Fidelity, dynamic structure factor, and susceptibility in critical phenomena

Motivated by the growing importance of fidelity in quantum critical phenomena, we establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through a newly introduced concept: fidelity susceptibility. Our discovery, as shown by some examples, facilitates the evaluation of fidelity in terms of susceptibility using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium.Comment: 4 pages, 2 figures, final version accepted by PR

Lower and upper bounds on the fidelity susceptibility

We derive upper and lower bounds on the fidelity susceptibility in terms of macroscopic thermodynamical quantities, like susceptibilities and thermal average values. The quality of the bounds is checked by the exact expressions for a single spin in an external magnetic field. Their usefulness is illustrated by two examples of many-particle models which are exactly solved in the thermodynamic limit: the Dicke superradiance model and the single impurity Kondo model. It is shown that as far as divergent behavior is considered, the fidelity susceptibility and the thermodynamic susceptibility are equivalent for a large class of models exhibiting critical behavior.Comment: 19 page

Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

We study exactly both the ground-state fidelity susceptibility and bond-bond correlation function in the Kitaev honeycomb model. Our results show that the fidelity susceptibility can be used to identify the topological phase transition from a gapped A phase with Abelian anyon excitations to a gapless B phase with non-Abelian anyon excitations. We also find that the bond-bond correlation function decays exponentially in the gapped phase, but algebraically in the gapless phase. For the former case, the correlation length is found to be $1/\xi=2\sinh^{-1}[\sqrt{2J_z -1}/(1-J_z)]$, which diverges around the critical point $J_z=(1/2)^+$.Comment: 7 pages, 6 figure

Fidelity susceptibility, scaling, and universality in quantum critical phenomena

We study fidelity susceptibility in one-dimensional asymmetric Hubbard model, and show that the fidelity susceptibility can be used to identify the universality class of the quantum phase transitions in this model. The critical exponents are found to be 0 and 2 for cases of half-filling and away from half-filling respectively.Comment: 4 pages, 4 figure

Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility

We study the critical properties of the Lipkin-Meshkov-Glick Model in terms of the fidelity susceptibility. By using the Holstein-Primakoff transformation, we obtain explicitly the critical exponent of the fidelity susceptibility around the second-order quantum phase transition point. Our results provide a rare analytical case for the fidelity susceptibility in describing the universality class in quantum critical behavior. The different critical exponents in two phases are non-trivial results, indicating the fidelity susceptibility is not always extensive.Comment: 3 figure

Effects of environmental parameters to total, quantum and classical correlations

We quantify the total, quantum, and classical correlations with entropic measures, and quantitatively compare these correlations in a quantum system, as exemplified by a Heisenberg dimer which is subjected to the change of environmental parameters: temperature and nonuniform external field. Our results show that the quantum correlation may exceed the classical correlation at some nonzero temperatures, though the former is rather fragile than the later under thermal fluctuation. The effect of the external field to the classical correlation is quite different from the quantum correlation.Comment: 6 pages, 4 figure

Entanglement manipulation by a local magnetic pulse

A scheme for controlling the entanglement of a two-qubit system by a local magnetic pulse is proposed. We show that the entanglement of the two-qubit system can be increased by sacrificing the coherence in ancillary degree of freedom, which is induced by a local manipulation.Comment: 4 pages, 2 figure

Density-functional fidelity approach to quantum phase transitions

We propose a new approach to quantum phase transitions in terms of the density-functional fidelity, which measures the similarity between density distributions of two ground states in parameter space. The key feature of the approach, as we will show, is that the density-functional fidelity can be measured easily in experiments. Both the validity and versatility of the approach are checked by the Lipkin-Meshkov-Glick model and the one-dimensional Hubbard model.Comment: 4 pages, 2 figures, submitted to Chin. Phys. Let

Universal role of correlation entropy in critical phenomena

In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the extensive properties of the thermal entropy $S($AB$)= S($A$)+S($B$)$ is violated. This observation motivates us to introduce the concept of correlation entropy between two points, as measured by mutual information in the information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of the subsystem formed by any two distant particles with long-range correlation. This relation actually indicates the universal role of the correlation entropy in understanding critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: two-dimensional Ising model and one-dimensional transverse field Ising model. Therefore, the correlation entropy provides us with a new physical intuition in critical phenomena from the point of view of the information theory.Comment: 10 pages, 9 figure

Phase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement

We study the ground-state phase diagram of a Bose-Fermi mixture loaded in a one-dimensional optical lattice by computing the ground-state fidelity and quantum entanglement. We find that the fidelity is able to signal quantum phase transitions between the Luttinger liquid phase, the density-wave phase, and the phase separation state of the system; and the concurrence can be used to signal the transition between the density-wave phase and the Ising phase.Comment: 4 pages 3 figure