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INTERACTING FERMIONS ON A LATTICE

Thierry Giamarchi

in Quantum Physics in One Dimension

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198525004
eISBN:
9780191711909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525004.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

This chapter examines the canonical microscopic models used to study interacting fermions. Most of these models are quite general and are not special to one dimension. These models try to implement ... More


Fermi and Fermi–Bose Hubbard models: methods of treatment

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.9006
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents various methods specific for fermionic systems and Fermi–Bose mixtures. It starts by discussing a lattice version of the BCS theory and then reviews BCS-BEC crossover theory for ... More


Models of Strongly Interacting Quantum Matter

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter introduces a select number of models of strongly interacting quantum many-particle physics and examines their basic properties. These models represent Bosonic and Fermionic systems as ... More


Numerical Studies of Metal—Insulator Transitions in Disordered Hubbard Models

S. Chiesa, R.T. Scalettar, P.J.H. Denteneer, P. Chakraborty, T. Paiva, and S. Story

in Conductor-Insulator Quantum Phase Transitions

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199592593
eISBN:
9780191741050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199592593.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews Determinant Quantum Monte Carlo studies of the disordered Hubbard Hamiltonian. The effect of the interplay of interactions and a variety of realizations of the randomness, ... More


Quantum simulators of condensed matter

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter presents an operational definition of quantum simulators, and discusses what kind of Hubbard models and spin models can, in principle, be simulated with ultracold atoms.


The ground state construction of the two-dimensional Hubbard model on the honeycomb lattice

Giuliani Alessandro

in Quantum Theory from Small to Large Scales: Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199652495
eISBN:
9780191741203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199652495.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

The fermionic Hubbard model on the two-dimensional hexagonal lattice at half-filling is the simplest model for undoped single layer graphene with screened interactions. It is remarkable that, in the ... More


Electron repulsion

Enric Canadell, Marie-Liesse Doublet, and Christophe Iung

in Orbital Approach to the Electronic Structure of Solids

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199534937
eISBN:
9780191774935
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534937.003.0012
Subject:
Physics, Condensed Matter Physics / Materials

This chapter shows that the repulsion between correlated electrons can take different mathematical forms depending on the Hamiltonian and wavefunction chosen to describe the n-interacting particles ... More


EXCITONIC INSULATORS, ELECTRON–HOLE LIQUIDS AND METAL–INSULATOR TRANSITIONS

T. Maurice Rice

in Problems of Condensed Matter Physics: Quantum coherence phenomena in electron-hole and coupled matter-light systems

Published in print:
2007
Published Online:
May 2008
ISBN:
9780199238873
eISBN:
9780191716652
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238873.003.0015
Subject:
Physics, Condensed Matter Physics / Materials

This chapter describes metal-insulator transitions in disorder-free crystals. It reviews excitonic insulators, electron-hole liquids, and metal-insulator transitions due to band crossing. The ... More


Cuprate superconductivity

A.J. Leggett

in Quantum Liquids: Bose condensation and Cooper pairing in condensed-matter systems

Published in print:
2006
Published Online:
January 2008
ISBN:
9780198526438
eISBN:
9780191711954
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526438.003.0007
Subject:
Physics, Condensed Matter Physics / Materials

Starting with an account of the chemical composition, crystalline structure, and phase diagram of the high-temperature (cuprate) superconductors, this chapter reviews the principal experimental ... More


Ultracold spinor atomic gases

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0007
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter focuses on ultracold gases of atoms that possess internal spin structure. First, it considers spinor interactions, and then turns to trapped spinor Bose–Einstein condensates. In ... More


Ultracold atoms in optical lattices

Immanuel Bloch

in Many-Body Physics with Ultracold Gases: Lecture Notes of the Les Houches Summer School: Volume 94, July 2010

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199661886
eISBN:
9780191748356
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199661886.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter provides an introduction to the field of strong correlation physics with ultracold atoms in optical lattices. After a basic introduction to the single-particle band structure and lattice ... More


Electronic Systems

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ... More


Ultracold dipolar gases

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter examines ultracold dipolar gases. First, it discusses the general properties of dipole–dipole interaction and explains how ultracold dipolar systems can be realized in experiments. The ... More


Optical lattices and quantum simulation

Massimo Inguscio and Leonardo Fallani

in Atomic Physics: Precise Measurements and Ultracold Matter

Published in print:
2013
Published Online:
December 2013
ISBN:
9780198525844
eISBN:
9780191780059
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198525844.003.0007
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter extends the investigation of ultracold atoms in optical lattices to the emerging field of ‘quantum simulation’, in which atoms are used to experimentally realize basic condensed-matter ... More


Practical Quantum Mechanics: Modern Tools and Applications

Efstratios Manousakis

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent ... More


Related Theories

Tuck C. Choy

in Effective Medium Theory: Principles and Applications

Published in print:
2015
Published Online:
January 2016
ISBN:
9780198705093
eISBN:
9780191774171
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198705093.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

In this chapter the analogies between EMT with CPA, ATA and RPA are established. Analogies are made with the mean field concept in statistical mechanics and its more subtle variations in areas like ... More


Many-Body Physics with Ultracold Gases: Lecture Notes of the Les Houches Summer School: Volume 94, July 2010

Christophe Salomon, Georgy V. Shlyapnikov, and Leticia F. Cugliandolo (eds)

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199661886
eISBN:
9780191748356
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199661886.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book gathers the lecture notes of courses given at the 2010 summer school in theoretical physics in Les Houches, France, Session XCIV. This book illustrates how the field of quantum gases has ... More


Atomic Bose fluids in optical lattices

Nathan Gemelke and Cheng Chin

in Novel Superfluids: Volume 2

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198719267
eISBN:
9780191788529
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198719267.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

The physics of bosonic atoms in optical lattices is described. Starting from the basic experimental tools available to create such systems, the chapter introduces a simple model (known as the ... More


Making second quantization work

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers how to build single-particle operators out of creation and annihilation operators, and this already gives enough information to discuss the tight-binding model of solid state ... More


Ultracold gases in optical lattices: basic concepts

Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger

in Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199573127
eISBN:
9780191775048
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573127.003.0003
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter describes basic methods to realise optical potentials and optical lattices, listing in detail what can be controlled in ultracold atomic systems. It revisits the properties of ... More


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