We present a mechanism for accelerated expansion of the universe in the generic case of negative-curvature compactifications of M-theory, with minimal ingredients. M-theory on a hyperbolic manifold with small closed geodesics supporting Casimir energ
y -- along with a single classical source (7-form flux) -- contains an immediate 3-term structure for volume stabilization at positive potential energy. Hyperbolic manifolds are well-studied mathematically, with an important rigidity property at fixed volume. They and their Dehn fillings to more general Einstein spaces exhibit explicit discrete parameters that yield small closed geodesics supporting Casimir energy. The off-shell effective potential derived by M. Douglas incorporates the warped product structure via the constraints of general relativity, screening negative energy. Analyzing the fields sourced by the localized Casimir energy and the available discrete choices of manifolds and fluxes, we find a regime where the net curvature, Casimir energy, and flux compete at large radius and stabilize the volume. Further metric and form field deformations are highly constrained by hyperbolic rigidity and warping effects, leading to calculations giving strong indications of a positive Hessian, and residual tadpoles are small. We test this via explicit back reacted solutions and perturbations in patches including the Dehn filling regions, initiate a neural network study of further aspects of the internal fields, and derive a Maldacena-Nunez style no-go theorem for Anti-de Sitter extrema. A simple generalization incorporating 4-form flux produces axion monodromy inflation. As a relatively simple de Sitter uplift of the large-N M2-brane theory, the construction applies to de Sitter holography as well as to cosmological modeling, and introduces new connections between mathematics and the physics of string/M theory compactifications.
We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds
for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.
We revisit the interplay between superconductivity and quantum criticality when thermal effects from virtual static bosons are included. These contributions, which arise from an effective theory compactified on the thermal circle, strongly affect fie
ld-theoretic predictions even at small temperatures. We argue that they are ubiquitous in a wide variety of models of non-Fermi liquid behavior, and generically produce a parametric suppression of superconducting instabilities. We apply these ideas to non-Fermi liquids in $d=2$ space dimensions, obtained by coupling a Fermi surface to a Landau-damped soft boson. Extending previous methods developed for $d=3-epsilon$ dimensions, we determine the dynamics and phase diagram. It features a naked quantum critical point, separated by a continuous infinite order transition from a superconducting phase with strong non-Fermi liquid corrections. We also highlight the relevance of these effects for (numerical) experiments on non-Fermi liquids.
Non-Fermi liquids in $d=2$ spatial dimensions can arise from coupling a Fermi surface to a gapless boson. At finite temperature, however, the perturbative quantum field theory description breaks down due to infrared divergences. These are caused by v
irtual static bosonic modes, and afflict both fermionic and bosonic correlators. We show how these divergences are resolved by self-consistent boson and fermion self-energies that resum an infinite class of diagrams and correct the standard Eliashberg equations. Extending a previous approach in $d=3-epsilon$ dimensions, we find a new thermal non-Fermi liquid regime that violates the scaling laws of the zero temperature fixed point and dominates over a wide range of scales. We conclude that basic properties of quantum phase transitions and quantum-classical crossovers at finite temperature are modified in crucial ways in systems with soft bosonic fluctuations, and we begin a study of some of the phenomenological consequences.
A zero-site density matrix renormalization algorithm (DMRG0) is proposed to minimize the energy of matrix product states (MPS). Instead of the site tensors themselves, we propose to optimize sequentially the message tensors between neighbor sites, wh
ich contain the singular values of the bipartition. This leads to a local minimization step that is independent of the physical dimension of the site. Conceptually, it separates the optimization and decimation steps in DMRG. Furthermore, we introduce two new global perturbations based on the optimal low-rank correction to the current state, which are used to avoid local minima. They are determined variationally as the MPS closest to the one-step correction of the Lanczos or Jacobi-Davidson eigensolver, respectively. These perturbations mainly decrease the energy and are free of hand-tuned parameters. Compared to existing single-site enrichment proposals, our approach gives similar convergence ratios per sweep while the computations are cheaper by construction. Our methods may be useful in systems with many physical degrees of freedom per lattice site. We test our approach on the periodic Heisenberg spin chain for various spins, and on free electrons on the lattice.
