Related papers: Lieb-Robinson bounds in the continuum via localize…
We revisit bosonization of non-relativistic fermions in one space dimension. Our motivation is the recent work on bubbling half-BPS geometries by Lin, Lunin and Maldacena (hep-th/0409174). After reviewing earlier work on exact bosonization…
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…
We establish the quantum mechanics of composite fermions based on the dipole picture initially proposed by Read. It comprises three complimentary components: a wave equation for determining the wave functions of a composite fermion in ideal…
The Hall effect, which originates from the motion of charged particles in magnetic fields, has deep consequences for the description of materials, extending far beyond condensed matter. Understanding such an effect in interacting systems…
The relational framework of canonical quantum gravity with non-ultralocal constraints is explored. After demonstrating the absence of anomalies, a spatially discretized version of the relational framework is introduced. This allows the…
In this paper we propose a model of the fractional quantum Hall effect within conventional one-dimensional bosonization. It is shown that in this formalism the resulting bosonized fermion operator corresponding to momenta of Landau gauge…
We consider interacting fermions in a magnetic field on a two-dimensional lattice with the periodic boundary conditions. In order to measure the Hall current, we apply an electric potential with a compact support. Then, due to the Lorentz…
It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape.…
We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case…
The difference between boson and fermion dynamics in quasi-one-dimensional lattices is studied with exact simulations of particle motion and by calculating the persistent current in small quantum rings. We consider three different lattices…
We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
The commutator between operators at different space and time has been a diagnostic for locality of unitary evolution. Most existing results are either for specific tractable (random) Hamiltonians(Out-of-Time-Order-Correlators calculations),…
Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…
We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the $z$ direction, the parallel component of the magnetic field introduces…
We investigate the dynamics of two identical spinless fermions on a one-dimensional lattice with open boundary conditions (OBC), subject to quasiperiodic long-range interactions. Using numerical exact diagonalization (ED), we study this…
We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.
We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a…
Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example the fractional quantum Hall effect at $\nu=n/(2pn\pm…
Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…