techreport
M. H. Freedman, C. Nayak, and K. Shtengel :
Non-Abelian topological phases in an extended Hubbard model .
Preprint ,
September 2003 .
ArXiv
cond-mat/0309120
Abstract
People
BibTeX
We describe four closely related Hubbard-like models (models A, B, C and D) of particles that can hop on a \( 2D \) Kagome lattice interacting via Coulomb repulsion. The particles can be either bosons (models A and B) or (spinless) fermions (models C and D). Models A and C also include a ring exchange term. In all four cases we solve equations in the model parameters to arrive at an exactly soluble point whose ground state manifold is the extensively degenerate “\( d \) -isotopy space” \( \bar{V}_d \) , \( 0 < d < 2 \) . Near the “special” values, \( d = 2 \cos \pi/k+2 \) , \( \bar{V}_d \) should collapse to a stable topological phase with anyonic excitations closely related to \( \mathit{SU}(2) \) Chern–Simons theory at level \( k \) . We mention simplified models \( A^- \) and \( C^- \) which may also lead to these topological phases.
@techreport {keycond-mat/0309120a,
AUTHOR = {Freedman, M. H. and Nayak, C. and Shtengel,
K.},
TITLE = {Non-{A}belian topological phases in
an extended {H}ubbard model},
TYPE = {Preprint},
MONTH = {September},
YEAR = {2003},
NOTE = {ArXiv:cond-mat/0309120.},
}
article
M. Freedman, C. Nayak, K. Shtengel, K. Walker, and Z. Wang :
“A class of \( P,T \) -invariant topological phases of interacting electrons Ann. Physics
310 : 2
(2004 ),
pp. 428–492 .
MR
2044743 Zbl
1057.81053
Abstract
People
BibTeX
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-\( T_c \) 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 \( Z_2 \) 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, \( 2\cos(\pi/(k+2)) \) , for positive integer \( k \) . The physical inference is that a material manifesting the \( Z_2 \) 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.
@article {key2044743m,
AUTHOR = {Freedman, Michael and Nayak, Chetan
and Shtengel, Kirill and Walker, Kevin
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TITLE = {A class of \$P,T\$-invariant topological
phases of interacting electrons},
JOURNAL = {Ann. Physics},
FJOURNAL = {Annals of Physics},
VOLUME = {310},
NUMBER = {2},
YEAR = {2004},
PAGES = {428--492},
DOI = {10.1016/j.aop.2004.01.006},
NOTE = {MR:2044743. Zbl:1057.81053.},
ISSN = {0003-4916},
}
M. H. Freedman, C. Nayak, and K. Shtengel :
“Line of critical points in \( 2+1 \) dimensions: Quantum critical loop gases and non-abelian gauge theory Phys. Rev. Lett.
94 : 14
(2005 ),
pp. 147205 .
Abstract
People
BibTeX
In this Letter, we
@article {key78927106,
AUTHOR = {Freedman, M. H. and Nayak, C. and Shtengel,
K.},
TITLE = {Line of critical points in \$2+1\$ dimensions:
{Q}uantum critical loop gases and non-abelian
gauge theory},
JOURNAL = {Phys. Rev. Lett.},
FJOURNAL = {Physical Review Letters},
VOLUME = {94},
NUMBER = {14},
YEAR = {2005},
PAGES = {147205},
NOTE = {Available at
http://dx.doi.org/10.1103/PhysRevLett.94.147205.},
ISSN = {0031-9007},
}
article
D. Das Sarma, M. H. Freedman, and C. Nayak :
“Topologically-protected qubits from a possible non-abelian fractional quantum Hall state Phys. Rev. Lett.
94 : 6
(2005 ),
pp. 166802 .
ArXiv
cond-mat/0412343
Abstract
People
BibTeX
The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at a Landau-level filling fraction \( \nu = 5/2 \) . This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the \( \nu = 5/2 \) state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by quasiparticle braiding. Using the measured excitation gap at \( \nu = 5/2 \) , we estimate the error rate to be \( 10^{-30} \) or lower.
@article {keycond-mat/0412343a,
AUTHOR = {Das Sarma, D. and Freedman, M. H. and
Nayak, C.},
TITLE = {Topologically-protected qubits from
a possible non-abelian fractional quantum
{H}all state},
JOURNAL = {Phys. Rev. Lett.},
FJOURNAL = {Physical Review Letters},
VOLUME = {94},
NUMBER = {6},
YEAR = {2005},
PAGES = {166802},
DOI = {10.1103/PhysRevLett.94.166802},
NOTE = {ArXiv:cond-mat/0412343.},
ISSN = {0031-9007},
}
M. Freedman, C. Nayak, and K. Shtengel :
“An extended Hubbard model with ring exchange: A route to a non-abelian topological phase Phys. Rev. Lett.
94 : 6
(2005 ),
pp. 066401 .
Abstract
People
BibTeX
We propose an extended Hubbard model on a \( 2D \) kagomé lattice with an additional ring exchange term. The particles can be either bosons or spinless fermions. We analyze the model at the special filling fraction \( 1/6 \), where it is closely related to the quantum dimer model. We show how to arrive at an exactly soluble point whose ground state is the “\( d \)-isotopy” transition point into a stable phase with a certain type of non-Abelian topological order. Near the “special” values, \( d=2\cos\pi/(k+2) \), this topological phase has anyonic excitations closely related to \( \mathit{SU}(2) \) Chern–Simons theory at level \( k \).
@article {key88878027,
AUTHOR = {Freedman, M. and Nayak, C. and Shtengel,
K.},
TITLE = {An extended {H}ubbard model with ring
exchange: {A} route to a non-abelian
topological phase},
JOURNAL = {Phys. Rev. Lett.},
FJOURNAL = {Physical Review Letters},
VOLUME = {94},
NUMBER = {6},
YEAR = {2005},
PAGES = {066401},
NOTE = {Available at
http://dx.doi.org/10.1103/PhysRevLett.94.066401.},
ISSN = {0031-9007},
}
techreport
M. Freedman, C. Nayak, and K. Walker :
Tilted interferometry realizes universal quantum computation in the Ising TQFT without overpasses .
Preprint ,
December 2005 .
ArXiv
cond-mat/0512072
Abstract
People
BibTeX
We show how a universal gate set for topological quantum computation in the Ising TQFT, the non-Abelian sector of the putative effective field theory of the \( \nu=5/2 \) fractional quantum Hall state, can be implemented. This implementation does not require overpasses or surgery, unlike the construction of Bravyi and Kitaev, which we take as a starting point. However, it requires measurements of the topological charge around time-like loops encircling moving quasiaparticles, which require the ability to perform ‘tilted’ interferometry measurements
@techreport {keycond-mat/0512072a,
AUTHOR = {Freedman, M. and Nayak, C. and Walker,
K.},
TITLE = {Tilted interferometry realizes universal
quantum computation in the {I}sing {TQFT}
without overpasses},
TYPE = {Preprint},
MONTH = {December},
YEAR = {2005},
NOTE = {ArXiv:cond-mat/0512072.},
}
M. Freedman, C. Nayak, and K. Walker :
“Towards universal topological quantum computation in the \( \nu=5/2 \) fractional quantum Hall state Phys. Rev. B
73 : 24
(2006 ),
pp. 245307 .
Abstract
People
BibTeX
The Pfaffian state, which may describe the quantized Hall plateau observed at Landau level filling fraction \( \nu = 5/2 \), can support topologically-protected qubits with extremely low error rates. Braiding operations also allow perfect implementation of certain unitary transformations of these qubits. However, in the case of the Pfaffian state, this set of unitary operations is not quite sufficient for universal quantum computation (i.e. is not dense in the unitary group). If some topologically unprotected operations are also used, then the Pfaffian state supports universal quantum computation, albeit with some operations which require error correction. On the other hand, if certain topology-changing operations can be implemented, then fully topologically-protected universal quantum computation is possible. In order to accomplish this, it is necessary to measure the interference between quasiparticle trajectories which encircle other moving trajectories in a time-dependent Hall droplet geometry [cond-mat/0512072].
@article {key51905847,
AUTHOR = {Freedman, M. and Nayak, C. and Walker,
K.},
TITLE = {Towards universal topological quantum
computation in the \$\nu=5/2\$ fractional
quantum {H}all state},
JOURNAL = {Phys. Rev. B},
FJOURNAL = {Physical Review B},
VOLUME = {73},
NUMBER = {24},
YEAR = {2006},
PAGES = {245307},
NOTE = {Available at
http://dx.doi.org/10.1103/PhysRevB.73.245307.},
ISSN = {1098-0121},
}
M. Freedman, S. Das Sarma, and C. Nayak :
“Topological quantum computation Physics Today
59 : 7
(July 2006 ),
pp. 32–38 .
Abstract
People
BibTeX
The search for a large-scale, error-free quantum computer is reaching an intellectual junction at which semiconductor physics, knot theory, string theory, anyons, and quantum Hall effects are all coming together to produce quantum immunity.
@article {key81708888,
AUTHOR = {Freedman, M. and Das Sarma, S. and Nayak,
C.},
TITLE = {Topological quantum computation},
JOURNAL = {Physics Today},
VOLUME = {59},
NUMBER = {7},
MONTH = {July},
YEAR = {2006},
PAGES = {32--38},
NOTE = {Available at
http://stationq.cnsi.ucsb.edu/~freedman/Publications/96.pdf.},
ISSN = {0031-9228},
}
article
P. Bonderson, M. Freedman, and C. Nayak :
“Measurement-only topological quantum computation Phys. Rev. Lett.
101 : 1
(2008 ),
pp. 010501 .
MR
2429542 Zbl
1228.81121 ArXiv
0802.0279
Abstract
People
BibTeX
We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.
@article {key2429542m,
AUTHOR = {Bonderson, Parsa and Freedman, Michael
and Nayak, Chetan},
TITLE = {Measurement-only topological quantum
computation},
JOURNAL = {Phys. Rev. Lett.},
FJOURNAL = {Physical Review Letters},
VOLUME = {101},
NUMBER = {1},
YEAR = {2008},
PAGES = {010501},
DOI = {10.1103/PhysRevLett.101.010501},
NOTE = {ArXiv:0802.0279. MR:2429542. Zbl:1228.81121.},
ISSN = {0031-9007},
}
article
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma :
“Non-abelian anyons and topological quantum computation Rev. Modern Phys.
80 : 3
(2008 ),
pp. 1083–1159 .
MR
2443722 Zbl
1205.81062 ArXiv
0707.1889
Abstract
People
BibTeX
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the \( \nu =5/2 \) state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the \( \nu =5/2 \) fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.
@article {key2443722m,
AUTHOR = {Nayak, Chetan and Simon, Steven H. and
Stern, Ady and Freedman, Michael and
Das Sarma, Sankar},
TITLE = {Non-abelian anyons and topological quantum
computation},
JOURNAL = {Rev. Modern Phys.},
FJOURNAL = {Reviews of Modern Physics},
VOLUME = {80},
NUMBER = {3},
YEAR = {2008},
PAGES = {1083--1159},
DOI = {10.1103/RevModPhys.80.1083},
NOTE = {ArXiv:0707.1889. MR:2443722. Zbl:1205.81062.},
ISSN = {0034-6861},
}
M. Freedman, C. Nayak, and K. Shtengel :
“Lieb–Schultz–Mattis theorem for quasitopological systems Phys. Rev. B
78
(2008 ),
pp. 174411 .
Abstract
People
BibTeX
In this paper we address the question of the existence of a spectral gap in a class of local Hamiltonians. These Hamiltonians have the following properties: their ground states are known exactly; all equal-time correlation functions of local operators are short-ranged; and correlation functions of certain nonlocal operators are critical. A variational argument shows gaplessness with \( \omega \propto k^2 \) at critical points defined by the absence of certain terms in the Hamiltonian, which is remarkable because equal-time correlation functions of local operators remain short ranged . We call such critical points, in which spatial and temporal scaling are radically different, quasitopological . When these terms are present in the Hamiltonian, the models are in gapped topological phases which are of special interest in the context of topological quantum computation.
@article {key34904990,
AUTHOR = {Freedman, M. and Nayak, C. and Shtengel,
K.},
TITLE = {Lieb--{S}chultz--{M}attis theorem for
quasitopological systems},
JOURNAL = {Phys. Rev. B},
FJOURNAL = {Physical Review B},
VOLUME = {78},
YEAR = {2008},
PAGES = {174411},
NOTE = {Available at
http://dx.doi.org/10.1103/PhysRevB.78.174411.},
ISSN = {1098-0121},
}
incollection
M. Freedman, C. Nayak, K. Walker, and Z. Wang :
“On picture \( (2+1) \) -TQFTs 19–106
in
Topology and physics
(Tianjin, China, 27–31 July 2007 ).
Edited by K. Lin, Z. Weng, and W. Zhang .
Nankai Tracts in Mathematics 12 .
World Scientific (Hackensack, NJ ),
2008 .
MR
2503392 Zbl
1168.81024 ArXiv
0806.1926
People
BibTeX
@incollection {key2503392m,
AUTHOR = {Freedman, Michael and Nayak, Chetan
and Walker, Kevin and Wang, Zhenghan},
TITLE = {On picture \$(2+1)\$-{TQFT}s},
BOOKTITLE = {Topology and physics},
EDITOR = {Kevin Lin and Zhenghan Weng and Weiping
Zhang},
SERIES = {Nankai Tracts in Mathematics},
NUMBER = {12},
PUBLISHER = {World Scientific},
ADDRESS = {Hackensack, NJ},
YEAR = {2008},
PAGES = {19--106},
DOI = {10.1142/9789812819116_0002},
NOTE = {(Tianjin, China, 27--31 July 2007).
ArXiv:0806.1926. MR:2503392. Zbl:1168.81024.},
ISBN = {9789812819109},
}
article
P. Bonderson, M. Freedman, and C. Nayak :
“Measurement-only topological quantum computation via anyonic interferometry Ann. Physics
324 : 4
(2009 ),
pp. 787–826 .
MR
2508474 Zbl
1171.81004 ArXiv
0808.1933
Abstract
People
BibTeX
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using “forced measurement” protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.
@article {key2508474m,
AUTHOR = {Bonderson, Parsa and Freedman, Michael
and Nayak, Chetan},
TITLE = {Measurement-only topological quantum
computation via anyonic interferometry},
JOURNAL = {Ann. Physics},
FJOURNAL = {Annals of Physics},
VOLUME = {324},
NUMBER = {4},
YEAR = {2009},
PAGES = {787--826},
DOI = {10.1016/j.aop.2008.09.009},
NOTE = {ArXiv:0808.1933. MR:2508474. Zbl:1171.81004.},
ISSN = {0003-4916},
}
article
L. Fidkowski, M. Freedman, C. Nayak, K. Walker, and Z. Wang :
“From string nets to nonabelions Comm. Math. Phys.
287 : 3
(2009 ),
pp. 805–827 .
MR
2486662 Zbl
1196.82072 ArXiv
cond-mat/0610583
Abstract
People
BibTeX
We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an \( \mathit{SO}(3)_3\times\mathit{SO}(3)_3 \) doubled Chern–Simons theory, with the appropriate non-abelian statistics governing the braiding of the low-lying quasiparticle excitations (nonabelions). Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.
@article {key2486662m,
AUTHOR = {Fidkowski, Lukasz and Freedman, Michael
and Nayak, Chetan and Walker, Kevin
and Wang, Zhenghan},
TITLE = {From string nets to nonabelions},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {287},
NUMBER = {3},
YEAR = {2009},
PAGES = {805--827},
DOI = {10.1007/s00220-009-0757-9},
NOTE = {ArXiv:cond-mat/0610583. MR:2486662.
Zbl:1196.82072.},
ISSN = {0010-3616},
}
techreport
P. Bonderson, S. Das Sarma, M. Freedman, and C. Nayak :
A blueprint for a topologically fault-tolerant quantum computer .
Preprint ,
March 2010 .
ArXiv
1003.2856
Abstract
People
BibTeX
The advancement of information processing into the realm of quantum mechanics promises a transcendence in computational power that will enable problems to be solved which are completely beyond the known abilities of any “classical” computer, including any potential non-quantum technologies the future may bring. However, the fragility of quantum states poses a challenging obstacle for realization of a fault-tolerant quantum computer. The topological approach to quantum computation proposes to surmount this obstacle by using special physical systems — non-Abelian topologically ordered phases of matter — that would provide intrinsic fault-tolerance at the hardware level. The so-called “Ising-type” non-Abelian topological order is likely to be physically realized in a number of systems, but it can only provide a universal gate set (a requisite for quantum computation) if one has the ability to perform certain dynamical topology-changing operations on the system. Until now, practical methods of implementing these operations were unknown. Here we show how the necessary operations can be physically implemented for Ising-type systems realized in the recently proposed superconductor-semiconductor and superconductor-topological insulator heterostructures. Furthermore, we specify routines employing these methods to generate a computationally universal gate set. We are consequently able to provide a schematic blueprint for a fully topologically-protected Ising based quantum computer using currently available materials and techniques. This may serve as a starting point for attempts to construct a fault-tolerant quantum computer, which will have applications to cryptanalysis, drug design, efficient simulation of quantum many-body systems, solution of large systems of linear equations, searching large databases, engineering future quantum computers, and — most importantly — those applications which no one in our classical era has the prescience to foresee.
@techreport {key1003.2856a,
AUTHOR = {Bonderson, P. and Das Sarma, S. and
Freedman, M. and Nayak, C.},
TITLE = {A blueprint for a topologically fault-tolerant
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TYPE = {Preprint},
MONTH = {March},
YEAR = {2010},
NOTE = {ArXiv:1003.2856.},
}
article
M. Freedman, M. B. Hastings, C. Nayak, X.-L. Qi, K. Walker, and Z. Wang :
“Projective ribbon permutation statistics: A remnant of non-Abelian braiding in higher dimensions Phys. Rev. B
83 : 11
(2011 ),
pp. 115132 .
ArXiv
1005.0583
Abstract
People
BibTeX
In a recent paper, Teo and Kane Phys. Rev. Lett. 104 046401 (2010) proposed a three-dimensional (3D) model in which the defects support Majorana fermion zero modes. They argued that exchanging and twisting these defects would implement a set \( R \) of unitary transformations on the zero-mode Hilbert space which is a “ghostly” recollection of the action of the braid group on Ising anyons in two dimensions. In this paper, we find the group \( T_{2n} \) , which governs the statistics of these defects by analyzing the topology of the space \( K_{2n} \) of configurations of \( 2n \) defects in a slowly spatially varying gapped free-fermion Hamiltonian: \( T_{2n}\equiv \pi_1(K_{2n}) \) . We find that the group \( T_{2n}=\mathbb{Z}\times T_{2n}^r \) , where the “ribbon permutation group” \( T_{2n}^r \) is a mild enhancement of the permutation group
\[ S_{2n}: T_{2n}^r\equiv \mathbb{Z}_2\rtimes E((\mathbb{Z}_2)^{2n}\rtimes S_{2n}) .\]
Here, \( E((\mathbb{Z}_2)^{2n}\rtimes S_{2n}) \) is the “even part” of \( (\mathbb{Z}_2)^{2n}\rtimes S_{2n} \) , namely, those elements for which the total parity of the element in \( (\mathbb{Z}_2)^{2n} \) added to the parity of the permutation is even. Surprisingly, \( R \) is only a projective representation of \( T_{2n} \) , a possibility proposed by Wilczek [hep-th/9806228]. Thus, Teo and Kane’s defects realize projective ribbon permutation statistics, which we show to be consistent with locality. We extend this phenomenon to other dimensions, codimensions, and symmetry classes. We note that our analysis applies to 3D networks of quantum wires supporting Majorana fermions; thus, these networks are not required to be planar. Because it is an essential input for our calculation, we review the topological classification of gapped free-fermion systems and its relation to Bott periodicity.
@article {key1005.0583a,
AUTHOR = {Freedman, Michael and Hastings, Matthew
B. and Nayak, Chetan and Qi, Xiao-Liang
and Walker, Kevin and Wang, Zhenghan},
TITLE = {Projective ribbon permutation statistics:
{A} remnant of non-{A}belian braiding
in higher dimensions},
JOURNAL = {Phys. Rev. B},
FJOURNAL = {Physical Review B},
VOLUME = {83},
NUMBER = {11},
YEAR = {2011},
PAGES = {115132},
DOI = {10.1103/PhysRevB.83.115132},
NOTE = {ArXiv:1005.0583.},
ISSN = {1098-0121},
}
