Speakers

Roger Melko (University of Waterloo) : TALK SLIDES

Welcome, and a general introduction to the Density Matrix Renormalization Group in the physical sciences.


Iván González (CESGA, Spain): TALK SLIDES

Pedagogical introduction to the Density Matrix Renormalization Group

Since its formulation by White et al. in 1992, the density matrix renormalization group algorithm has become a standard numerical technique to treat low-dimensional quantum systems, allowing the calculation of properties of both fermionic and bosonic systems with unprecedented precision. In my talk I will provide pedagogical introduction to the technique, first explaining briefly its theoretical basis in connection to quantum entanglement, and later discussing its implementation in a computer code.  The talk will serve as a basis for the subsequent talks on advanced topics as well as for the hands-on tutorial session. 


Dominika Zgid (Cornell University) 

Pedagogical introduction to the application of DMRG methods to quantum chemistry

Many molecules studied by theoretical chemistry methods are in a weakly correlated regime and can be described successfully by perturbative methods. Still, the most challenging ones are systems like transition metal complexes, extended pi-electron systems, or multi-radicals that fall into a "strongly correlated" regime.
Historically these "strongly correlated" systems were studied using exact diagonalization, limiting the systems size to a small number of orbitals. In 1999 the Density Matrix Renormalization Group was introduced to theoretical chemistry audience and the first molecular calculations were performed, and by now the quantum chemistry version of DMRG has evolved into a standard method capable of advanced molecular calculations on strongly correlated molecules. I will discuss the differences and similarities of the strongly correlated molecular problem studied in chemistry and analogous problems in physics. I will illustrate the historical progress of the DMRG method in quantum chemistry and I will illustrate some of the differences between physics and chemistry codes. I will then present results of the most challenging molecular calculations done with DMRG so far. Finally, I will discuss the limitations of the DMRG in this context and illustrate possible solutions.


Fabian Heidrich-Meisner (LMU Munich, Germany): TALK SLIDES

Following the time evolution of a many-body wave-function using DMRG methods

While DMRG was originally mostly used for the calculation of ground state properties (such as energies and correlation functions), excitation gaps, or spectral functions, recent advances have paved the way for the calculation of the explicit time-dependence of many-body wave functions. I will present the basic ideas of this approach and its implementation both in a traditional DMRG code and in one that is formulated using matrix-product states. While ground state DMRG is a method that works well for mildly entangled states (which is a typical property of ground state wave functions in one dimension), a time-dependent wave-function in general explores large parts of the Hilbert space and is ultimately limited by the inherent entanglement growth. This important aspect will be discussed in examples and an intuitive explanation will be given. The time-dependent DMRG is now being used to study non-equilibrium dynamics, steady-state transport, and to calculate spectral functions. I will give some examples for the method's successful application in the fields of condensed matter physics, ultra-cold atomic gases and nanostructures. Finally, I  will discuss generalizations to finite temperatures and I will touch upon more recent algorithms as well.


Ryan Mishmash (University of California, Santa Barbara): TALK SLIDES

Gapless Bose Metals and Insulators on Multi-Leg Ladders

I will present on recent work using DMRG to establish compelling evidence for the existence of quasi-one-dimensional descendants of the "d-wave Bose liquid" (DBL), a novel gapless quantum phase of uncondensed itinerant bosons moving in two dimensions [1].  In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the N-leg ladder square lattice with frustrating four-site ring exchange. In this talk, I'll focus on two novel phases:  an incompressible gapless Mott insulator on the 3-leg ladder and a compressible gapless Bose metal on the 4-leg ladder.  The former is a fundamentally quasi-1D phase that is insulating along the ladder but has two 1D gapless modes and power law transverse density-density correlations at incommensurate wave vectors [2]; extensions of this phase to full 2D will be discussed.  The latter, on the other hand, is conducting along the ladder and has five 1D gapless modes, one more than the number of legs; this represents a significant step forward in establishing the existence of the DBL in two dimensions.  In both cases, we can
understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a DMRG solution of the model Hamiltonian.

[1]  O. I. Motrunich and M. P. A. Fisher, PRB 75, 235116 (2007).
[2]  M. S. Block, R. V. Mishmash, R. K. Kaul, D. N. Sheng, O. I.
Motrunich, and M. P. A. Fisher, PRL 106, 046402 (2011).

Erik Sørensen (McMaster University): TALK SLIDES

          The Kondo Problem: A DMRG perspective

The single impurity Kondo problem is likely the most well known quantum impurity model.  In this model a spin impurity with is coupled to a free electron gas that at low temperature will 'screen' the impurity through the formation of a singlet. Associated with the formation of this singlet is a typical length scale, the size of the screening cloud (mist). In this talk I will describe how this phenomenon can be observed using DMRG methods using various different measures.  In particular I will focus on describing how the impurity becomes entangled with the rest of the system by calculating the entanglement entropy arising from the impurity.