Non-equilibrium phases, criticality and information scrambling in low-dimensional quantum systems

Abstract

This thesis contains research works encompassing different areas of quantum condensed matter physics in low dimensions ranging from non-equilibrium phases of matter, quantum criticality in equilibrium systems and quantum information scrambling in spin-chains.

In the first chapter of the thesis, we introduce different concepts and methods relevant to the later chapters.

In the second chapter, we demonstrate in a variety of tight-binding models, with and without a staggered on-site potential, that periodic driving can generate non-topological states localized at the ends of a finite-sized system. Further, we study transport in this periodically driven model using the Floquet scattering matrix formalism and show that these edge states in a short wire can give rise to zero-bias peaks in the differential conductance at energies equal to the quasienergies of the edge states. Additionally, we look at the effects of interaction on a periodically driven bosonic Hubbard model and show that periodic driving can enhance the possibility of the formation of two-body bound states localized at the ends of the system.

In the third chapter of the thesis, we discuss a non-equilibrium pathway to engineer a tunable spin model with non-trivial three-spin interactions using a periodically varying electric field on a strongly correlated electronic system on a triangular lattice. Using Floquet perturbation theory, we find that the effective Hamiltonian up to the third order in the hopping has two-spin Heisenberg couplings with different magnitudes in the three different directions and a three-spin chiral interaction term. Consequently, we show numerically using Exact Diagonalization (ED), that this effective spin model hosts several ordered (three collinear and one coplanar) and three spin-liquid phases.

In the fourth chapter, we study the equilibrium critical phenomena in a one-dimensional spin-1/2 model with Ising type three-spin interaction and a transverse magnetic field which is a generalization of the transverse field Ising model preserving the duality. Using large-scale ED and DMRG we find that model undergoes a continuous phase transition at the self-dual point like the transverse field Ising model. However, the criticality is found to be more subtle and we present evidence that the universality class might be same as that of the 4-state Potts model. Another facet of the model is that the model albeit being non-integrable hosts eigenstates exactly at the middle of the spectrum which do not thermalize and are known as quantum many-body scars. We also show that many of these scar states can be represented exactly using products of spin-singlets and triplets.

The last part of this thesis consists of two chapters related to the quantum information scrambling in quantum many-body systems, quantified using the out-of-time-ordered correlator (OTOC) of local operators.

In the fifth chapter, we discuss the effect of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain. We find that both kind of edge states trap quantum information in the sense of OTOC at the edge of the system. Additionally, the OTOC in presence of the non-topological end modes exhibit pronounced oscillations at the end, whose frequency is given by the gap between the quasienergies of these mode. This study also reveals an intriguing behaviour of spin-operators, which are non-local in terms of Jordan Wigner fermions, shows an ‘unscrambling’ effect upon reflection from the end of the system in addition to scrambling.

In the sixth chapter, the last work chapter we attempt to understand the mechanism of the unscrambling phenomena in a simpler setting. To this end we consider the ground state OTOCs in the transverse field Ising model which also shows similar phenomena. Using a perturbative approach, we explicitly show that in the paramagnetic phase, the scrambling and unscrambling are due to the scattering of a pair of low-energy spin-flip excitations. In the ferromagnetic phase, these are explained by the motion of a domain-wall excitation. At the end, we summarise our results and discuss possible future studies in these areas of research.