Quantum criticality in the pseudogap Bose-Fermi Anderson ...
Knotted field distributions of order parameters in pseudogap phase states
description
Transcript of Knotted field distributions of order parameters in pseudogap phase states
Knotted field distributions of order parameters
in pseudogap phase states
L. Martina
Dipartimento di Fisica, Università del Salento
Sezione INFN - Lecce
• A. Protogenov, V. Verbus , RAS - Nizhny Novgorod, Russia•EINSTEIN – RFBR •cond-mat.str-el/0706.0639 Nonlinear Physics V
2-components Ginzburg – Landau Model
3D
•Two – Higgs doublet model (T.D. Lee, Phys. Rev. D 8 (1973) 1226)
•Spin – Charge decomposition in Yang – Mills (L. Faddeev A. Niemi (2006)•Spin – density waves in cuprate •two charged condensates .•two charged condensates of tightly bounded fermion pairs, • two-band superconductor •(Nb, T , V , Nb-doped SrT iO3, hT MgB2 ) (E. Babaev, L.V. Faddeev, A.J. Niemi,
Phys. Rev. B 65 (2002) 10051)
221, C
Mermin – Ho vorticity
the densities of the Cooper pairs
paramagnetic current
Gauge-invariant vector field
mass
Nonlinear Physics V
the magnetic order (Néel) vector
Group Theoretical Classification
of the Local Minima of V(, n) I.P. Ivanov, cond-mat/0802.2107
b d
Phases
Skyrme – Faddeev
1 component Ginzburg-Landau in E.M.
Inhomogeneous Superconductor
Quasi-1 dim distribution b
dL
24
bGL
2
Nonlinear Physics V
A.F. Vakulenko and L.V. Kapitanskii, Sov. Phys. Dokl. 24, 433 (1979)L. Faddeev, A. Niemi, Nature 387, 1 May (1997) 58..R.S. Ward, Nonlinearity 12 (1999) 241 V. M. H. Ruutu et al, Nature 382 (1996) 334.
Skyrme – Faddeev model
Hopf Invariant
Stability of large-Q configurations
/1min
L. Faddeev, Quantisation of Solitons, preprint IAS-75-QS70, 1975;
Nonlinear Physics V
/2,/1 knotknot RR
Q=1
M.F. Atiyah, N.S. Manton, Phys. Lett. A 222 (1989) 438
nvrin ,exp 22:, SSv
QvWinding ,
0,20
Trial function
r
tghr 12
5.4
min SFS 7.116 2
min
SFS
L. Faddeev, A.J. Niemi, Nature 387 (1997),59 Nonlinear Physics V
y
x
-2 -1 0 1 2
-2
-1
0
1
2
x
z
Q=1
Nonlinear Physics V
-2 -1 0 1 2
-2
-1
0
1
2
n-field
H-field
-2 -1 0 1 2
-2
-1
0
1
2
y
x
-2 -1 0 1 2
-2
-1
0
1
2
x
z
r
hr
Ok4
2
2
2
22 sec
2cos1
8n
,
/
/11
2g
r
rfb d
bb
Inhomogeneous Superconductor Vconst min
V. I. Arnold and B. A. Khesin: Topological methods in hydrodynamics..A. P. Protogenov Physics-Uspekhi 49, 667 (2006).
Hoelder
Ladyzhenskaya
2
4/32 132
Q
LQS h
QL
SFh SS Nonlinear Physics V
216
Quasi 1- dim distribution
0,, ndbBB
Compressible fluid
X.G. Wen, A. Zee, Phys. Rev. B 46 (1992) 2290
Nonlinear Physics V
General Case
Closed quasi 1-dimdistribution
Packing parameter
cnh SSS 0 TOROID STATE
V.M. Dubovik, V.V. Tugushev Phys. Rep. 187, 145 (1990).
Dense packing, anti-chirality Nonlinear Physics V
Toroid Moment
T
Toroid distributions:Near inhomogeneous superconductorQuasi – planar knotsAntiferromagnetic ordering
Topological phase transition : hom. SuperC. Toroid order
mrdxTmdx 33
2
1,0
Nonlinear Physics V
Conclusions
2-component Ginzburg – Landau ModelSpecial class of phasesTopological classificationEstimate of parametersAppearence of nets of toroi solutionsAnalogy with Dimeric system on the Lattice
Open problemsExplicit construction of solutions (approximated)Discretization schemes based on group invarianceFractional – Statistics of toroid distributionRoksar-Kivelson type Hamiltonian