A class of P,T-invariant topological phases of interacting electrons

By Michael H. Freedman, C. Nayak, K. Shtengel, Kevin Walker, Zhenghan Wang. 2003

169 citations recorded by the source corpus.

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 by particle-like excitations exhibiting exotic braiding statistics. P and T invariance are maintained by a ‘doubling’ of the low-energy degrees of freedom which occurs naturally without doubling the underlying microscopic degrees of freedom. The simplest examples have been the subject of considerable interest as proposed mechanisms for high-Tc superconductivity. One is the ‘doubled’ version of the chiral spin liquid. The chiral spin liquid gives rise to anyon superconductivity at finite doping and the corresponding field theory is U(1) Chern–Simons theory at coupling constant m=2. The ‘doubled’ theory is two copies of this theory, one with m=2 the other with m=−2. The second example corresponds to Z2 gauge theory, which describes a scenario for spin-charge separation. Our main concern, with an eye towards applications to quantum computation, are richer models which support non-Abelian statistics. All of these models, richer or poorer, lie in a tightly organized discrete family indexed by the Baraha numbers, 2cos(π/(k+2)), for positive integer k. The physical inference is that a material manifesting the Z2 gauge theory or a doubled chiral spin liquid might be easily altered to one capable of universal quantum computation. These phases of matter have a field-theoretic description in terms of gauge theories which, in their infrared limits, are topological field theories. We motivate these gauge theories using a parton model or slave-fermion construction and show how they can be solved exactly. The structure of the resulting Hilbert spaces can be understood in purely combinatorial terms. The highly constrained nature of this combinatorial construction, phrased in the language of the topology of curves on surfaces, lays the groundwork for a strategy for constructing microscopic lattice models which give rise to these phases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/0c8f1ee1d832e440fc28efb4da731e67ea641309

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Quantum magnetism and criticality (2007, methodology): “[41] have presented a classification of topological quantum phases using Chern-Simons gauge theory in which the Z2 × Z2 state is the simplest case.”
Non-Abelian Anyons and Topological Quantum Computation (2007, background): “hases, in particular, the SU(2)kanalog of (120) (Cattaneo et al., 1995): S = Sk CS(a+e) −Sk CS(a−e) = k 4π Z tr e∧ f+ 1 3 e∧ e∧ e (121) We will call this theory doubled SU(2)kChern-Simons theory (Freedman et al., 2004). We would like a microscopic lattice model whose lowenergy Hilbert space is com”
Anyons in an exactly solved model and beyond (2005, unknown): “S5 [24], A5 [32, 33] and S3 [34]), and double Chern-Simons models [35, 36 , 37].”