Spectral function and fidelity susceptibility in quantum critical phenomena

In this paper, we derive a simple equality that relates the spectral function $I(k,omega)$ and the fidelity susceptibility $chi_F$, i.e. $% chi_F=lim_{etarightarrow 0}frac{pi}{eta} I(0, ieta)$ with $eta$ being the half-width of the resonance peak in the spectral function. Since the spectral function can be measured in experiments by the neutron scattering or the angle-resolved photoemission spectroscopy(ARPES) technique, our equality makes the fidelity susceptibility directly measurable in experiments. Physically, our equality reveals also that the resonance peak in the spectral function actually denotes a quantum criticality-like point at which the solid state seemly undergoes a significant change.

Construct order parameter from the spectra of mutual information

In this paper, we try to establish a connection between a quantum information concept, i.e. the mutual information, and the conventional order parameter in condensed matter physics. We show that a non-vanishing mutual information at a long distance means the existence of long-range order. By analyzing the entanglement spectra of the reduced density matrix that are used to calculate the mutual information, we show how to find the local order operator used to identify various phases with long-rang order.

A spin chain with spiral orders: perspectives of quantum information and mechanical response

In this paper, we study the ground state of a one-dimensional exactly solvable model with a spiral order. While the models energy spectra is the same as the one-dimensional transverse field Ising model, its ground state manifests spiral order with various periods. The quantum phase transition from a spiral-order phase to a paramagnetic phase is investigated in perspectives of quantum information science and mechanics. We show that the modes of the ground-state fidelity and its susceptibility can tell the change of periodicity around the critical point. We study also the spin torsion modulus which defines the coefficient of the potential energy stored under a small rotation. We find that at the critical point, it is a constant; while away from the critical point, the spin torsion modulus tends to zero.

Scaling of quantum Zeno dynamics in thermodynamic systems

We study the quantum Zeno effect (QZE) in two many-body systems, namely the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick (LMG) model, coupled to a central qubit. Our result shows that in order to observe QZE in the Ising model, the frequency of the projective measurement should be of comparable order to that of the system sizes. The same criterion also holds in the symmetry broken phase of the LMG model while in the models polarized phase, the QZE can be easily observed.

An optical example for classical Zeno effect

In this brief report, we present a proposal to observe the classical zeno effect via the frequent measurement in optics.

Repeater-assisted Zeno effect in classical stochastic processes

As a classical state, for instance a digitized image, is transferred through a classical channel, it decays inevitably with the distance due to the surroundings interferences. However, if there are enough number of repeaters, which can both check and recover the states information continuously, the states decay rate will be significantly suppressed, then a classical Zeno effect might occur. Such a physical process is purely classical and without any interferences of living beings, therefore, it manifests that the Zeno effect is no longer a patent of quantum mechanics, but does exist in classical stochastic processes.

Entropy majorization, thermal adiabatic theorem, and quantum phase transitions

Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the systems quantum critical point. We show that the systems temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in adiabatic processes. We take the one-dimensional transverse-field Ising model and spinless fermion system as concrete examples to show that the inverse temperature might become divergent around their critical points. Since the temperature is a measurable quantity in experiments, our work, therefore, provides a practicable proposal to detect quantum phase transitions.

Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models

We study the fidelity susceptibility in the two-dimensional(2D) transverse field Ising model and the 2D XXZ model numerically. It is found that in both models, the fidelity susceptibility as a function of the driving parameter diverges at the critical points. The validity of the fidelity susceptibility to signal for the quantum phase transition is thus verified in these two models. We also compare the scaling behavior of the extremum of the fidelity susceptibility to that of the second derivative of the ground state energy. From those results, the theoretical argument that fidelity susceptibility is a more sensitive seeker for a second order quantum phase transition is also testified in the two models.

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with $delta$-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the $SU(2|2)$ supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.

Scaling dimension of fidelity susceptibility in quantum phase transitions

We analyze ground-state behaviors of fidelity susceptibility (FS) and show that the FS has its own distinct dimension instead of real systems dimension in general quantum phases. The scaling relation of the FS in quantum phase transitions (QPTs) is then established on more general grounds. Depending on whether the FSs dimensions of two neighboring quantum phases are the same or not, we are able to classify QPTs into two distinct types. For the latter type, the change in the FSs dimension is a characteristic that separates two phases. As a non-trivial application to the Kitaev honeycomb model, we find that the FS is proportional to $L^2ln L$ in the gapless phase, while $L^2$ in the gapped phase. Therefore, the extra dimension of $ln L$ can be used as a characteristic of the gapless phase.