Welcome to the SRG home page!
This website is maintained by Dick Furnstahl (furnstahl.1@osu.edu)
and his collaborators (including Eric Anderson, Scott Bogner,
Eric Jurgenson, Robert Perry, Lucas Platter,
Achim Schwenk, and Kyle Wendt).
It will be updated at irregular intervals with new pictures, movies,
and links.
You are invited to send email with suggestions for new content or
questions on what you see.
The research results presented here were supported in part by the
National Science Foundation under Grant Nos. PHY0354916 and
PHY0653312 and by the UNEDF
SciDAC Collaboration under DOE
grant DEFC0207ER41457.
Recent changes to this page:
Contents
Background:
The similarity renormalization group (SRG) for lowenergy
nuclear physics is based on unitary
transformations that suppress offdiagonal matrix elements, forcing the
hamiltonian towards a banddiagonal form.
A simple SRG transformation
applied to nucleonnucleon interactions leads to
greatly improved convergence properties while preserving observables,
and provides a method to consistently evolve manybody potentials
and other operators.
General references on the SRG and related
Hamiltonian Flow Equations

The
Flow Equation Approach to ManyParticle Systems,
Stefan Kehrein (Springer, Berlin, 2006).

Renormalization
of Hamiltonians, S.D. Glazek and K.G. Wilson,
Phys. Rev. D 48, 5863 (1993).

Flow Equations for Hamiltonians, F. Wegner,
Annalen der Physik (Leipzig) 3, 77 (1994).

Flow Equations for Hamiltonians, F. Wegner,
Physics Reports 348, 77 (2001).

Perturbative
renormalization group for Hamiltonians,
S.D. Glazek and K.G. Wilson, Phys. Rev. D 49, 4214 (1994).

Asymptotic
freedom and bound states in Hamiltonian dynamics,
S.D. Glazek and K.G. Wilson, Phys. Rev. D 57, 3558 (1998),
[hepth/9707028].

Limit
cycles in quantum theories,
S.D. Glazek and K.G. Wilson,
Phys. Rev. Lett. 89, 230401 (2002),
[hepth/0203088].

Flow Equations
and Normal Ordering, E. Koerding and F. Wegner,
condmat/0509801.

Flow Equations and Normal Ordering. A Survey, F. Wegner,
condmat/0511660.

Limit cycles
of effective theories,
S.D. Glazek, Phys. Rev. D 75, 025005 (2007),
[hepth/0611015].

From lowmomentum interactions to nuclear structure, S.K. Bogner, R.J. Furnstahl, and A. Schwenk,
to be published in Progress in Particle and Nuclear Physics.
This is an overview of lowmomentum interactions for nuclear physics,
including the SRG results.

Similarity renormalization group
for nucleonnucleon
interactions, S.K. Bogner, R.J. Furnstahl,
and R.J. Perry, Phys. Rev. C 75, 061001(R) (2007),
[nuclth/0611045].
This is probably the best place to start for learning about
how the SRG can be applied to lowenergy nuclear physics.

Are lowenergy nuclear
observables sensitive to highenergy phase shifts?,
S.K. Bogner, R.J. Furnstahl, R.J. Perry, and A. Schwenk,
Phys. Lett. B 649, 488 (2007),
[nuclth/0701013].
This paper shows how the SRG decouples lowenergy from highenergy
physics.

The Unitary Correlation Operator Method from
a similarity renormalization group perspective,
H. Hergert and R. Roth,
Phys. Rev. C. 75, 051001(R) (2007),
[nuclth/0703006].
The UCOM method of unitary transformations is related to the SRG.

Threebody forces produced by a similarity renormalization group
transformation in a simple model, S.K. Bogner, R.J. Furnstahl,
and R.J. Perry, Ann. Phys. (NY) 323, 1478 (2008),
[arXiv:0708.1602].
This is a pedagogical paper that shows in detail using a very simple model
(only 2x2 matrices!) how the SRG works for two and threebody interactions.
A diagrammatic approach to the SRG equations is introduced and applied.

Convergence in the nocore shell model with
lowmomentum twonucleon interactions,
S.K. Bogner, R.J. Furnstahl, P. Maris, R.J. Perry, A. Schwenk,
and J.P. Vary, Nucl. Phys. A801, 21 (2008)
[arXiv:0708.3754].
Application of the SRG with only NN interactions (no threebody)
to fewbody systems up to Li7 to show the improved convergence
with SRG running.

Decoupling in the similarity renormalization
group for nucleonnucleon forces,
E.D. Jurgenson, S.K. Bogner, R.J. Furnstahl, and R.J. Perry,
Phys. Rev. C 78, 014003 (2008)
[arXiv:0711.4252].
This paper explores in detail how decoupling plays out in the SRG.

Block diagonalization using srg flow
equations,
E. Anderson,
S.K. Bogner, R.J. Furnstahl, E.D. Jurgenson, R.J. Perry, and A. Schwenk,
Phys. Rev. C 77, 037001 (2008)
[arXiv:0801.1098].
This paper shows how one can choose different generators for the SRG
to get different patterns of decoupling in a Hamiltonian. In
particular, block diagonalization.

The impact of bound states on similarity renormalization group
transformations, S.D. Glazek and R.J. Perry,
Phys. Rev. D 78, 045011 (2008)
[arXiv:0803.2911].
This paper examines the convergence properties of SRG transformations
with Wegner's transformation and a simpler transformation used in
most of the nuclear physics applications to date.

Similarity Renormalization
Group Evolution of ManyBody Forces in a OneDimensional Model,
E.D. Jurgenson and R.J. Furnstahl
[arXiv:0809.4199].
Manybody forces are evolved in a translationally invariant harmonic
oscillator basis using a onedimensional model as a test case.

Nuclear matter from chiral lowmomentum interactions,
S.K. Bogner, R.J. Furnstahl, A. Nogga, and A. Schwenk.
Nuclear matter calculation based on lowmomentum interactions,
including SRG interactions.

Evolution of Nuclear ManyBody Forces with the Similarity Renormalization Group,
E.D. Jurgenson, P. Navratil, R.J. Furnstahl,
Phys. Rev. Lett. 103, 082501 (2009)
[arXiv:0905.1873].
Evolution of 3N forces in a harmonic oscillator basis.

Applications of the Similarity Renormalization Group to the Nuclear Interaction, E.D. Jurgenson.
This is Eric Jurgenson's thesis. Lots of good info here!
Return to Contents

The Similarity
Renormalization Group (SRG),
talk by Robert Perry at the INT workshop on New applications of the
renormalization group
method in nuclear, particle and condensed matter physics,
February, 2010.

Similarity RG and ManyBody
Operators,
talk by Dick Furnstahl at the INT workshop on New applications of the
renormalization group
method in nuclear, particle and condensed matter physics,
February, 2010. Many extra slides.

Factorization
of Operators Evolved with the Similarity Renormalization
Group, 10minute talk by Eric Anderson at the APS
Spring meeting, February, 2010.

The Similarity Renormalization
Group with Spurious Deep Bound States,
10minute talk by Kyle Wendt at the APS
Spring meeting, February, 2010.

Operator Evolution
Using SRG Flow Equations for FewBody Systems, 10minute talk by Eric Anderson at the APS
Division of Nuclear Physics meeting, October, 2009.

Similarity
Renormalization Group Evolution of ManyBody Forces
in a OneDimensional Model,
10minute talk by Eric Jurgenson at the APS
Division of Nuclear Physics meeting, October, 2008.

Calculation of
Observables Using the SRG Flow Equations, 10minute talk by Eric Anderson at the APS
Division of Nuclear Physics meeting, October, 2008.

Nuclear Forces / DFT for Nuclei
[I]
[II]
[III]
[IV]
[V],
Lectures by Dick Furnstahl at the TRIUMF Summer Institute, August,
2008.

Simlarity
Renormalization Group Methods for Nuclear Physics,
talk by Scott Bogner at AbInitio Nuclear Structure  Where do we stand?
Bad Honnef, Germany, July, 2008.

Atomic Nuclei at
Low Resolution, talk by Dick Furnstahl at the INT Program
on Atomic, Chemical, and Nuclear Developments in Coupled Cluster Methods,
June, 2008.

Simlarity
Renormalization Group Methods for Nuclear Physics,
talk by Scott Bogner at From Quarks to the Nuclear ManyBody
Problem, Oslo, Norway, May, 2008.

Decoupling
with the SRG, talk by Eric Jurgenson at the
Hayes Graduate Research Forum, April, 2008.

Atomic Nuclei at Low
Resolution, colloquium by Dick Furnstahl at the University
of Tennessee, January, 2008.

Decoupling with the Similarity
Renormalization Group (SRG),
10minute talk by Eric Jurgenson at the APS
Division of Nuclear Physics meeting, October, 2007.


Operator Evolution Via the Similarity
Renormalization Group, 10minute talk by Eric Anderson at the APS
Division of Nuclear Physics meeting, October, 2007.


Similiary Renormalization Group
For FewBody Systems, talk by Dick Furnstahl at the EFB20, Pisa, Italy,
September, 2007.

LowMomentum Interactions for Few
and ManyBody Systems,
talk by Scott Bogner at the EFB20, Pisa, Italy,
September, 2007.

The Similarity Renormalization
Group  In Pictures, talk by Eric Anderson at the National
Nuclear Physics Summer School, Tallahassee, FL, July, 2007.

Decoupling with the SRG,
talk by Eric Jurgenson at the National Nuclear Physics summer School,
Tallahassee, FL, July, 2007.

Three Nucleon Forces and the
Similarity Renormalization Group,
talk by Robert Perry at TRIUMF ThreeBody workshop, Vancouver, BC,
March, 2007.
Return to Contents
Return to Contents
The Similarity Renormalization Group (SRG) and V_{low k}
potentials evolve as a parameter is lowered. For the SRG, it
is lambda, which is a measure of the spread of the momentumspace
potential about the diagonal. For V_{low k}, it is the
momentum cutoff Lambda.
There is a rough correspondence between the potentials at numerically
similar values of lambda and Lambda.
The units of the potentials are fm (hbar^{2}/M = 1).
The movies here depict the evolution of the potentials (and related
quantities) with lambda and Lambda.
SRG Evolved V_{srg}
 V_{srg} evolved from the
Argonne V18 potential
 V_{srg} evolved from the N3LO Entem/Machleidt potential
with 500 MeV
and 600 MeV cutoffs
 V_{srg} evolved from the N3LO Epelbaum et al. potential
with 600/550 MeV cutoff
 V_{srg} evolved from the N3LOW Entem/Machleidt potential
with 400 MeV cutoff
SRG Evolved Operators (other than the hamiltonian)
Cutoff Evolved V_{low k}
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Included here are both color contour plots and ordinary figures.
SRG Evolved V_{srg}
Deuteron Properties for V_{srg} and V_{low k}
Shown are the binding energy and asymptotic D/S ratio, which are observables,
and the Dstate probability, which is not, as a function of
lambda or Lambda.
Return to Contents
 Stan Glazek
is a leading expert on the SRG (and one of its inventors).
Here we link to some videos created by Stan and his students.
 Flow
Equations for Hamiltonians page from the University of
Heidelberg. Many references are available here.
Return to Contents
Your comments and
suggestions are appreciated.
[OSU Physics]
[Math and Physical Sciences]
[Ohio State University]
SRG for Nuclear Physics.
Last modified: .
furnstahl.1@osu.edu