HUBBARD CHAIN EXTENDED TO INCORPORATE THE PEIERLS INSTABILITY

1992 ◽  
Vol 06 (11) ◽  
pp. 637-647
Author(s):  
ADRIAAN M. J. SCHAKEL
Keyword(s):  
Sigma Model ◽  
Qualitative Difference ◽  
Fundamental Property ◽  
Nonlinear Sigma Model ◽  
One Dimensional ◽  
Long Wavelength ◽  
Peierls Instability ◽  
Two Phases ◽  
The Continuum ◽  
Topological Term

The Hubbard chain is extended so as to incorporate the Peierls instability which is a fundamental property of one-dimensional metals. The resulting theory is analysed in the continuum. In the limit of low-energy and long-wavelength it is described by the O(3) nonlinear sigma model. It is argued that the theory has two phases. In one phase the excitation spectrum is gapless, while in the other phase it has a gap. This qualitative difference between the two states is shown to arise from the fact that in the massless phase the O(3) model acquires a topological term. Besides changing the spectrum of the theory, this term is shown to also change statistics.

EFFECTIVE ACTION AND ADIABATIC EXPANSIONS FOR THE 1-D AND 2-D HUBBARD MODELS AT HALF-FILLING

1994 ◽  
Vol 08 (10) ◽  
pp. 1391-1416 ◽  
Author(s):  
M. DI STASIO ◽  
E. ERCOLESSI ◽  
G. MORANDI ◽  
R. RIGHI ◽  
A. TAGLIACOZZO ◽  
...  
Keyword(s):  
Effective Action ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Adiabatic Expansion ◽  
Hubbard Models ◽  
Half Filling ◽  
Fermionic Representation ◽  
Two Space Dimensions ◽  
The Continuum ◽  
Expansion Scheme

We analyze here the occurrence of antiferromagnetic (AFM) correlations in the half-filled Hubbard model in one and two space dimensions using a natural fermionic representation of the model and a newly proposed way of implementing the half-filling constraint. We find that our way of implementing the constraint is capable of enforcing it exactly already at the lowest levels of approximation. We discuss how to develop a systematic adiabatic expansion for the model and how Berry’s phase contributions arise quite naturally from the adiabatic expansion. At low temperatures and in the continuum limit the model gets mapped onto an O(3) nonlinear sigma model (NLσ). A topological, Wess-Zumino term is present in the effective action of the 1D NLσ as expected, while no topological terms are present in 2D. Some specific difficulties that arise in connection with the implementation of an adiabatic expansion scheme within a thermodynamic context are also discussed, and we hint at possible solutions.

scholarly journals METAPLECTIC SPINOR FIELDS AND GLOBAL ANOMALIES

1995 ◽  
Vol 10 (01) ◽  
pp. 65-88 ◽  
Author(s):  
M. REUTER
Keyword(s):  
Phase Space ◽  
Sigma Model ◽  
Target Space ◽  
Spin Manifold ◽  
Nonlinear Sigma Model ◽  
Metaplectic Representation ◽  
One Dimensional ◽  
Path Integral Representation ◽  
Infinite Dimensional ◽  
Spinor Fields

We investigate spinor fields on phase spaces. Under local frame rotations they transform according to the (infinite-dimensional, unitary) metaplectic representation of Sp(2N), which plays a role analogous to the Lorentz group. We introduce a one-dimensional nonlinear sigma model whose target space is the phase space under consideration. The global anomalies of this model are analyzed, and it is shown that its fermionic partition function is anomalous exactly if the underlying phase space is not a spin manifold, i.e. if metaplectic spinor fields cannot be introduced consistently. The sigma model is constructed by giving a path integral representation to the Lie transport of spinors along the Hamiltonian flow.

scholarly journals Phases of the ( 2+1 ) Dimensional SO(5) Nonlinear Sigma Model with Topological Term

2021 ◽  
Vol 126 (4) ◽  
Author(s):  
Zhenjiu Wang ◽  
Michael P. Zaletel ◽  
Roger S. K. Mong ◽  
Fakher F. Assaad
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Topological Term

scholarly journals THE EFFECTIVE LAGRANGIAN OF THREE DIMENSIONAL QUANTUM CHROMODYNAMICS

1992 ◽  
Vol 07 (32) ◽  
pp. 7989-8000 ◽  
Author(s):  
G. FERRETTI ◽  
S.G. RAJEEV ◽  
Z. YANG
Keyword(s):  
Quantum Chromodynamics ◽  
Sigma Model ◽  
Three Dimensional ◽  
Low Energy ◽  
Nonlinear Sigma Model ◽  
Flavor Symmetry ◽  
Energy Limit ◽  
Long Wavelength ◽  
Effective Lagrangian ◽  
Chern Simons

We consider the low energy limit of three dimensional quantum chromodynamics (QCD) with an even number of flavors. We show that parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective Lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern-Simons terms are necessary in the Lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess-Zumino-Witten-Novikov model. Since three dimensional QCD is believed to be a model for quantum antiferromagnetism, our effective Lagrangian can describe their long wavelength excitations (spin waves).

ANOMALOUS TOPOLOGICAL CURRENT IN THE NONLINEAR SIGMA MODEL

1991 ◽  
Vol 06 (08) ◽  
pp. 1267-1286 ◽  
Author(s):  
KERSON HUANG ◽  
YUJI KOIKE ◽  
JANOS POLONYI
Keyword(s):  
Bound States ◽  
Sigma Model ◽  
World Line ◽  
Coarse Graining ◽  
Nonlinear Sigma Model ◽  
Current Conservation ◽  
Coupling Phase ◽  
Lattice Regularization ◽  
Topological Current ◽  
The Continuum

It is proposed that a classically conserved current may not be conserved in quantum theory due to singular configurations in the path integral. This is illustrated in the (2+1)-dimensional O(3) nonlinear sigma model with lattice regularization. The current here is that of the topological charge density of “Skyrmions”. On the lattice the current is always “anomalous”, due to the existence of Dirac monopoles. The reason is that the world line of a Skyrmion can be regarded as a Dirac string (in a particular gauge), which is terminated by a monopole. Monte-Carlo simulations indicate that, in the continuum limit, current conservation obtains in a weak-coupling phase, in which monopole and anti-monopoles form bound states that disappear upon coarse-graining; but the anomaly persists in a strong-coupling phase, in which the above-mentioned bound states dissociate into a plasma. In the plasma phase rotational invariance will be broken in the presence of a “Hopf term” in the action.

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