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We study the single-particle density of states of one-dimensional and two-dimensional quantum disordered systems with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two…
The N-vector cubic model relevant, among others, to the physics of the randomly dilute Ising model is analyzed in arbitrary dimension by means of an exact renormalization-group equation. This study provides a unified picture of its critical…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
We study the non-equilibrium dynamics of a coherently split one-dimensional (1d) Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to…
We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index $\k$ which relates $\g_{string}$ for the bosonic string to the exponent $\a$ of the specific heat…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map…
A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic…
In this doctoral thesis we have studied the quantum properties of several models which have been classified as statical and dynamical systems. The first part has been devoted to investigate the properties of the statical models including…
We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
It has been shown that the conditional probability distributions obtained by performing measurements on an uncharacterized physical system can be used to infer its underlying dimension in a device-independent way both in the classical and…
Domain walls and droplet-like excitation of the random-field Ising magnet are studied in d={3,4,5,6,7} dimensions by means of exact numerical ground-state calculations. They are obtained using the established mapping to the…
A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…
We study the quantum fidelity (groundstate overlap) near quantum phase transitions of the Ising universality class in one dimensional (1D) systems of finite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls, the…
We compare quantum dynamics in the presence of Markovian dephasing for a particle hopping on a chain and for an Ising domain wall whose motion leaves behind a string of flipped spins. Exact solutions show that on an infinite chain, the…
As the realization of a fully operational quantum computer remains distant, quantum simulation, whereby one quantum system is engineered to simulate another, becomes a key goal of great practical importance. Here we report on a variational…
We review some recent work on the occurrence of coalescing eigenstates at exceptional points in non-Hermitian systems and their influence on physical quantities. We particularly focus on quantum dynamics near exceptional points in open…
Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that…