Application of Matrix Product Methods to Strongly Correlated Systems

PhD típus: 
Fizikai Tudományok Doktori Iskola
Munkahely neve: 
Budapest University of Technology and Economics

When Wilson created his famous Numerical Renormalization Group to solve the Kondo problem [1], he has not quite realized that the states

constructed by his numerical procedure belonged to the class of so-called Matrix Product States (MPS). More recently, matrix product state

approaches such as Steve White’s  Density Matrix Renormalization Group (DMRG) Method, or Vidal’s Time Evolving Block Decimation (TEBD)

Approach [2] proved to be powerful tools to study zero- or one-dimensional strongly interacting quantum systems and their time evolution.

Currently, a lot of effort is being devoted to extend these structures to describe higher dimensional systems within the Tree Tensor

Network (TTN) approach [3], and non-equilibrium systems within the Matrix Product Operator approach [4].

The task of the PhD student would be to study correlated nano systems with long-ranged interactions and nuclear systems by using these

methods, in collaboration with the ‘Momentum’ groups of Prof. Örs Legeza and that of Prof. Gergely Zaránd. The PhD student will apply and

further develop symmetry-based codes to study topological states in carbon nanotubes, and correlation effects and dynamics in heavy nuclei.


[1] K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem}, Rev. Mod. Phys. 47 ,773-840 (1975).

[2] F. Verstraete, V. Murg, and J. I. Cirac, Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems, Advances in Physics 57, 143-224 (2008).

[3] V. Murg, F. Verstraete, F. Ö. Legeza, and R. M. Noack, Simulating strongly correlated quantum systems with tree tensor networks, Phys. Rev. B,

  82, 205105 (2010). Sz. Szalay, M. Pfeffer, V. Murg, G. Barcza, F. Verstraete, R. Schneider, Ö. legeza, Tensor product methods and entanglement optimization for ab initio quantum chemistry, Int. J. Quant. Chem. 115, 1342 (2015)

[4] U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96 - 192, (2011).


Requested preliminary experience includes: good programming skills, excellent background in quantum mechanics, and basic notions of many-body theory (second quantization and its applications).

Legeza Örs
Email cím:
Wigner Research Centre for Phyics
scientific advisor
Tudományos fokozat: 
Zaránd Gergely
Email cím:
Institute of Physics
Tudományos fokozat: 
Member of the Hungarian Academy of Sciences