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Register a new userLow energy physics of interacting bosons with a moat spectrum, and the implications for condensed matter and cold nuclear matter
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We discuss bosonic models with a moat spectrum, where in momentum space the minimum of the dispersion relation is on a sphere of nonzero radius. For spinless bosons with $O(N)$ symmetry, we emphasize the essential difference between $N=2$ and $N > 2$. When $N=2$, there are two phase transitions: at zero temperature, a transition to a state with Bose condensation, and at nonzero temperature, a transition to a spatially inhomogeneous state. When $N > 2$, previous analysis suggests that a mass gap is generated dynamically at any temperature. In condensed matter, a moat spectrum is important for spin-orbit-coupled bosons. For cold nuclear or quarkyonic matter, we suggest that the transport properties, such as neutrino emission, are dominated by the phonons related to a moat spectrum; also, that at least in the quarkyonic phase the nucleons may be a non-Fermi liquid.
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Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in $2+1$ dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the $2+1$-dimensional analog of QED with a single Dirac fermion (a theory known as $U(1)_{1/2}$) is identified with the $O(2)$ Wilson-Fisher fixed point. The gauged version of that fixed point with a Chern-Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped boundary states) and the problem of electrons in the lowest Landau level at half filling. (Our techniques also clarify some points in the fractional Hall effect and its description using flux attachment.) In addition to presenting several consistency checks, we also present plausible (but not rigorous) derivations of the dualities and relate them to $3+1$-dimensional $S$-duality.
The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents $(gamma,delta)$ that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the $(gamma,delta)$ plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when $gamma=delta$ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole $(gamma,delta)$ plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.
We present here a theory of fractional electro-magnetism which is capable of describing phenomenon as disparate as the non-locality of the Pippard kernel in superconductivity and anomalous dimensions for conserved currents in holographic dilatonic models. The starting point for our analysis is the observation that the standard current conservation equations remain unchanged if any differential operator that commutes with the total exterior derivative multiplies the current. Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of Nothers second theorem. Here we develop a consistent theory of electromagnetism that exploits this hidden redundancy in which the standard gauge symmetry in electromagnetism is modified by the rotationally invariant operator, the fractional Laplacian. We show that the resultant theories all allow for anomalous (non-traditional) scaling dimensions of the gauge field and the associated current. Using well known extension theorems and the membrane paradigm, we show that either the boundary (UV) or horizon (IR) theory of holographic dilatonic models are both described by such fractional electromagnetism. We also show that the non-local Pippard kernel introduced to solve the problem of the Meissner effect in elemental superconductors can also be formulated as a special case of fractional electromagnetism. We show that the standard charge quantization rules fail when the gauge field acquires an anomalous dimension. The breakdown of charge quantization is discussed extensively in terms of the experimentally measurable modified Aharonov-Bohm effect in the strange metal phase of the cuprate superconductors.
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here Ill supply some broad, unifying context, both conceptual and historical, for the abundance of results reported at the Nobel Symposium on New Forms of Matter, Topological Insulators and Superconductors. Since they distill some most basic ideas in their simplest forms, these concluding remarks might also serve, for non-specialists, as an introduction.
We derive the free energy for fermions and bosons from fragmentation data. Inspired by the symmetry and pairing energy of the Weizsacker mass formula we obtain the free energy of fermions (nucleons) and bosons (alphas and deuterons) using Landaus free energy approach. We confirm previously obtained results for fermions and show that the free energy for alpha particles is negative and very close to the free energy for ideal Bose gases. Deuterons behave more similarly to fermions (positive free energy) rather than bosons. This is due to their low binding energy, which makes them very fragile, i.e., easily formed and destroyed. We show that the {alpha}-particle fraction is dominant at all temperatures and densities explored in this work. This is consistent with their negative free energy, which favors clusterization of nuclear matter into {alpha}-particles at subsaturation densities and finite temperatures. The role of finite open systems and Coulomb repulsion is addressed.
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