# String-net condensation: A physical mechanism for topological phases

@article{Levin2005StringnetCA, title={String-net condensation: A physical mechanism for topological phases}, author={Michael Levin and Xiao-Gang Wen}, journal={Physical Review B}, year={2005}, volume={71}, pages={045110} }

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,'' become highly fluctuating and condense. We construct a large class of exactly soluble 2D spin Hamiltonians whose ground states are string-net condensed. Each ground state corresponds to a different parity invariant topological phase. The models reveal the mathematical framework underlying topological…

## Figures from this paper

## 780 Citations

String-net condensation and topological phases in quantum spin systems by

- 2006

For many years, it was thought that Landau's theory of symmetry breaking could describe essentially all phases and phase transitions. However, in the last twenty years, it has become clear that at…

Topological order in three-dimensional systems and 2-gauge symmetry

- Physics
- 2017

Topological order is a new paradigm for quantum phases of matter developed to explain phase transitions which do not fit the symmetry breaking scheme for classifying phases of matter. They are…

Novel quantum phases on graphs using abelian gauge theory

- Physics, MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In…

Fermion condensation and super pivotal categories

- Physics, Mathematics
- 2017

We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion.…

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.…

Condensate-induced transitions between topologically ordered phases

- Physics
- 2009

We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory…

Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids

- Physics
- 2009

Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Anyons emerge as quasiparticles in fractional…

Theory of Twist Liquids: Gauging an Anyonic Symmetry

- Physics
- 2015

Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological…

Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters

- PhysicsPhysical Review B
- 2021

Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of Projected Entangled Pair States (PEPS), topological order is characterized by…

Three-dimensional topological lattice models with surface anyons

- Physics
- 2013

We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they…

## References

SHOWING 1-10 OF 85 REFERENCES

Quantum order from string net condensations and origin of light and massless fermions

- Physics
- 2003

Recently, it was pointed out that quantum orders and the associated projective symmetry groups can produce and protect massless gauge bosons and massless fermions in local bosonic models. In this…

Topological Orders in Rigid States

- Physics
- 1990

We study a new kind of ordering — topological order — in rigid states (the states with no local gapless excitations). We concentrate on characterization of the different topological orders. As an…

Quantum orders and symmetric spin liquids

- Physics
- 2002

A concept-quantum order-is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize the universality classes of…

Topological Order and Conformal Quantum Critical Points

- Physics
- 2003

Abstract We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the…

Fermions, strings, and gauge fields in lattice spin models

- Physics
- 2003

We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a stringlike…

Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems

- Physics
- 2000

We develop a new theoretical framework for describing and analyzing exotic phases of strongly correlated electrons which support excitations with fractional quantum numbers. Starting with a class of…

Ground States of Quantum Antiferromagnets in Two Dimensions

- Physics
- 2002

Abstract We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and…

An introduction to lattice gauge theory and spin systems

- Physics
- 1979

This article is an interdisciplinary review of lattice gauge theory and spin systems. It discusses the fundamentals, both physics and formalism, of these related subjects. Spin systems are models of…

Mean-field theory of spin-liquid states with finite energy gap and topological orders.

- Physics, MedicinePhysical review. B, Condensed matter
- 1991

The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge…

Fractionalization in an easy-axis Kagome antiferromagnet

- Physics
- 2002

We study an antiferromagnetic spin-$1/2$ model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a…