Nonlocal Conformal Theories Have State-dependent Central Charges

Using the recently developed fractional Virasoro algebra cite{la_nave_fractional_2019}, we construct a class of nonlocal CFTs with OPEs of the form $T_k(z)Phi(w) sim frac{ h_gamma Phi}{(z-w)^{1+gamma}}+frac{partial_w^gamma Phi}{z-w},$ and $T_k(z)T_k(w) sim frac{ c_kZ_gamma}{(z-w)^{3gamma+1}}+frac{(1+gamma ) T_k(w)}{(z-w)^{1+gamma}}+frac{partial^gamma_w T_k}{z-w}$ which naturally results in a central charge, $c_k$, that is state-dependent, with $k$ indexing a particular grading. Our work indicates that only those theories which are nonlocal have state-dependent central charges, regardless of the pseudo-differential operator content of their action. All others, including certain fractional Laplacian theories, can be mapped onto an equivalent local one using a suitable covering/field redefinition. In addition, we discuss various perturbative implications of deformations of fractional CFTs that realize a fractional Virasoro algebra through the lense of a degree/state-dependent refinement of the 2 dimensional C-theorem.

Free at Last: Bose Metal Uncaged

A Bose metallic phase disrupts the classic two-state superconductor-insulator picture.

Exact Superconducting Instability in a Doped Mott Insulator

Because the cuprate superconductors are doped Mott insulators, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. We consider the Hatsugai-Kohmoto model, an exactly solvable system that is a prototypical Mott insulator above a critical interaction strength at half filling. Upon doping or reducing the interaction strength, our exact calculations show that the system becomes a non-Fermi liquid metal with a superconducting instability. In the presence of a weak pairing interaction, the instability produces a thermal transition to a superconducting phase, which is distinct from the BCS state, as evidenced by a gap-to-transition temperature ratio exceeding the universal BCS limit. The elementary excitations of this superconductor are not Bogoliubov quasiparticles but rather superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. An unexpected feature of this model is that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies as seen in the cuprates as well as a suppression of the superfluid density relative to that in BCS theory.

Local Entropies across the Mott Transition in an Exactly Solvable Model

We study entanglement in the Hatsugai-Kohmoto model, which exhibits a continuous interaction-driven Mott transition. By virtue of the all-to-all nature of its center-of-mass conserving interactions, the model lacks dynamical spectral weight transfer, which is the key to intractability of the Hubbard model for $d>1$. In order to maintain a non-trivial Mott-like electron propagator, SU(2) symmetry is preserved in the Hamiltonian, leading to a ground state that is mixed on both sides of the phase transition. Because of this mixture, even the metal in this model is unentangled between any pair of sites, unlike free fermions whose ground state carries a filling-dependent site-site entanglement. We focus on the scaling behavior of the one- and two-site entropies $s_1$ and $s_2$, as well as the entropy density $s$, of the ground state near the Mott transition. At low temperatures in the two-dimensional Hubbard model, it was observed numerically (Walsh et al., 2018, arXiv:1807.10409) that $s_1$ and $s$ increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model, $s_1$ acquires the constant value $ln4$ even at the Mott transition. The ground states non-trivial entanglement structure is manifest in $s_2$ and $s$ which decrease into the metal, and thereby act as sharp signals of the Mott transition in any dimension. Specifically, we find that in one dimension, $s_2$ and $s$ exhibit kinks at the transition while in $d=2$, only $s$ exhibits a kink.

Quantum Critical Diffusion and Thermodynamics in Lifshitz Holography

We present the full charge and energy diffusion constants for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. Therein we compute the fully renormalized static thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking entropy and Smarr-like relationship. Our exact computation demonstrates a modification to the Lifshitz Ward identity for the EMD theory. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. While our exact results corroborate anticipated bounds, we are able to demonstrate that the diffusivities are governed by the engineering dimension of the diffusion coefficient, $[D]=2-z$. Consequently, a $beta$-function defined as the derivative of the trace of the diffusion matrix with respect to the effective lattice spacing changes sign precisely at $z=2$. At $z=2$, the diffusion equation exhibits perfect scale invariance and the corresponding diffusion constant is the pure number $1/d_s$ for both the charge and energy sectors, where $d_s$ is the number of spatial dimensions. Further, we find that as $ztoinfty$, the charge diffusion constant vanishes, indicating charge localization. Deviation from universal decoupled transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions.