# Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order

@article{Chen2010LocalUT, title={Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order}, author={Xie Chen and Zheng-Cheng Gu and Xiao-Gang Wen}, journal={Physical Review B}, year={2010}, volume={82}, pages={155138} }

Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped ground states remain within the same phase under local unitary transformations. Therefore, local unitary transformations define an equivalence relation and the equivalence classes are the universality classes that define the different phases for gapped quantum systems. Since local unitary… Expand

#### Figures from this paper

#### 426 Citations

Local Transformations and Long-Range Entanglement

- Physics
- 2019

To understand the origin of the topological phenomena discussed in the previous chapters, we need a microscopic theory for topological order. It was realized that the key microscopic feature of… Expand

Bifurcation in entanglement renormalization group flow of a gapped spin model

- Physics
- 2014

We study entanglement renormalization group transformations for the ground states of a spin model, called cubic code model $H_A$ in three dimensions, in order to understand long-range entanglement… Expand

Quantum Phase Transition and Entanglement in Topological Quantum Wires

- Physics, Medicine
- Scientific Reports
- 2017

It is shown that the topological phase transition of the Su-Schrieffer-Heeger (SSH) model is signified by a nonanalyticity of local entanglement, which becomes discontinuous for finite even system sizes, and that this non Analyticity has a topological origin. Expand

Renormalization group constructions of topological quantum liquids and beyond

- Physics
- 2016

We give a detailed physical argument for the area law for entanglement entropy in gapped phases of matter arising from local Hamiltonians. Our approach is based on renormalization group (RG) ideas… Expand

Symmetry protected entanglement renormalization

- Physics
- 2013

Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multiscale entanglement renormalization ansatz (MERA), a tensor… Expand

Topological Order and Universal Properties of Gapped Quantum Systems

- Physics
- 2018

Phases of gapped quantum liquids are topologically ordered and have very interesting physical features that are completely robust against any local perturbation that do not close the bulk energy gap.… Expand

Exponential clustering of bipartite quantum entanglement at arbitrary temperatures

- Physics, Mathematics
- 2021

Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using… Expand

Local reversibility and entanglement structure of many-body ground states

- Physics, Mathematics
- 2015

The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong… Expand

Quantum Information Theory in Condensed Matter Physics

- Physics
- 2017

In the “standard” Gizburg-Landau approach, a phase transition is intimately connected to a local order parameter, that spontaneously breaks some symmetries. In addition to the “traditional”… Expand

Classical criticality establishes quantum topological order

- Physics
- 2020

We establish an important duality correspondence between topological order in quantum many body systems and criticality in ferromagnetic classical spin systems. We show how such a correspondence… Expand