Planar systems admit quantum states that are neither bosons nor fermions, ie, whose
angular momentum is neither integer nor half-integer. After a discussion of some examples …

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals
with classical and quantum dualities in a unified fashion explaining the precise connection …

Presenting the physics of the most challenging problems in condensed matter using the
conceptual framework of quantum field theory, this book is of great interest to physicists in …

We present a systematic recipe for generating and classifying duality transformations in one-
dimensional quantum lattice systems. Our construction emphasizes the role of global …

Gauge field theories play a central role in modern physics and are at the heart of the
Standard Model of elementary particles and interactions. Despite significant progress in …

According to a fundamental result in quantum computing, any unitary transformation on a
composite system can be generated using so-called 2-local unitaries that act only on two …

We present a theory of the fractional quantum Hall effect (FQHE) based on a second-
quantized fermion path-integral approach. We show that the problem of interacting electrons …

Considering recent advancements and successes in the development of efficient quantum
algorithms for electronic structure calculations—alongside impressive results using machine …

We investigate the simulation of fermionic systems on a quantum computer. We show in
detail how quantum computers avoid the dynamical sign problem present in classical …

Physical systems, characterized by an ensemble of interacting constituents, can be
represented and studied by different algebras of operators (observables). For example, a …