Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions

TL;DR

This work describes quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions, and uses this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions.

Abstract

We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We use this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions.

Figures (2)

• Figure 1: Graphical representation of MPS in 1 dimension (a), in 2 dimensions (b), and of PEPS (c). The bonds represent pairs of maximally entangled D--dimensional auxiliary spins and the circles denote projectors that map the inner auxiliary spins to the physical ones.
• Figure 2: Imaginary time evolution with the Heisenberg and a frustrated Heisenberg interaction on a $4\times 4$ lattice, and $D=2,D_f=16$ (dotted) and $D=3,D_f=35$ (dashed); the $D=3$ results are almost indistinguishable from the exact ones (full line). The insert presents the evolution for $D=2$ on a $10\times 10$ lattice.