Related papers: Constructing Quantum Spin Liquids Using Combinator…
We argue that higher spin fields originate from Hamiltonian mechanics and play a role of gauge fields ensuring covariance of geometric observables such as length and volume with respect to canonical transformations in the same way as a…
In the model of a fermion field coupled to loop quantum gravity, we consider the Gauss and the Hamiltonian constraints. According to the explicit solutions to the Gauss constraint, the fermion spins and the gravitational spin networks…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to non-trivial permutation symmetries (beyond…
We construct the Hermitian Schr\"{o}dinger Hamiltonian of spin-less as well as the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field that are confined to cylindrical and spherical surfaces. The approach does…
Symmetry is a guiding principle in physics that allows to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role because it protects topological…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
The interplay of symmetry and topological order leads to a variety of distinct phases of matter, the Symmetry Enriched Topological (SET) phases. Here we discuss physical observables that distinguish different SETs in the context of Z$_2$…
Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to…
Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a…
The neat formulation that describes the gauge interactions associated with internal symmetries is extended to the case of a simple, yet non-trivial, symmetry group structure which mixes gravity and electromagnetism by associating a gauge…
The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the $N$ site $\mathfrak{sl}_{2}$ $XXX$ spin chain (for infinite dimensional…
The aim of the present article is to describe the symmetry structure of a general gauge (singular) theory, and, in particular, to relate the structure of gauge transformations with the constraint structure of a theory in the Hamiltonian…
In a quantum ring connected with two external leads the spin properties of an incoming electron are modified by the spin-orbit interaction resulting in a transformation of the qubit state carried by the spin. The ring acts as a one qubit…
In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…
We show that Hall conductance and its non-abelian and higher-dimensional analogs are obstructions to promoting a symmetry of a state to a gauge symmetry. To do this, we define a local Lie algebra over a Grothendieck site as a pre-cosheaf of…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
We suggest that the physically irrelevant choice of a representative worldline of a relativistic spinning particle should correspond to a gauge symmetry in an action approach. Using a canonical formalism in special relativity, we identify a…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…