 Award ID(s):
 1914679
 Publication Date:
 NSFPAR ID:
 10337803
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 3
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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A bstract We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the “tail” part of the propagator and can be summed using a variant of Starobinsky’s stochastic formalism involving a curvaturedependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvaturedependent renormalizations. Explicit results are derived at 1loop and 2loop orders.

Dimerized valence bond solids appear naturally in spin1/2 systems on bipartite lattices, with the geometric frustrations playing a key role both in their stability and the eventual `melting' due to quantum fluctuations. Here, we ask the question of the stability of such dimerized solids in spin1 systems, taking the anisotropic square lattice with bilinear and biquadratic spinspin interactions as a paradigmatic model. The lattice can be viewed as a set of coupled spin1 chains, which in the limit of vanishing interchain coupling are known to possess a stable dimer phase. We study this model using the density matrix renormalization group (DMRG) and infinite projected entangledpair states (iPEPS) techniques, supplemented by the analytical meanfield and linear flavor wave theory calculations. While the latter predicts the dimer phase to remain stable up to a reasonably large interchaintointrachain coupling ratio r≲0.6, the DMRG and iPEPS find that the dimer solid melts for much weaker interchain coupling not exceeding r≲0.15. We find the transition into a magnetically ordered state to be first order, manifested by a hysteresis and order parameter jump, precluding the deconfined quantum critical scenario. The apparent lack of stability of dimerized phases in 2D spin1 systems is indicative of strong quantummore »

One dimensional (1d) interacting systems with local Hamiltonianscan be studied with various welldeveloped analytical methods.Recently novel 1d physics was found numerically in systems witheither spatially nonlocal interactions, or at the 1d boundary of2d quantum critical points, and the critical fluctuation in thebulk also yields effective nonlocal interactions at the boundary.This work studies the edge states at the 1d boundary of 2dstrongly interacting symmetry protected topological (SPT) states,when the bulk is driven to a disorderorder phase transition. Wewill take the 2d AffleckKennedyLiebTasaki (AKLT) state as anexample, which is a SPT state protected by the SO(3) spinsymmetry and spatial translation. We found that the original(1+1)d boundary conformal field theory of the AKLT state isunstable due to coupling to the boundary avatar of the bulkquantum critical fluctuations. When the bulk is fixed at thequantum critical point, within the accuracy of our expansionmethod, we find that by tuning one parameter at the boundary,there is a generic direct transition between the long rangeantiferromagnetic Néel order and the valence bond solid (VBS)order. This transition is very similar to the NéelVBStransition recently found in numerical simulation of a spin1/2chain with nonlocal spatial interactions. Connections between ouranalytical studies and recent numerical results concerning theedge states of the 2dmore »

Abstract We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1 + 1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian
H _{Δ}. The holonomy correction inH _{Δ}is implemented by the scheme regularization with a Planckian area scale Δ (which often chosen as the minimal area gap in loop quantum gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. $\overline{\mu}$R _{μνρσ}R ^{μνρσ}∼ 1/Δ^{2}. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry dS_{2}×S ^{2}with Planckian radii . The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of blackholetowhitehole transition. $\sim \sqrt{\mathrm{\Delta}}$ 
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χ _{0}is the noninteracting Pauli susceptibility.