Related papers: Scale invariant transfer matrices and Hamiltionian…
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…
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…
Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At…
The noncompact homogeneous sl(3) invariant spin chains are considered. We show that the transfer matrix with generic auxiliary space is factorized into the product of three sl(3) invariant commuting operators. These operators satisfy the…
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form $S…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…
For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds…
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 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…
Scale invariance supplemented by the requirement of the absence of new heavy particles may play an important role in addressing the hierarchy problem. We discuss how the Standard Model may become scale invariant at the quantum level above a…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
Finite precision measurement factors the Hilbert space of a quantum system into a tensor product $H_{coarse} \otimes H_{fine}$. This is mathematically equivalent to the partition into system and environment which forms the arena for…
The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…
Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the…