Title: Phse Diagram of Two Color QCD with Staggered Fermions
1Phse Diagram of Two Color QCD with Staggered
Fermions
- Shailesh Chandrasekharan
- Duke University
- in collaboration with Fu-Jiun Jiang
- hep-lat/0602031
- Supported in part by US DOE
2Outline
- Motivation
- Strong Coupling Two color Lattice QCD (2CLQCD)
- Model
- Dimer-Baryonloop representation
- Symmetries and Breaking Patterns
- m 0 and finite T physics
- non-zero m and finite T physics
- T0 physics
- T-m Phase Diagram
- Conclusions
3Motivation
- Chiral Limit in QCD-like theories is difficult to
study - Algorithms slow down
- Matching of low energy physics with chiral
perturbation theory (CHPT), although widely
accepted, remains untested in many interesting
cases. - T- m phase diagrams in many cases unclear.
- New opportunities at strong coupling (staggered
fermions) - confinement and chiral symmetry breaking natural
- models with all kinds of chiral symmetries can be
constructed - cluster algorithms can be formulated in the
chiral limit - diquark correlation functions easy to measure
- large lattices with relative ease
4Strong Coupling Two Color Lattice QCDDagotto,
Karsch, Moreo Wolff (1987), Klatke Mutter
(1990)
- Action (infinite gauge coupling)
- Partition function
- Parameters of the theory
5Dimer-Baryonloop RepresentationRossi Wolff,
Nucl. Phys. B248, 105 (1984)
- Partition function can be rewritten as a
statistical mechanics of dimer-baryonloop
configurations - A directed-path update algorithm can be
constructed. Adams SC (2003), Jiang SC
hep-lat/0602031. - Many observables, including diquark correlators,
are easy to compute.
6Symmetries of 2CLQCDHands, Kogut, Lombardo
Morrisson (1999)
- Define
- Action can be rewritten as
- Symmetries at m 0
7Symmetries in Dimer-Baryonloop language
Every baryonloop can be flipped into a dimer loop
Two current conservations visible in the
configurations
8Symmetry Breaking Pattern
- The following three components transform as a
complex 3-vector under U(2). - Since at m0 we expect the chiral condensate to
be non-zero, the symmetry breaking pattern should
be - This is called collinear order in condensed
matter physics. - This symmetry and breaking pattern is encountered
in superfluid Helium-3.
or equivalently
9Predictions in the low temperature phase
- One expects three Goldstone bosons
- The chiral Lagrangian (at leading order) is given
by - The decay constants can be obtained from
- Finite size scaling
Kogut, Sinclair and Toublan (2003)
Hasenfratz Leutwyler, NPB 343 (1990) 241
10Results T1.0, m0, LxLxLxL lattice
The decay constants are almost the same
(different within errors)! Is this an accident ?
or can we understand it from some symmetry?
11A consistency check
- Condensate
- We can measure
- Finite size scaling gives
- A one parameter fit using L8,12,16,24 data gives
H L, NPB 343 (1990) 241
12Finite T results m 0, T2.918 (4xLxLxL lattice)
Need 3d chiral perturbation theory
13First Order Phase Transition at m 0
14Weakness of the transition
15Physics at non-zero m
- The symmetry of the action and breaking pattern
is - There are two Goldstone bosons governed by the
chiral Lagrangian - The finite size scaling in 3d is given by
- Close to the phase transition the two decay
constants are now indistinguishable.
16Second Order Phase Transition at m 0.3
- Diquark susceptibility
- Finite size scaling from chiral perturbation
theory. - Diquark susceptibilty is a monotonic function of
L across the phase transition and fits well to a
power close to Tc.
17Second order phase transition at m0.3
Consistent with two universality classes
18Universality
- Linear sigma model can be used to discuss the
transition - Sign of v determines the ordering
- v lt 0 leads to collinear order.
- For complex 2-vectors
- a stable decoupled XY fixed point exists
- For complex 3-vectors
- e-exapansion predicts a fluctuation driven first
order transition. - Recent resummation techniques suggest a second
order transition.
Kawamura (1988)
Prato, Pelisetto and Vicari (2004)
19Zero Temperature (T1.0, LxLxLxL lattice)
- As m increases a transition occurs due to
saturation of baryons on the lattice - If second order it should be described by a
non-relativistic field theory - mean field universality class
- Mean field theory prediction
- For m gt mc, one expects excitations are gapped
holes with a non-relativistic dispersion
relation. - gap vanishes at mc.
- perhaps of interest in condensed matter
Nishida, Fukushima and Hatsuda (2004)
20Results at zero temperature
21Conjectured Phase Diagram
22Conclusions
- Strong coupling QCD provides a unique opportunity
to explore the chiral limit of QCD-like theories
from first principles - Two color QCD can be solved very accurately!
- Puzzle 1 why are the two decay constants almost
same? - Puzzle 2 pion masses appear inconsistent with
CHPT? - Easy to build models
- make baryons heavy in 2CLQCD ? richer phase
diagram! - include more number of flavors ? richer symmetry
structure - first principles understanding of possible phase
diagrams. - A new approach to bosonic field theories on the
lattice - with discrete variables!