Related papers: The breaking of continuous scale invariance to dis…
We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time.…
One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale…
We introduce models of one-dimensional $n(\geq3)$-body problems that undergo phase transition from a continuous scale-invariant phase to a discrete scale-invariant phase. In this paper, we focus on identical spinless particles that interact…
We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase…
Scale invariance in quantum mechanics can be broken in several ways. A well-known example is the breakdown of continuous scale invariance to discrete scale invariance, whose typical realization is the Efimov effect of three-body problems.…
This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions; namely, the coupling of the order-parameter fluctuations to other soft modes, and the resulting impossibility of…
We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level. A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
The spontaneous breaking of a global discrete translational symmetry in the finite, lattice quantum sine-Gordon model is demonstrated by a density matrix renormalization group. A phase diagram in the coupling constant - inverse system size…
We re-consider the quantum mechanics of scale invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
We construct a class of theories which are scale invariant on quantum level in all orders of perturbation theory. In a subclass of these models scale invariance is spontaneously broken, leading to the existence of a massless dilaton. The…
The collective behavior of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics[1]. Characteristic features near the phase transition are that the thermodynamic observables follow…
Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By…
The large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at…
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have…
We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
The cosmological consequences of a simple scalar field model for the generation of Newton's constant through the spontaneous breaking of scale invariance in a curved space-time are again presented and discussed. Such a model leads to a…
Universality, where microscopic details become irrelevant, takes place in thermodynamic phase transitions. The universality is captured by a singular scaling function of the thermodynamic variables, where the scaling exponents are…