arXiv subjects
Publications and source records attributed to Alexander M. Czajka.
We develop a rigorous topological theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states. We also construct $Ω$-spectra of a class of invertible states and quantum cellular automata, which allows us to classify both anomalies and symmetry protected topological phases up to blend equivalence.
The Nambu-Jona-Lasinio (NJL) model has been widely studied for investigating the chiral phase structure of strongly interacting matter. The study of the thermodynamics of field theories within the framework of Lattice Field Theory is limited by the sign problem, which prevents Monte Carlo evaluation of the functional integral at a finite chemical potential. Using the quantum imaginary time evolution (QITE) algorithm, we construct a quantum simulation for the $(1+1)$ dimensional NJL model at finite temperature and finite chemical potential. We observe consistency among digital quantum simulation, exact diagonalization, and analytical solution, indicating further applications of quantum computing in simulating QCD thermodynamics.
To describe the chiral magnetic effect, the chiral chemical potential $μ_5$ is introduced to imitate the impact of topological charge changing transitions in the quark-gluon plasma under the influence of an external magnetic field. We employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral phase structure and chirality charge density of strongly interacting matter with finite chiral chemical potential $μ_5$ in a quantum simulator. By performing the Quantum imaginary time evolution (QITE) algorithm, we simulate the (1+1) dimensional NJL model on the lattice at various temperature $T$ and chemical potentials $μ$, $μ_5$ and find that the quantum simulations are in good agreement with analytical calculations as well as exact diagonalization of the lattice Hamiltonian.