Colloquium on April 25th, 2005

Ignacio Cirac
Max Planck Institute of Quantum Optics

Simulation of quantum many-body systems

Many-body quantum systems are very hard to simulate numerically since the dimension of the corresponding Hilbert space scales exponentially with the number of systems. Based on different ideas borrowed from the field of Quantum Information Theory, we have developed efficient simulation techniques [1,2,3] which allow us to treat certain quantum many-body problems numerically. The basic idea is to use a new representation of quantum states in terms of what we call "projected entangled pair states" [3], which provide a very economic representation of several kind of states found in familiar systems. In this talk I will review the properties of such states, and explain the basic ideas behind the numerical algorithms.

[1] DMRG and periodic boundary conditions: a quantum information perspective,
F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004)

[2] Matrix Product Density Operators: Simulation of finite-T and dissipative systems,
F. Verstraete, J. J. Garcia-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004)

[3] Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions,
F. Verstraete and J. I. Cirac, cond-mat/0407066