Origin of the Mott Gap

We show exactly that the only charged excitations that exist in the strong-coupling limit of the half-filled Hubbard model are gapped composite excitations generated by the dynamics of the charge $2e$ boson that appears upon explicit integration of the high-energy scale. At every momentum, such excitations have non-zero spectral weight at two distinct energy scales separated by the on-site repulsion $U$. The result is a gap in the spectrum for the composite excitations accompanied by a discontinuous vanishing of the density of states at the chemical potential when $U$ exceeds the bandwidth. Consequently, we resolve the long-standing problem of the cause of the charge gap in a half-filled band in the absence of symmetry breaking.Comment: 6 pages, 2 figures: Expanded Published versio

Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants

We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral on $M_n$ defines a quantum state on the boundary, in the $n$-fold tensor product of the torus Hilbert space. We focus on the case where $M_n$ is the link-complement of some $n$-component link inside the three-sphere $S^3$. The entanglement entropies of the resulting states define framing-independent link invariants which are sensitive to the topology of the chosen link. For the Abelian theory at level $k$ ($G= U(1)_k$) we give a general formula for the entanglement entropy associated to an arbitrary $(m|n-m)$ partition of a generic $n$-component link into sub-links. The formula involves the number of solutions to certain Diophantine equations with coefficients related to the Gauss linking numbers (mod $k$) between the two sublinks. This formula connects simple concepts in quantum information theory, knot theory, and number theory, and shows that entanglement entropy between sublinks vanishes if and only if they have zero Gauss linking (mod $k$). For $G = SU(2)_k$, we study various two and three component links. We show that the 2-component Hopf link is maximally entangled, and hence analogous to a Bell pair, and that the Whitehead link, which has zero Gauss linking, nevertheless has entanglement entropy. Finally, we show that the Borromean rings have a "W-like" entanglement structure (i.e., tracing out one torus does not lead to a separable state), and give examples of other 3-component links which have "GHZ-like" entanglement (i.e., tracing out one torus does lead to a separable state).Comment: 37 pages, 19 figure

The effects of a background potential in star cluster evolution: a delay in the relaxation time-scale and runaway collision processes

Runaway stellar collisions in dense star clusters are invoked to explain the presence of very massive stars or blue stragglers in the center of those systems. This process has also been explored for the first star clusters in the Universe and shown to yield stars that may collapse at some points into an intermediate mass black hole. Although the early evolution of star clusters requires the explicit modeling of the gas out of which the stars form, these calculations would be extremely time-consuming and often the effects of the gas can be accurately treated by including a background potential to account for the extra gravitational force. We apply this approximation to model the early evolution of the first dense star clusters formed in the Universe by performing $N$-body simulations, our goal is to understand how the additional gravitational force affects the growth of a very massive star through stellar mergers in the central parts of the star cluster. Our results show that the background potential increases the velocities of the stars, causing an overall delay in the evolution of the clusters and in the runaway growth of a massive star at the center. The population of binary stars is lower due to the increased kinetic energy of the stars, initially reducing the number of stellar collisions, and we show that relaxation processes are also affected. Despite these effects, the external potential enhances the mass of the merger product by a factor $\sim$2 if the collisions are maintained for long times.Comment: 16 pages. Accepted for publication in Astronomy and Astrophysic

Interfaces and the extended Hilbert space of Chern-Simons theory

The low energy effective field theories of $(2+1)$ dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In \cite{Fliss:2017wop} the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.Comment: 46 pages, many figures, 1 appendix; v2: fixed affiliations, minor revisions, added reference

Dynamics of the DBI Spike Soliton

We compare oscillations of a fundamental string ending on a D3-brane in two different settings: (1) a test-string radially threading the horizon of an extremal black D3-brane and (2) the spike soliton of the DBI effective action for a D3-brane. Previous work has shown that overall transverse modes of the test-string appear as l=0 modes of the transverse scalar fields of the DBI system. We identify DBI world-volume degrees of freedom that have dynamics matching those of the test-string relative transverse modes. We show that there is a map, resembling T-duality, between relative and overall transverse modes for the test-string that interchanges Neumann and Dirichlet boundary conditions and implies equality of the absorption coefficients for both modes. We give general solutions to the overall and relative transverse parts of the DBI coupled gauge and scalar system and calculate absorption coefficients for the higher angular momentum modes in the low frequency limit. We find that there is a nonzero amplitude for l>0 modes to travel out to infinity along the spike, demonstrating that the spike remains effectively 3+1-dimensional.Comment: 15 pages, 1 figur