1. Introduction

Understanding complexity and strong correlations are two central questions in modern theoretical physics. Without exaggeration one may say that at present there is not a single challenging problem in physics that would not, at least in part, belong to one of these two areas of research.

The idea behind the Theory Institute for Strongly Correlated and Complex Systems (TISCCS) was to use a pool of external expertise to strengthen the already impressive scientific standing of BNL. The TISCCS became operational in September 2002.  It has already hosted a number of visits by world famous physicists including Profs. ), I. Affleck (Boston University), B. L. Altshuler (Princeton), A. M. Finkelstein (Weizmann Institute), L. Glazman (U. of Minnesota), T. M. Rice (ETH Zurich), B. Roehner (U. of Paris), K. Sneppen (Niels Bohr Institute), and Y.-C. Zhang (Fribourg).  These visitors have contributed significantly to the intellectual climate at BNL and have been extremely productive in collaborative research projects.  After a year of existence, collaborations initiated by of existence, collaborations initiated by the Institute have resulted in 14 papers being published or submitted. There are 6 more projects prepared for publication.  A complete list of these publications is presented at the end of this paper.

Apart from hosting extended visits of individual scientists, the Institute organized a 4-day Workshop on "Field Theory Methods in Correlated Nanoscale Systems" with more than 50 participants. The workshop attracted speakers of international reputation such as e.g. Profs. L. Levitov  and X.-G. Wen (MIT), F.D.M. Haldane and S. Sondhi (Princeton), P. Coleman and N. Andrei (Rutgers) and S. Sachdev (Yale). BNL is keen to continue the operation of the Institute and indeed to expand its role.  Apart from the continuation of visits from distinguished scientists it is also envisioned that the workshop will become an annual event, taking on the characteristics of the extended workshops held at Theory Institute in Santa Barbara. Thus we hope to initiate an annual summer visitor program that will extend over a period of two months and culminates in a workshop.  The topics covered by the workshop would change each year.  A detailed proposal for FY 2004 is given at the end of this paper.

2. Current progress:

The existing strengths of the BNL Condensed Matter Theory group in Strongly Correlated Physics and Complex Systems have recently been complimented through the addition of Wei Ku, an electronic structure theorist.  These in-house capabilities combined with the presence of visitors to the Institute has resulted in a large number of collaborations and publications.  In the following we discuss these publications and research successes.  The following papers represent a coherent effort in the areas of Strongly Correlated (Tsvelik and Essler) and Complex (Maslov) Systems.

2.1 Strongly Correlated Systems (including Magnetism):

The publications in the area of Strongly Correlated Systems can be roughly divided into two groups: papers [1],[4],[5],[12] and [16] investigate interaction effects in nano-systems such as (arrays of) quantum dots, quantum wires and long molecules.  Papers [2],[13] and [15] are concerned with quantum magnets and Mott insulators.  The position of the Institute in these research areas is unique due the background and expertise of its founders and the outstanding quality of the visitors.  The Coqblin-Schrieffer model [1] describes the Coulomb blockade regime in realistic multi-channel quantum dots with a broken rotational symmetry.  Paper [1] contains analytical results for the thermodynamics of such dots.  Quasi-1D Quantum magnets constitute many of the best realizations of quantum critical systems.  A new paradigm for the evolution between two different quantum critical phases has recently been discovered by neutron scattering experiments on the chain compound Cs2CoCl4.  Paper [2] develops a theoretical description of the observed behavior.  Ferromagnetic droplets [5] appear in disordered mesoscopic systems close to a ferromagnetic instability (like manganites) and research in this direction is technologically important.  We present an exact solution for a model of a droplet imbedded in a metallic paramagnetic host.  Paper [4] provides theoretical foundations for experiments conducted on arrays of superconducting islands.  Paper [12] contains detailed many-body calculations for the collective excitation spectrum of the armchair carbon nanotube at half filling.  We predict that when the graphite band in such a nanotube is exactly half filled it becomes a Mott insulator with a rather complicated spectrum of collective modes.  Carbon nanotubes are now intensely studied (in BNL by the group of J. Misewich) and recent progress in the synthesis of long, straight tubes should eventually result in the experimental observation of the predicted phenomena.  Paper [13] investigates whether particles with fractional quantum numbers exist in more than one spatial dimension. Excitations with fractional statistics constitute one of the most exciting and unusual features of one-dimensional systems.  For example, it is well established that the electron “falls apart” into at least two pieces, one of which carries spin but no charge and one carrying charge but no spin.  The former are called spinons and the latter holons.  An important question is whether such particles can exist in two or three-dimensional systems.  With the exception of Fractional Quantum Hall systems the answer is thought to be negative.  However, new theoretical models indicate that there are certain configurations of magnetic structure in two dimensions that would allow for the existence of such particles.  Furthermore, recent work has extended this possibility to three and higher dimensions.  These new developments could have an important impact on our understanding of high-Tc superconductivity, where the possible existence of spinons has long been a topic of debate.  Paper [15] is a collaborative effort between the X-ray scattering group at BNL, the theory group and a visitor (H. Benthien). A theoretical understanding of resonant inelastic x-ray scattering experiments on the chain cuprate Sr2CuO3 is developed.  Paper [16] is concerned with determining dynamical properties of Peierls-Hubbard chains.  This is an important step towards developing a theoretical understanding of polymers such as polydiacetylene.

2.2 Complex Systems:

Publications in the area of Complex Systems concentrate on the following topics:  Papers [3,6-9] study the statistical properties of complex networks.  In Ref. [3] methods borrowed from statistical physics (diffusion, transfer matrix formalism, etc.), and condensed matter physics (the theory of localization) are applied to detect modularity and extreme edges in the network of the Internet.  Paper [6] extends the network randomization algorithm used in our earlier publications by introducing a Metropolis-like energy function.  This new algorithm allows one to conserve any desired topological property of a complex network in addition to its degree distribution. The new scheme is then applied to measure the correlation profile of the Internet and interpret it in terms of the hierarchy of its nodes. This idea is further extended in the paper [14], where the concept of the shortest hierarchical distance between nodes of a complex network is introduced and studied, both numerically and analytically.  Papers [7,9] deal with the question of evolution of bio-molecular networks. Using the recent system-wide data describing the genetic regulatory network in yeast it was demonstrated that gene duplications play an important role in the evolution of such networks.  It was also found that the genetic regulatory network evolves on a much shorter timescale than that of protein-protein interactions.  Paper [8] explores the question of hierarchical structure in complex networks and introduces a novel algorithm allowing one to generate the hierarchical or anti-hierarchical structure in a network with a given degree distribution.  Finally, papers [10,11] explore strong and universal collective effects taking place in complex multi-agent systems, such as financial markets, which makes them somewhat similar to strongly correlated materials in condensed matter physics.

3. Report on the 2003 Workshop on "Field Theory Methods in Correlated

Nanoscale Systems":

On Aug. 26-30 2003 the Institute hosted the "International Workshop on Field Theory Methods in Correlated Nanoscale Systems". The workshop focussed on applications of field theory methods to low-dimensional and nanoscale systems such as quantum dots, quantum wires and Fractional Quantum Hall systems. The objective was to explore the recent advances in the field in an interactive fashion and to facilitate collaborations. The list of invitees included A. Chubukov, E. Fradkin, T. Giamarchi, F.D.M. Haldane, L. Levitov, A. Millis, S. Sachdev, X.-G. Wen, P. Wiegmann and others. The budget of the workshop was 35K of which 30K were provided by the Institute.

The entire program of the Workshop is attached to this White Paper and is also available online on http://www.cmth.bnl.gov/workshop.  We had 39 talks given by leading researchers from the United States, United Kingdom, Germany, France, Israel, Italy, Switzerland, Canada, and Sweden. Several of the letters written by the participants in appreciation of the workshop are included as an attachment.  By any standard the workshop was an unqualified success. It is clear from many of the talks that correlation effects play an important role in many nanoscale systems and lead to new and unexpected physical behavior. Among the many exciting new developments reported during the workshop are

* Edge and surface states in a variety of low-dimensional systems (Haldane)

* Kondo physics in nonequilibrium nanoscale devices (Coleman)

* Superconductivity in carbon nanotube ropes (de Martino)

* Many-body Effects in Multi-Qubit Arrays (Khveshchenko)

* Electronic liquid crystal phases of strongly correlated systems (Fradkin)

* Transport in quantum wire devices (Chamon, Giamarchi, Matveev, Schoenhammer and Starykh)

* New states of matter in layered geometries (Sachdev and Wen)

4. Proposed future workshops:

     We intend to extend the concept of the workshop in future years.  In the framework of the existing program individual researchers in various fields visit BNL for several weeks at a time.  As an extension of this modus operandi we propose to institute an annual summer program.  This program will take place for a period of four to eight weeks during the summer months. A group of about five scientists specializing in a particular sub-field of strongly correlated or complex systems will visit the TISCCS at the same time and collaborate on research projects of mutual interest. At some time during the program a workshop with about 10-15 invited speakers will be organized.  These summer programs will be loosely modeled on those run by the ITP in Santa Barbara. In the next three years we plan to hold a summer program on the following topics.

"Frustrated Magnetism" with visitors

A. Abanov (Stony Brook),

I. Affleck (UBC)

F.H.L. Essler (Oxford)

R. Moessner (Ecole Normale Paris)

O. Starykh (Hofstra)

The program will take place in August –September 2004. A workshop will be held in the first week of September, possibly at the Montauk Yacht Club. Each visitor will spend about one month at the Institute.  We expect this program to be highly beneficial for BNL attracting attention and interest of local researchers such as Drs. Wei Ku (the new member of CMT group and himself a member of the Institute), I. Zaliznyak, J.Tranquada, S. Shapiro, J. Misewich, I. Bozovic, C. Homes, J. Hill and others.

Possible topics for the subsequent years are

"Strongly Correlated Nanosystems" with visitors

I. Affleck (UBC)

R. Egger (Duesseldorf)

A. Gogolin (Imperial College London)

K. Matveev (Duke)

A. Nersesyan (Trieste)

"Complex Networks" with visitors

S. Bornholdt (Bremen)

K. Eriksen (Lund)

K. Sneppen (Niels Bohr Institute)

C. Tang (NEC, Princeton)

Y.-C. Zhang (Fribourg)

Publications:

1.         V. V. Bazhanov, S. L. Lukyanov and A. M. Tsvelik, “Analytical Results for Coqblin-Schrieffer model in a generalized magnetic field”, to appear in Phys. Rev. B, cond-mat/0305237.

2.         J.-S. Caux, F.H.L. Essler and U. Low, “Dynamical Structure Factor of the Anisotropic Heisenberg Chain in a Transverse Field”, to appear in Phys. Rev. B, cond-mat/0303587.

3.         K. A. Eriksen, I. Simonsen, S. Maslov and K. Sneppen, “Modularity and Extreme Edges of the Internet”, Phys. Rev. Lett., 90, 148701 (2003), cond-mat/0212001.

4.         V. Gurarie and A. M. Tsvelik, “Superconductor-Insulator Transition in a One-Dimensional Josephson array”, submitted to Phys. Rev. B, cond-mat/0305245.

5.         S. L. Lukyanov and A. M. Tsvelik, “The exact solution of a model of Ferromagnetic Droplet”, in preparation.

6.         S. Maslov,  K. Sneppen and A. Zaliznyak, “Detection of Topological Patterns in Complex Networks: Correlation Profile of the Internet”, accepted for publication in PhysicaA, cond-mat/0205379.

7.         S. Maslov,  K. Sneppen and K. Eriksen, “Upstream Plasticity and Downstream Robustness in Evolution of Molecular Networks”,  submitted to Trends in Genetics.

8.         A. Trusina, S. Maslov, P. Minnhagen, and K. Sneppen, “Hierarchy and Anti-Hierarchy in Real and Model Networks”, submitted to Phys. Rev. Lett., cond-mat/0308339 (2003).

9.         S. Maslov and K. Sneppen, "Topological and Evolutionary Patterns in Protein Networks”,  an invited book chapter in “Power Laws, Scale-free Networks and Genome Biology”, edited by E. Koonin, Y. Wolf and G. Karev, to be published by Landes Biosciences, (2003).

10.       S. Maslov, B. Roehner, “The conundrum of stock vs. bond prices”, in preparation.

11.       S. Maslov, B. Roehner, “Does the Price Multiplier Effect also Holds for Stocks?”, accepted for publication in Int. J.of Modern Physics C, (2003).

12.       A. A. Nersesyan and A. M. Tsvelik, “Coulomb blockade regime in a single-wall carbon nanotube”, submitted to Phys. Rev. B, cond-mat/0305311.

13.       F. A. Smirnov and A. M. Tsvelik, “A model of propagating spinons beyond one dimension”, to appear in Phys. Rev. B, cond-mat/0304634.

14.       V. S. Lebedev and A. M. Tsvelik, “Theoretical foundations of optical measurements on sub-wavelength scales “, in preparation.

15.       Y. Kim,  J. Hill, H.R.H. Benthien, F.H.L. Essler et al, “Resonant inelastic X-ray scattering study of holon-antiholon continuum in SrCuO2”; cond-mat/0307497.

16.       A. Grage, F.H.L. Essler, F. Gebhard et al, “Dynamical Properties of an extended Hubbard model with Dimerization”, in preparation.

17. M. Pustilnik, L.I. Glazman and W. Hofstetter , "Singlet-triplet transition in a lateral quantum dot", cond-mat/0304688.

18. A. Altland, L.I. Glazman and A. Kamenev , "Electron Transport in Granular Metals", cond-mat/0305246.

19. I. Affleck and F.H.L. Essler, “The spin-1 Heisenberg chain with crystal field anisotropy in a magnetic field”, in preparation.

20. Y-J.Kim, J.P.Hill, H.Benthien, F.H.L.Essler, E.Jeckelmann, H.S.Choi, T.W.Noh, N. Motoyama, K.M.Kojima, S.Uchida, D.Casa and T.Gog , "Resonant inelastic x-ray scattering study of holon-antiholon continuum in SrCuO2", cond-mat/0307497