In the paper, 1 the rescaled function (χ m − χ )/χ [Eq. (8)] was defined as a function of L ν (λ − λ m ) and the exponent ν was identified as the critical exponent of the correlation length. In fact, the exponent of L should have been written as 1/ν in order for ν to be the critical exponent of the correlation length. Accordingly, the corresponding values of ν, including those obtained in Refs. 2-4, should be changed to 1/ν. In particular, scaling relations such as Eq. (9) should read(1)[Eq. (9) has d = 1 substituted.] This does not affect the results of the paper.

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.PACS numbers: 05.70.Fh, 71.10.Fd, Quantum phase transitions (QPTs) at zero temperature are characterized by the significant change in the ground state of a many-body system as a parameter λ in the system Hamiltonian H(λ) is varied across a point λ c [1]. This primary observation enlightens people to explore the role of fidelity, a concept emerging from quantum information theory [2], in the critical phenomena [3,4]. Since fidelity is a measure of similarity between states, a dramatic change in the structure of the ground state around a quantum critical point should result in a great difference between the two ground states on the both sides of the critical point. Such a fascinating prospect was firstly confirmed in the 1D XY model where the fidelity shows a narrow trough at the phase transition point [3,4]. From then on, the fidelity was further used to characterize the QPTs in fermionic [5] and bosonic systems [6]. As fidelity is purely a quantum information concept, an obvious advantage is that it can be a promising candidate to characterize the QPT [7,8,9,10,11,12] because no a priori knowledge of the order parameter and the symmetry of the system is needed. Therefore, these works established another connection between quantum information theory and condensed matter physics, in addition to the recent studies on entanglement in QPTs [13,14,15,16,17,18].The fidelity actually reflects the response of the ground state to a small change of the driving parameter. Zanardi et al. introduced the Riemannian metric tensor [8] inherited from the parameter space to denote the leading term in the fidelity, and argued that the singularity of this metric is in correspondence with the QPTs. While You et al introduced another concept, so-called fidelity susceptibility (FS) [9], and established a general relation between the leading term in the fidelity and the structure factor of the driving term in the Hamiltonian. This relation implies that the fidelity may not have singular behavior in those transitions of infinite order, such as Kosterlitz-Thouless (KT) transitions [19].In this work, we study the FS in 1D asymmetric Hubbard model (AHM) [21], and show that the FS can be * Electronic address: sjgu@phy.cuhk.edu.hk used to characterize the universality class [20] in quantum critical phenomena. The intrinsic relation between the FS and the Landau's symmetry-breaking theory (LSBT) is firstly clarified by a simple QPT occurred in a wellstudied 1D transverse-field Ising model. Then we mainly focus on the critical behavior of the FS in the 1D AHM. Since the AHM can be used to describe a mixture of two species of fermionic atoms in an optical lattice, which is able to be realized by recent experiments on the c...

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 .

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 analytic case for the fidelity susceptibility in describing the universality class in quantum critical behavior. The different critical exponents in two phases are nontrivial results, indicating that the fidelity susceptibility is not always extensive.

In quantum phase transitions induced by continuous level crossing, global-state fidelity drops to zero at every level crossing point, making finite-size scaling not applicable to study the criticality. In this paper, we calculate the partial-state fidelity in two models, i.e., the Lipkin-Meshkov-Glick ͑LMG͒ model and onedimensional Heisenberg model. We show that it can spot the second-order phase transition point in the thermodynamic limit, where continuous level crossing occurs. The finite-size scaling shows the partial-state fidelity susceptibility diverges as N for the isotropic LMG model and N 3 for the Heisenberg model.