Related papers: Phase transitions in spinor quantum gravity on a l…
This series of lectures gives a simple and self-contained introduction to the non-perturbative and background independent loop approach of canonical quantum gravity. The Hilbert space of kinematical quantum states is constructed and a…
When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase…
Loop quantum gravity, a non-perturbative and manifestly background free, quantum theory of gravity implies that at the kinematical level the spatial geometry is discrete in a specific sense. The spirit of background independence also…
We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric…
We propose a model with quantum bosons on the fcc lattice, which has a stable algebraic Bose liquid phase at low energy. We show that this phase is described by emergent quantum gravity at the Gaussian z = 3 Lifshitz fixed point in 3+1…
Some important rigorous results on phase transitions accompanied by the spontaneous breaking of symmetries in statistical mechanics and relativistic quantum field theory are reviewed. Basic ideas, mainly inspired by quantum field theory,…
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge…
Quantum treatment of physical reference frame leads to the Ricci flow of quantum spacetime, which is a quite rigid framework to quantum and renormalization effect of gravity. The theory has a low characteristic energy scale described by a…
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with…
An effective theory is constructed for analyzing a generic phase transition between the quantum spin Hall and the insulator phases. Occurrence of degeneracies due to closing of the gap at the transition are carefully elucidated. For systems…
In this work, we show that the quantum compass model on an square lattice can be mapped to a fermionic model with local density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular…
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to…
Following the reasoning of Claudson and Halpern, it is shown that "fifth-time" stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbitrary, initial and…
We consider a classical fermion and a classical scalar, propagating on two different kinds of 4-dimensional diffeomorphism breaking gravity backgrounds, and we derive the one-loop effective dispersion relation for matter, after integrating…
We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
The phase transition in frustrated spin systems is a fascinated subject in statistical physics. We show the result obtained by the Wang-Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple…
We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional…
A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…