Fidelity susceptibility, scaling, and universality in quantum critical phenomena

Abstract

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...

At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited

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Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

“…This basic idea was behind suggesting fidelity -the overlap between the ground states of the system for slightly shifted values of the external parameter J -as a universal probe of quantum criticality [2]. Dramatic change of the system's properties across the critical point results in a drop of fidelity enabling both the location of the critical point and the determination of the universal critical exponent ν characterizing the divergence of the correlation length [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The fidelity has applications in as wide a context as that of the quantum phase transitions themselves.…”

Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model

“…We can account for the divergence around quantum critical points (QCPs) in the AQRM by formulating a so-called finite-h scaling theory [10,25], in parallel with the scaling theory for finite-size effects in a many-body system, and here h plays a similar role as system size in the latter case. universal information could be decoded from the scaling behavior of the fidelity susceptibility [56][57][58]. The fidelity susceptibility exhibits stronger dependence on h across the critical point than in the non-critical region.…”