Phse Diagram of Two Color QCD with Staggered Fermions

1
Phse 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

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Outline

• 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

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Motivation

• 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

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Strong Coupling Two Color Lattice QCDDagotto,
Karsch, Moreo Wolff (1987), Klatke Mutter
(1990)

• Action (infinite gauge coupling)
• Partition function
• Parameters of the theory

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Dimer-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.

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Symmetries of 2CLQCDHands, Kogut, Lombardo
Morrisson (1999)

• Define
• Action can be rewritten as
• Symmetries at m 0

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Symmetries in Dimer-Baryonloop language
Every baryonloop can be flipped into a dimer loop
Two current conservations visible in the
configurations
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Symmetry 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
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Predictions 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
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Results 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?
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A 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
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Finite T results m 0, T2.918 (4xLxLxL lattice)
Need 3d chiral perturbation theory
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First Order Phase Transition at m 0
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Weakness of the transition
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Physics 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.

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Second 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.

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Second order phase transition at m0.3
Consistent with two universality classes
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Universality

• 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)
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Zero 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)
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Results at zero temperature
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Conjectured Phase Diagram
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Conclusions

• 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!