Critical behavior of lattice models in atomic and molecular, condensed matter and particle

Date :From 2012-07-24 To 2012-08-31
Advisory committee :
Local coordinators :Chuan Liu (Beijing University), Gang Su (Graduate University of CAS),Zhengyu Weng (IAS Tsinghua U.), Tao Xiang(ITP,CAS) and Yue Yu (ITP, CAS).
International coordinators :Lu-Ming Duan (U. Michigan), Yannick Meurice (U. Iowa), Shan-Wen Tsai (U. C. Riverside), Zhen-Han Wang (Microsoft Q) and Xiao-Gang Wen (M. I. T.).

The goal of the program is to bring together lattice practitioners working in atomic, molecular, condensed matter and high energy physics. In condensed matter, lattices appear naturally as physical entities in various types of solids. In high energy physics the lattice is used as a regulator and lattice gauge theory provides the best known nonperturbative formulation of strongly interacting particles models such as quantum chromodynamics (QCD) or extensions beyond the standard model. In atomic and molecular physics, the possibility of physically building lattice models with tunable interactions by trapping cold atoms or molecules in opticallattices is a very exciting new development. This brings the fascinating possibility that problems that are plagued by severe sign problems such as the Hubbard model, QCD at finite temperature and density or real time evolution in various models, could find a satisfactory treatment by building suitable optical lattices.

In recent years, there has been considerable interest in quantum systems which show novel behavior of the whole system emerging from the collective behavior and interaction of the constituent local degrees of freedom. In condensed matter the novel phenomena include fractional quantum number, fractional statistics, topologically protected gapless bulk/edge excitations and topologically protected zero modes. New type of critical theories are not expressed in terms of the order parameters (as in Landau-Ginzburg-Wilson theory), but involves fractionalized degrees of freedom and an emergent topological conservation law. The topics of the workshop will include the emergence of gauge fields, fractionalized particles, topological order, topological insulators, and quantum spin liquids.

The questions of chiral symmetry breaking and deconfinement are central themes in lattice gauge theory and condensed matter. Models of graphene have quasi-particles that obey a relativistic massless Dirac equation. In lattice gauge theory, recent simulations provide indications for new infrared fixed points and conformal windows in QCD-like models with more flavors or higher order representations. The continuum physics seems quite different from QCD: absence of confinement and chiral symmetry breaking (“unparticle physics”). In optical lattice, there has been a lot of activity about introducing gauge interactions and the possibility of emerging local symmetries is wide open and will be a general topic of the workshop.

Despite the very different ways the various communities look at their own lattices, the large distance behavior of lattice models has universal features that can be approached with the Renormalization Group (RG) method. This provides a universal language spoken by scientists working in very different areas. It applies equally well for relativistic and non-relativistic systems and has interesting complex extensions. Generating closer interactions among the various areas is a desirable endeavor that has already been pursued at recent workshops ( “New Applications of the Renormalization Group Method in Nuclear, Particle and Condensed Matter Physics” at the Institute for Nuclear Theory in Seattle in February 2010 and “Critical Behavior of Lattice Models in Condensed Matter and Particle Physics” at the Aspen Center for Physics in summer 2010).

The long-range quantum entanglement plays a critical role in generating and understanding some of the novel phenomena discussed above. A recent focus has been put on the link between quantum simulations and quantum information and the extension to far-from-equilibrium dynamics as possible in ultracold atom gases. The density-matrix renormalization group and multiscale entanglement renormalization both emphasize this
aspect in a way that can be directly related to conformal field theory. Entanglement also plays a role in the understanding of the confinement in lattice gauge theory. One of the goal of the workshop will be the study of emergent and entanglement properties as well as new numerical methods they motivated.

This program is co-sponsored by: