Tensor-product representations for string-net condensed states

TL;DR

This paper introduces a tensor product state (TPS) representation for string-net condensed states, enabling a unified description of both short-range and long-range entangled quantum states, and offers a new approach to study topological quantum phase transitions.

Contribution

It develops a tensor product state framework for string-net condensed states, providing a mean-field-like description and fixed-point properties under renormalization group transformations.

Findings

TPS can describe states with both short-range and long-range entanglement

Constructed TPS are fixed points under wave-function renormalization

Provides a new tool for studying topological quantum phase transitions

Abstract

We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry breaking states) and states with long-range entanglement (such as string-net condensed states with topological/quantum order). The tensor product representation provides a kind of 'mean-field' description for topologically ordered states and could be a powerful way to study quantum phase transitions between such states. As an attempt in this direction, we show that the constructed TPS's are fixed-points under a certain wave-function renormalization group transformation for quantum states.