Dresden 2014 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 59: Low-Dimensional Systems: 2D - Theory (organized by TT)

TT 59.9: Talk

Wednesday, April 2, 2014, 11:45–12:00, BEY 81

Efficient 2D density matrix renormalization group in mixed real- and momentum-space representation — •Johannes Motruk¹, Michael P. Zaletel², Roger S. K. Mong³, and Frank Pollmann¹ — ¹Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany — ²Department of Physics, University of California, Berkeley, California 94720, USA — ³Department of Physics, California Institute of Technology, Pasadena, California 91125, USA

Density matrix renormalization group (DMRG) is a powerful numerical technique for both 1D and 2D systems. The traditional implementation for a 2D system requires an ordering of sites to form an effective 1D chain for simulation. We present a variation of the DMRG technique that utilizes a real-space representation in one direction and momentum-space representation in the perpendicular direction of the lattice. We demonstrate how the mixed representation reduces the computational costs by using momentum as a conserved quantity—and as a by product—produces the momentum-resolved entanglement spectrum. As an application, we map out the phase diagram of a tight-binding model of spinless fermions with nearest-neighbour interactions on the square lattice. For this model, we give performance benchmarks comparing the mixed basis to the traditional real-space basis.