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Register a new userQuantum wire networks with local Z2 symmetry
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For a large class of networks made of connected loops, in the presence of an external magnetic field of half flux quantum per loop, we show the existence of a large local symmetry group, generated by simultaneous flips of the electronic current in all the loops adjacent to a given node. Using an ultra-localized single particle basis adapted to this local Z_2 symmetry, we show that it is preserved by a large class of interaction potentials. As a main physical consequence, the only allowed tunneling processes in such networks are induced by electron-electron interactions and involve a simultaneous hop of two electrons. Using a mean-field picture and then a more systematic renormalization-group treatment, we show that these pair hopping processes do not generate a superconducting instability, but they destroy the Luttinger liquid behavior in the links, giving rise at low energy to a strongly correlated spin-density-wave state.
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The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can support Majorana bound states which play a crucial role in the realm of quantum computation. In this work we examine the boundary modes in an interacting quantum wire with a proximity induced pairing term. We solve the system exactly by Bethe Ansatz and show that for certain boundary conditions the spectrum contains bound states localized about either edge. The model is shown to exhibit a first order phase transition as a function of the interaction strength such that for attractive interactions the ground state has bound states at both ends of the wire while for repulsive interactions they are absent. In addition we see that the bound state energy lies within the gap for all values of the interaction strength but undergoes a sharp avoided level crossing for sufficiently strong interaction, thereby preventing its decay. This avoided crossing is shown to occur as a consequence of an exact self-duality which is present in the model.
Landaus spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landaus spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the NH terms splits the spontaneous biorthogonal Z2 symmetry breaking from a (biorthogonal) order-disorder phase transition with gap closing. The sudden change of similarity for two degenerate ground states indicates a new type of quantum phase transition without gap closing accompanied by spontaneous biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model as an example to investigate the anomalous spontaneous symmetry breaking. The numerical results were consistent with the theoretical predictions.
We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.
Motivated by the close correlation between transition temperature ($T_c$) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin Kondo effect is suppressed to low temperatures by Hunds coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground-state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.
Quantum impurity models are prevalent throughout many body physics, providing some prime examples of strongly correlated systems. Aside from being of great interest in themselves they can provide deep insight into the effects of strong correlations in general. The classic example is the Kondo model wherein a magnetic impurity is screened at low energies by a non interacting metallic bath. Here we consider a magnetic impurity coupled to a quantum wire with pairing interaction which dynamically generates a mass gap. Using Bethe Ansatz we solve the system exactly finding that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground state density of states and magnetization in both phases as well as the excitations. In contrast to the well studied case of magnetic impurities in superconductors we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but with quantum fluctuations.
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