# Detecting topological order in a ground state wave function.

@article{Levin2006DetectingTO,
title={Detecting topological order in a ground state wave function.},
author={Michael A. Levin and Xiao-Gang Wen},
journal={Physical review letters},
year={2006},
volume={96 11},
pages={
110405
}
}
• Published 23 October 2005
• Physics, Medicine
• Physical review letters
A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, di, F(lmn)(ijk), delta(ijk). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the "topological entropy" which directly measures the total quantum dimension D= Sum(id2i).
1,054 Citations

#### Figures and Topics from this paper

Characterizing topological order by the information convex
• Physics
• Physical Review B
• 2019
Motivated by previous efforts in detecting topological orders from the ground state(s) wave function, we introduce a new quantum information tool, coined the information convex, to capture the bulkExpand
Experimental preparation of topologically ordered states via adiabatic evolution
Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization ofExpand
Experimental implementation of adiabatic passage between different topological orders.
• Physics, Medicine
• Physical review letters
• 2014
An experimental quantum simulation of the Wen-plaquette spin model with different topological orders in a nuclear magnetic resonance system is reported and the adiabatic transition between two Z(2) topological Orders through a spin-polarized phase is observed by measuring the nonlocal closed-string (Wilson loop) operator. Expand
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
• Physics
• 2014
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of thisExpand
Characterizing Topological Order with Matrix Product Operators
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism ofExpand
The topological order of the space
Topological order is a new type order that beyond Landau’s symmetry breaking theory. The topological entanglement entropy provides a universal quantum number to characterize the topological order inExpand
Exact topological quantum order in D=3 and beyond : Branyons and brane-net condensates
• Physics
• 2007
We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-netExpand
A hierarchy of topological tensor network states
• Physics
• 2013
We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independentExpand
Topological entropy of realistic quantum Hall wave functions
• Physics
• 2008
The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglementExpand
A witness for topological order and stable quantum memories in abelian anyonic systems
We propose a novel parameter, the anyonic topological entropy, designed to detect the error correcting phase of a topological memory. Unlike similar quantities such as the topological entropy, theExpand

#### References

SHOWING 1-10 OF 26 REFERENCES
Topological Orders and Edge Excitations in FQH States
Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss the characteri- zation and classification of the new ordersExpand
String-net condensation: A physical mechanism for topological phases
• Physics
• 2005
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called string-nets,''Expand
A class of P,T-invariant topological phases of interacting electrons
• Physics
• 2004
Abstract We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized byExpand
Topological entanglement entropy.
• Medicine, Physics
• Physical review letters
• 2006
The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. Expand
Bipartite entanglement and entropic boundary law in lattice spin systems (10 pages)
• Physics
• 2005
We investigate bipartite entanglement in spin-1/2 systems on a generic lattice. For states that are an equal superposition of elements of a group G of spin flips acting on the fully polarized stateExpand
Quantum dimer model on the kagome lattice: solvable dimer-liquid and ising gauge theory.
• Medicine, Physics
• Physical review letters
• 2002
This work introduces quantum dimer models on lattices made of corner-sharing triangles, which realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Expand
Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
• Physics
• 2005
We define for quantum many-body systems a quasiadiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy densityExpand
Gauge theory of high-temperature superconductors and strongly correlated Fermi systems.
• Physics, Medicine
• Physical review. B, Condensed matter
• 1988
In this paper we show that the development of resonating valence bond correlations and the subsequent superconducting order in the high-T/sub c/ oxide superconductors are described by an U(1) latticeExpand
Fault tolerant quantum computation by anyons
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. MeasurementsExpand
Large-n limit of the Heisenberg-Hubbard model: Implications for high-Tc superconductors.
• Physics, Medicine
• Physical review. B, Condensed matter
• 1988
The Heisenberg-Hubbard model is solved in the large-n limit to gain insight into its relevance to the coppper-oxide materials. A gapless disordered ground state is found for the Heisenberg model.Expand