Related papers: The higher-order phase transition in toroidal CDT
Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…
The role of topology change in a fundamental theory of quantum gravity is still a matter of debate. However, when regarding string theory as two-dimensional quantum gravity, topological fluctuations are essential. Here we present a third…
The chiral phase transition at finite temperature T and/or chemical potential $\mu$ is studied using the QCD-like theory with a variational approach. The ``QCD-like theory'' means the improved ladder approximation with an infrared cutoff in…
Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but…
Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry.…
"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of the sum over spacetime histories, providing us with a non-perturbative formulation of quantum gravity. The ultraviolet fixed points of the lattice theory can be…
The two-dimensional causal dynamical triangulations ($2$d CDT) is a lattice model of quantum geometry. In $2$d CDT, one can deal with the quantum effects analytically and explore the physics through the continuum limit. The continuum theory…
The Causal Dynamical Triangulation model of quantum gravity (CDT) is a proposition to evaluate the path integral over space-time geometries using a lattice regularization with a discrete proper time and geometries realized as simplicial…
We consider a model of restricted dimers coupled to two-dimensional causal dynamical triangulations (CDT), where the dimer configurations are restricted in the sense that they do not include dimers in regions of high curvature. It is shown…
We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently…
We analyze the phase diagram of compact QED on the torus with a chirally symmetric four fermion interaction added to the usual Wilson action. Inside a mean field approximation for the four fermion term, a line of first order phase…
We report on recently performed simulations of Causal Dynamical Triangulations (CDT) in 2+1 dimensions aimed at studying its effective dynamics in the continuum limit. Two pieces of evidence from completely different measurements are…
Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature…
We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of…
We predict the existence of novel first-order phase transitions in a general class of multi-qubit-cavity systems. Apart from atomic systems, the associated super-radiant phase transition should be observable in a variety of solid-state…
Causal Dynamical Triangulations (CDT) is a lattice theory where aspects of quantum gravity can be studied. Two-dimensional CDT can be solved analytically and the continuum (quantum) Hamiltonian obtained. In this article we show that this…
We study bosonic symmetry protected topological (SPT) phases with $C_{2}$ rotational symmetry in four spatial dimensions which is not captured by the group cohomology classification. By using the topological crystal approach, we show that…
In these lectures we describe how a theory of quantum gravity may be constructed in terms of a lattice formulation based on so-called causal dynamical triangulations (CDT). We discuss how the continuum limit can be obtained and how to…
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came…
Using Monte-Carlo computer simulations, we study the impact of matter fields on the geometry of a typical quantum universe in the CDT model of lattice quantum gravity. The quantum universe has the size of a few Planck lengths and the…