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.

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 OF SIGMA MODEL ANOMALIES WITH EXTERNAL GAUGE FIELDS

1986 ◽  
Vol 01 (01) ◽  
pp. 23-27 ◽  
Author(s):  
YIE-LIANG WU ◽  
YAN-BO XIE ◽  
GUANG-ZHAO ZHOU
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Effective Action ◽  
Sigma Model ◽  
Original Model ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Consistency Conditions ◽  
Goldstone Bosons ◽  
External Gauge

The nonlinear sigma model describes Goldstone bosons originating from spontaneous symmetry breaking. A set of local counterterms is found to shift the anomaly of the nonlinear sigma model to that of the original model with fermions interacting with external gauge fields. The ‘t Hooft consistency conditions are matched automatically.

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.

scholarly journals One-loop effective action and the Riemann zeros

2014 ◽  
Vol 29 (31) ◽  
pp. 1450182 ◽  
Author(s):  
J. G. Dueñas ◽  
N. F. Svaiter ◽  
G. Menezes
Keyword(s):  
Asymptotic Behavior ◽  
Effective Action ◽  
Sigma Model ◽  
Dimensional Space ◽  
Nonlinear Sigma Model ◽  
Nontrivial Zeros ◽  
The Riemann Zeta Function ◽  
Point Correlation ◽  
Riemann Zeta ◽  
The Fourier Transform

We present a remarkable connection between the asymptotic behavior of the Riemann zeros and one-loop effective action in Euclidean scalar field theory. We show that in a two-dimensional space, the asymptotic behavior of the Fourier transform of two-point correlation functions fits the asymptotic distribution of the nontrivial zeros of the Riemann zeta function. We work out an explicit example, namely the nonlinear sigma model in the leading order in 1/N expansion.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe

scholarly journals Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Yutaka Akagi ◽  
Yuki Amari ◽  
Nobuyuki Sawado ◽  
Yakov Shnir
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Type Interaction
Sign in / Sign up

Export Citation Format

Share Document