Related papers: Topology, geometry and quantum interference in con…
Motivated by the connection between gauge field topology and the axial anomaly in fermion currents, I use the fourth power of the naive Dirac operator to define a local lattice measure of topological charge. For smooth gauge fields this…
We show that, quite generally, quantum geometry plays a major role in determining the low-energy physics in strongly correlated lattice models at fractional band fillings. We identify limits in which the Fubini Study metric dictates the…
Important progress in understanding the behavior of hadronic matter at high density has been achieved recently, by adapting the techniques of condensed matter theory. At asymptotic densities, the combination of asymptotic freedom and BCS…
Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…
Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of…
The observable properties of topological quantum matter are often described by topological field theories. We here demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional…
We present a formulation of Quantum Electrodynamics in terms of an antisymmetric tensor gauge field. In this formulation the topological current of this field appears as a source for the electromagnetic field and the topological charge…
We discuss the computation of the quantum effective action of strongly interacting field theories using holographic duality, and its use to determine quasi-equilibrium parameters of first order phase transitions relevant for gravitational…
For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
We apply the ideas of effective field theory to nonrelativistic quantum mechanics. Utilizing an artificial boundary of ignorance as a calculational tool, we develop the effective theory using boundary conditions to encode short-ranged…
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone…
When energy is not conserved, imprints of new physics on observable cosmology might not follow the rules of local effective actions. By capturing dissipative and diffusive effects, open effective field theories account for the possibly…
In this work, we explore topological phases of matter obtained by effectively gauging or fermionizing a system, where the Gauss law constraint is only enforced energetically. In contrast to conventional gauging or fermionization, the…
The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the…
I start by giving a brief overview over new developments in the area of confinement and topology. As an example for the interrelations between topological objects, instantons at finite temperature are discussed. Then I focus on new insights…
We develop the effective field theory approach to torsional modified gravities, a formalism that allows for the systematic investigation of the background and perturbation levels separately. Starting from the usual effective field theory…
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited…