardcore Fermi gas
34
1.5.2
Charged
fermions:
the electron gas
..... 39
1.6
Electrons and phonons: Migdal-Ehashberg theory
. 46
1.6.1
Weak coupling theory: BCS
........ 48
1.6.2
The normal state:
Migdal
theory
. ... . . 52
1.6.3
BCS theory: Greene function approach
... 56
1.6.4
Superconductivity: EUashberg theory
. . . 58
1.7
Conclusion: field theory and many particle physics
63
viii CONTENTS
2
Critical Phenomena 69
Somendra
Ar,
Bhattacharjee
2.1
Preamble
....................... 70
2.1.1
Large system: Thermodynamic limit
.... 72
2.2
Where is the problem?
................ 72
2.3
Recapitulation
-
A few formal stuff
........ 74
2.3.1
Extensivity
.................. 74
2.3.2
Convexity: Stability
............. 76
2.4
Consequences of divergence
............. 78
2.5
Generalized scaling
................. 81
2.5.1
One variable: Temperature
......... 81
2.5.2
Solidarity with thermodynamics
...... 87
2.5.3
More variables: Temperature and field
... 88
2.5.4
On exponent relations
............ 92
2.6
Relevance, irrelevance and universality
....... 93
2.7
Digression
....................... 95
2.7.1
A first-order transition: q=1
........ 95
2.7.2
Example: Polymers
:
no ordering
. . · · 97
2.8
Exponents and correlations
............. 99
2.8.1
Correlation function
............. 99
2.8.2
Relations among the exponents
.......
Ю1
2.8.3
Length-scale dependent parameters
..... 103
2.9
Models as examples: Gaussian and
φ4
.......
Ю5
2.9.1
Specific heat for the Gaussian model
.... 106
2.9.2
Cut-off and anomalous dimensions
.....
Ю7
2.9.3
Through correlations
.............
110
2.10
Epilogue ..I...
...... . ..........
112
S
Phase Transitions and Critical Phenomena 119
3.1
Introduction
.. ,.·.■,,,, . .................. 120
3.2
Thermodynamic stability
........ ...··· 121
3.3
Lattice gas
:
mean field approximation
. ... ... 126
^Џ^
■
^
.
, . . ■■:■
I34
CONTENTS ix
3.5
Spatial
correlations
.................. 138
3.6
Breakdown of mean field theory
........... 141
3.7
Ginzburg-Landau free energy functional
...... 143
3.8
Renormalisation
group (RG)
............ 144
3.9
RG for a one dimensional Ising chain
........ 146
3.10
RG for a two-dimensional Ising model
....... 150
3.11
General features of RG
............... 158
3.11.1
Irrelevant variables
.............. 163
3.12
RG scaling for correlation functions
......... 164
3.13
RG for Ginzburg-Landau model
........... 167
3.13.1
Tree-level approximation
........... 170
3.13.2
Critical exponents for
d
> 4......... 172
3.13.3
Anomalous dimensions
............ 175
3.14
Perturbation series for
d
< 4............. 176
3.15
Generalisation to a
η
-component
model
...... 183
4
Topologicei
Defects
189
Ajit M. Srivastava
4.1
The subject of topological defect
.......... 191
4.2
What is a topological defect?
............ 193
4.2.1
Meaning of order parameter
......... 194
4.2.2
Spontaneous symmetry breakdown(SSB)
. . 195
4.2.3
SSB in particle physics
............ 197
4.2.4
Order parameter space
............ 197
4.3
The domain wall
................... 198
4.3.1
Why defect?
................. 200
4.3.2
Why topological?
....... . ....... 201
4.3.3
Energy considerations
............ 202
4.4
Examples of topological defects
.... . . . . . . . 203
4.5
Condensed matter versus particle physics
. . . . . 209
4.6
Detailed understanding of a topological defect
. . . 213
4.6.1
Free homotopy of maps
..... . . . . . . 216
4.6.2
Based homotopy and the fundamental group
217
4.7
Classification of
defecte
using homotopy
groupe
. . 219
4.8
Defect structure in liquid crystals
. . . . . ... . .227
t
CONTENTS
4.8.1
Defects in nematics
..............228
4.8.2
Non
abelian
щ
-
biaxial nematics
......230
4.9
Formation of topological defects
...........231
S
Introduction to Bosonization
239
Sumathi Rao and Diptiman Sen
5.1
Fermi and Luttinger liquids
.............240
5.2
Bosonization
.....................247
5.2.1
Bosonization of a fermion with one chirality
248
5.2.2
Bosonisation with two chiralities
...... 257
5.2.3
Field theory near the Fermi momenta
... 265
5.3
Correlation functions and dimensions of operators
268
5.4
RG analysis of perturbed models
.......... 272
5.5
Applications of bosonization
............· 231
5.6
Quantum antiferromagnetic spin
1/2
chain
..... 282
5.7
Hubbard model
.................... 300
5.8
Transport in a Luttinger liquid
-
clean wire
.... 309
5.9
Transport in the presence of isolated impurities
. . 319
5.10
Concluding remarks
................. 328
β
Quantum
Hall
Effect 335
R. Rajaraman
6.1
Classical Hall effect
..................336
6.2
Quantized HaU effect
................. 337
6.3
Landau problem
.... ..... . . . .....····· 338
6.4
Degeneracy counting
.....
r
. . . . · · · · · · · 340
6.5
Laughlin wavefunction
»«.»... . ,.■.·- · · · -341
6Λ
Plasma analogy ;4.·.·,;..,
+;<,..,,., .·,.■■.,,...,...,. ,.?:. · · · 342
6.7 Quagi-hoke
and their Laughlin wavefunction
... 344
6.8
LocaUzation physics and the QH plateaux
.... - · · 345
■■■UM-memméaBš^msk^^
-»ы
.»··>.,>
v
>■,*-;. · -/> - · · 348
6.10
Vortices in the
CS
field and quasihoks
-.·- ■
^
6.11
Jam s theory of
composite fermions
...
о*љ-
·■- ♦
CONTENTS xi
7
Low-dimensional
Quantum Spin Systems 359
Indrani
Bose
7.1
Introduction
..................... 360
7.2
Ground and excited states
.............. 365
7.3
Theorems and rigorous results for antiferromagnets
369
7.3.1
Lieb-Mattis theorem
............. 369
7.3.2
Marshall s sign rule
............. 370
7.3.3 Lieb, Schultz
and
Mattis
theorem
..... 372
7.3:4
Mermin-Wagner theorem
.......... 376
7.4
Possible ground states and excitation spectra
. . . 376
7.5
The Bethe
Ansatz.................. 387
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| genre_facet | Konferenzschrift |
| id | DE-604.BV017167304 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:14:34Z |
| institution | BVB |
| isbn | 0750308761 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010350368 |
| oclc_num | 50848017 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-11 |
| physical | XIV, 408 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | IoP |
| record_format | marc |
| series2 | Series in condensed matter physics |
| spelling | Field theories in condensed matter physics ed. by Sumathi Rao Bristol [u.a.] IoP 2002 XIV, 408 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series in condensed matter physics Condensed matter Congresses Field theory (Physics) Congresses Statistical mechanics Congresses Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Kondensierte Materie (DE-588)4132810-3 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Rao, Sumathi Sonstige oth Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010350368&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Field theories in condensed matter physics Condensed matter Congresses Field theory (Physics) Congresses Statistical mechanics Congresses Quantenfeldtheorie (DE-588)4047984-5 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4132810-3 (DE-588)1071861417 |
| title | Field theories in condensed matter physics |
| title_auth | Field theories in condensed matter physics |
| title_exact_search | Field theories in condensed matter physics |
| title_full | Field theories in condensed matter physics ed. by Sumathi Rao |
| title_fullStr | Field theories in condensed matter physics ed. by Sumathi Rao |
| title_full_unstemmed | Field theories in condensed matter physics ed. by Sumathi Rao |
| title_short | Field theories in condensed matter physics |
| title_sort | field theories in condensed matter physics |
| topic | Condensed matter Congresses Field theory (Physics) Congresses Statistical mechanics Congresses Quantenfeldtheorie (DE-588)4047984-5 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| topic_facet | Condensed matter Congresses Field theory (Physics) Congresses Statistical mechanics Congresses Quantenfeldtheorie Kondensierte Materie Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010350368&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT raosumathi fieldtheoriesincondensedmatterphysics |