Studying strongly correlated systems with tensor network state methods and quantum information theory

Miklós Antal Werner, Andor Menczer, Örs Legeza

Benedikt Bruognolo

Shenghao Li, Yuanyuan Wu, Yuancheng Luo

Tensor network (TN) algorithms for strongly correlated electron lattice systems have become one of the most important numerical methods for studying such systems. Based on the tensor network algorithm for spin ladder systems, the study of quantum phase transitions (QPTs) in spin ladder systems through string order parameters has shown that quantum information theory provides a universal method for studying quantum phase transitions: without knowing the local or non-local order parameters of the system, or whether local or non-local order parameters exist, the ground-state wave function of the system can be obtained. If the ground-state lacks the traditional Landau long-range order and thus has no local order parameters, or if several non-local order parameters are found through other means, some topological quantum phases can be completely described, thereby greatly enriching the traditional Landau symmetry-breaking phase transition theory.

Stefanie Czischek

Mari Carmen Bañuls

<!--HTML-->*Theory Colloquium* The term Tensor Network States (TNS) designates a number of ansatzes that can efficiently represent certain states of quantum many-body systems. In particular, ground states and thermal equilibrium of local Hamiltonians, and, to some extent, real time evolution can be numerically studied with TNS methods. Quantum information theory provides tools to understand why they are good ansatzes for physically relevant states, and some of the limitations connected to the simulation algorithms. Originally introduced in the context of condensed matter physics, these methods have become a state-of-the-art technique for strongly correlated one-dimensional systems. Their applicability extends nevertheless to other fields. As an example, in the last few years it has been shown that TNS are also suitable to study lattice gauge theories and other quantum field problems. This talk gives an overview of the possibilities and limitations of these methods, and some of their recent applications to this kind of problems.

Rui-Zhen Huang, Haijun Liao, Zhiyuan Liu +5 more

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.