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5.0

Jun 29, 2018
06/18

by
Dominic J. Williamson

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Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and post-gauging models and use this to construct short-range entangled phases with fractal-like symmetries, one of which is...

Topics: Quantum Physics, Condensed Matter, High Energy Physics - Lattice, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1603.05182

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3.0

Jun 29, 2018
06/18

by
Dominic J. Williamson; Zhenghan Wang

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We present commuting projector Hamiltonian realizations of a large class of (3+1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our Hamiltonians are unitary state sum topological quantum fields theories (TQFTs) that appear to capture all known constructions in the literature, including the...

Topics: Mathematics, Quantum Physics, Condensed Matter, Quantum Algebra, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1606.07144

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4.0

Jun 30, 2018
06/18

by
Dominic J. Williamson; Stephen D. Bartlett

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Adiabatic quantum transistors allow quantum logic gates to be performed by applying a large field to a quantum many-body system prepared in its ground state, without the need for local control. The basic operation of such a device can be viewed as driving a spin chain from a symmetry protected phase to a trivial phase, and this perspective offers an avenue to generalise the adiabatic quantum transistor and to design several improvements. The performance of quantum logic gates is shown to depend...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1408.3415

3
3.0

Jun 29, 2018
06/18

by
Dominic J. Williamson; Nick Bultinck; Jutho Haegeman; Frank Verstraete

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We introduce the concept of fermionic matrix product operators, and show that they provide a natural representation of fermionic fusion tensor categories. This allows for the classification of two dimensional fermionic topological phases in terms of matrix product operator algebras. Using this approach we give a classification of fermionic symmetry protected topological phases with respect to a group $G$ in terms of three cohomology groups: $H^1(G,Z_2)$, describing which matrix product...

Topics: Quantum Physics, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1609.02897

4
4.0

Jun 29, 2018
06/18

by
Nick Bultinck; Dominic J. Williamson; Jutho Haegeman; Frank Verstraete

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We develop the formalism of fermionic matrix product states (fMPS) and show how irreducible fMPS fall in two different classes, related to the different types of simple $\mathbb{Z}_2$ graded algebras, which are physically distinguished by the absence or presence of Majorana edge modes. The local structure of fMPS with Majorana edge modes also implies that there is always a two-fold degeneracy in the entanglement spectrum. Using the fMPS formalism we make explicit the correspondence between the...

Topics: Quantum Physics, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1610.07849

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108

Jul 20, 2013
07/13

by
Ross C. McPhedran; Lindsay C. Botten; Dominic J. Williamson; Nicolae-Alexandru P. Nicorovici

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We present further results on a class of sums which involve complex powers of the distance to points in a two-dimensional square lattice and trigonometric functions of their angle, supplementing those in a previous paper (McPhedran {\em et al}, 2008). We give a general expression which permits numerical evaluation of members of the class of sums to arbitrary order. We use this to illustrate numerically the properties of trajectories along which the real and imaginary parts of the sums are zero,...

Source: http://arxiv.org/abs/1007.4111v1

9
9.0

Jun 28, 2018
06/18

by
Nick Bultinck; Michael Mariën; Dominic J. Williamson; Mehmet B. Şahinoğlu; Jutho Haegeman; Frank Verstraete

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Quantum tensor network states and more particularly projected entangled-pair states provide a natural framework for representing ground states of gapped, topologically ordered systems. The defining feature of these representations is that topological order is a consequence of the symmetry of the underlying tensors in terms of matrix product operators. In this paper, we present a systematic study of those matrix product operators, and show how this relates entanglement properties of projected...

Topics: Quantum Physics, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1511.08090

3
3.0

Jun 30, 2018
06/18

by
Dominic J. Williamson; Nick Bultinck; Michael Mariën; Mehmet B. Sahinoglu; Jutho Haegeman; Frank Verstraete

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Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to describe on-site symmetries, as occurring in systems exhibiting symmetry-protected topological (SPT) quantum order, in terms of virtual symmetries of the local tensors expressed as a set of matrix product operators (MPOs) labeled by distinct group elements....

Topics: Quantum Physics, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1412.5604