arXiv subjects

Brian Swingle

Publications and source records attributed to Brian Swingle.

152 records · Page 9Linked to original sources

arXiv2010

Correlated Topological Insulators and the Fractional Magnetoelectric Effect

Topological insulators are characterized by the presence of gapless surface modes protected by time-reversal symmetry. In three space dimensions the magnetoelectric response is described in terms of a bulk theta term for the electromagnetic field. Here we construct theoretical examples of such phases that cannot be smoothly connected to any band insulator. Such correlated topological insulators admit the possibility of fractional magnetoelectric response described by fractional theta/pi. We show that fractional theta/pi is only possible in a gapped time reversal invariant system of bosons or fermions if the system also has deconfined fractional excitations and associated degenerate ground states on topologically non-trivial spaces. We illustrate this result with a concrete example of a time reversal symmetric topological insulator of correlated bosons with theta = pi/4. Extensions to electronic fractional topological insulators are briefly described.

cond-mat.str-el↗

arXiv2010

Highly entangled quantum systems in 3+1 dimensions

Many systems exhibit boundary law scaling for entanglement entropy in more than one spatial dimension. Here I describe three systems in 3+1 dimensions that violate the boundary law for entanglement entropy. The first is free Weyl fermions in a magnetic field, the second is a holographic strong coupling generalization of the Weyl fermion system, and the third is a strong topological insulator in the presence of dislocations. These systems are unified by the presence of a low energy description that includes many gapless 1+1 dimensional modes. I conclude with some comments on the search for highly entangled states of quantum matter and some potential experimental signatures.

cond-mat.str-el↗

arXiv2010

Entanglement Entropy and the Fermi Surface

Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size $L$ in $d$ spatial dimensions is $S\sim L^{d-1} \log{L}$, a result that should be contrasted with the usual boundary law $S \sim L^{d-1}$. This term depends only on the geometry of the Fermi surface and on the boundary of the region in question. I give an intuitive account of this anomalous scaling based on a low energy description of the Fermi surface as a collection of one dimensional gapless modes. Using this picture, I predict a violation of the boundary law in a number of other strongly correlated systems.

cond-mat.str-el↗

arXiv2010

Conformal Field Theory on the Fermi Surface

The Fermi surface may be usefully viewed as a collection of 1+1 dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground state properties of the Fermi gas including entanglement entropy and number fluctuations. The 1+1 dimensional picture also generalizes to finite temperature and the presence of interactions. Finally, I argue that the low energy entanglement structure of Fermi liquid theory is universal, depending only on the geometry of the interacting Fermi surface.

cond-mat.str-el↗

arXiv2010

Topological Properties of Tensor Network States From Their Local Gauge and Local Symmetry Structures

Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor network state from the tensors that form the state. Motivated by the concepts of gauge group and projective symmetry group in the slave-particle/projective construction, and by the low-dimensional gauge-like symmetries of some exactly solvable Hamiltonians, we study the $d$-dimensional gauge structure and the $d$-dimensional symmetry structure of a tensor network state, where $d\leq d_{space}$ with $d_{space}$ the dimension of space. The $d$-dimensional gauge structure and $d$-dimensional symmetry structure allow us to calculate the string operators and $d$-brane operators of the tensor network state. This in turn allows us to calculate many topological properties of the tensor network state, such as ground state degeneracy and quasiparticle statistics.

cond-mat.str-el↗

arXiv2009

Entanglement Entropy at Finite Density from Extremal Black Holes

I compute the entanglement entropy of a strongly coupled 2+1d quantum field theory containing fermions at finite density using gauge/gravity duality. The dual geometry is an extremal black hole in 3+1d Einstein-Maxwell theory. This system was recently shown to exhibit non-Fermi liquid behavior, but the leading geometrical contribution to the entanglement entropy does not produce an expected violation of the boundary law. I discuss this negative result in the context of attempts to find highly entangled states of quantum matter.

hep-th↗

arXiv2009

Entanglement Renormalization and Holography

I show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The generalization is based upon organizing information in a quantum state in terms of scale and defining a higher dimensional geometry from this structure. While states with a finite correlation length typically give simple geometries, the state at a quantum critical point gives a discrete version of anti de Sitter space. Some finite temperature quantum states include black hole-like objects. The gross features of equal time correlation functions are also reproduced in this geometric framework. The relationship between this framework and better understood versions of holography is discussed.

cond-mat.str-el↗

arXiv2008

Tensor-product representations for string-net condensed states

We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry breaking states) and states with long-range entanglement (such as string-net condensed states with topological/quantum order). The tensor product representation provides a kind of 'mean-field' description for topologically ordered states and could be a powerful way to study quantum phase transitions between such states. As an attempt in this direction, we show that the constructed TPS's are fixed-points under a certain wave-function renormalization group transformation for quantum states.

cond-mat.str-el↗