Related papers: Weak integrability breaking perturbations in class…
We study the slowly varying, non-autonomous quantum dynamics of a translation invariant spin or fermion system on the lattice $\mathbb Z^d$. This system is assumed to be initially in thermal equilibrium, and we consider realizations of…
The highly tunable nature of synthetic quantum materials -- both in the solid-state and cold atom contexts -- invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors.…
Quench dynamics in a two-dimensional system of interacting fermions is analyzed within the semiclassical truncated Wigner approximation (TWA). The models with short-range and long-range interactions are considered. We show that in the…
The charge instabilities of electron systems in the square lattice are analyzed near the Van Hove singularity by means of a wilsonian renormalization group approach. We show that the method preserves the spin rotational invariance at all…
The quench dynamics of the Hubbard model in tilted and harmonic potentials is discussed within the semiclassical picture. Applying the fermionic truncated Wigner approximation (fTWA), the dynamics of imbalances for charge and spin degrees…
We study the transition from integrability to chaos for the three-particle Fermi-Pasta-Ulam- Tsingou (FPUT) model. We can show that both the quartic b-FPUT model ($\alpha$ = 0) and the cubic one ($\beta$ = 0) are integrable by introducing…
The inhomogeneity of the media or the external forces usually destroy the integrability of a system. We propose a systematic construction of a class of quantum models, which retains their exact integrability inspite of their explicit…
The thesis contains theoretical study of number of systems in low dimension, which are related to quantum Ising model. The main results are emergence of Majorana fermions in condensed matter system. We discuss an array of cavity-QED system,…
High temperature is usually expected to destroy order: as the Gibbs state approaches the infinite-temperature limit, it becomes an equal-weight ensemble over all states and the system is generically disordered. Recent works showed that…
Traditional theories of electron transport in crystals are based on the Boltzmann equation and do not capture physics arising from quantum coherence. We introduce a transport formalism based on ''orbital Wigner functions'', which accurately…
Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the…
We examine a basic lattice model of interacting fermions that exhibits quadratic band crossing points (QBCPs) in the non-interacting limit. In particular, we consider spinless fermions on the honeycomb lattice with nearest neighbor hopping…
We develop a molecular dynamics framework to compute the mode-resolved phonon spectral density from classical correlations of an annihilation-like phonon variable. For harmonic oscillators, classical molecular dynamics exactly reproduces…
We introduce the parafermionic truncated Wigner approximation ($p$TWA), a semiclassical phase-space framework for simulating the nonequilibrium dynamics of lattice systems with fractional exchange statistics. The method extends truncated…
The weak Mott insulating regime of the triangular lattice Hubbard model exhibits a rich magnetic phase diagram as a result of the ring exchange interaction in the spin Hamiltonian. These phases include the Kalmeyer-Laughlin type chiral spin…
Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…
We discuss weak coupling perturbation theory for lattice actions in which the fermions couple to smeared gauge links. The normally large integrals that appear in lattice perturbation theory are drastically reduced. Even without detailed…
In this essay, we first sketch the development of ideas on the extraordinary dynamics of integrable classical nonlinear and quantum many body Hamiltonians. In particular, we comment on the state of mathematical techniques available for…
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear…
We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical…