The quantum anomaly can be written alternatively into a form violating conservation laws or as non-gauge invariant currents seen explicitly on the example of chiral anomaly. By reinterpreting the many-body averaging, the connection to Pauli-Villars regularization is established which gives the anomalous term a new interpretation as arising from quantum fluctuations by many-body correlations at short distances. This is exemplified by using an effective many-body quantum potential which realizes quantum Slater sums by classical calculations. It is shown that these quantum potentials avoid the quantum anomaly but approaches the same anomalous result by many-body correlations. A measure for the quality of quantum potentials is suggested to describe these quantum fluctuations in the mean energy. Consequently quantum anomalies might be a short-cut way of single-particle field theory to account for many-body effects. This conjecture is also supported since the chiral anomaly can be derived by a completely conserving quantum kinetic theory.
One fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept, challenging our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single site resolved measurements we track the relaxation dynamics of an initially prepared out-of-equ…
We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thouroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two `toy applications' from the world of Luttinger liquid physics: the survival of power laws in lowly-excited states as well as the spectral function of high-energy `block' excitations which feature several single-parti…
Short length quantum wires (quantum contacts) exhibit a conductance structure at the value of conductance close to 0.7 \times 2e^2/h. The structure is also called the conductance anomaly. In longer contacts the structure evolves to the lower values of conductance. We demonstrate that this structure is related to the development of charge density waves within the contact. This is a precursor for Wigner crystallization. Many-body Hartree-Fock calculations of conductance are performed. The results are in agreement with experimental data.
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make an important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that -in contradiction to the conventional Hertz-Millis-Moriya theory- its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electro…
A shallow potential well in a near-perfect quantum wire will bind a single-electron and behave like a quantum dot, giving rise to spin-dependent resonances of propagating electrons due to Coulomb repulsion and Pauli blocking. It is shown how this may be used to generate full entanglement between static and flying spin-qubits near resonance in a two-electron system via singlet or triplet spin-filtering. In a quantum wire with many electrons, the same pairwise scattering may be used to explain conductance, thermopower and shot-noise anomalies, provided the temperature/energy scale is sufficientl…
A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws"' could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative n…
In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum systems including symmetry-protected topological states and topologically ordered states. Chapter 1. Introduction. Chapter 2. Geometric phase, wavefunction overlap, spacetime path integral and topological invariants. Chapter 3. Aspects of Symmetry. Chapter 4. Aspects of Topology. Chapter 5. Aspects of Anomalies. Chapter 6. Quantum Statistics and Spacetime Surgery.…
Strong disorder in interacting quantum systems can give rise to the phenomenon of Many-Body Localization (MBL), which defies thermalization due to the formation of an extensive number of quasi local integrals of motion. The one particle operator content of these integrals of motion is related to the one particle orbitals of the one particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015); Ann. Phys. 529, 1600356 (2017)]. We study the properties of the one particle orbitals of many-body eigenstates…
We report on a study of electronic transport in semi-metallic Bi$_{0.96}$Sb$_{0.04}$. At zero field, the system is a very dilute Fermi liquid displaying a T$^{2}$ resistivity with an enhanced prefactor. Quantum oscillations in resistivity as well as in Hall, Nernst and Seebeck responses of the system are detectable and their period quantifies the shrinking of the Fermi surface with antimony doping. For a field along the trigonal axis, the quantum limit was found to occur at a field as low as 3T. An ultraquantum anomaly at twice this field was detected in both charge transport and Nernst respon…
