Fidelity approach to Gaussian transitions

Tzeng, Yu-Chin; Hung, Hsiang-Hsuan; Chen, Yung‐Chung; Yang, Min-Fong

doi:10.1103/physreva.77.062321

Cited by 55 publications

(114 citation statements)

References 54 publications

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“…[10], and D c ∼ 0.97 in Ref. [26]. Among these works, only a single study [15] was based on the analysis of the string order, although data from the numerical-diagonalization calculations in this study for small clusters might not be sufficient to show the transition point.…”

Section: B Haldane-large-d Transition Linementioning

confidence: 99%

“…[9], in which the estimate of c gradually deviates from c = 1 around J z 1. In the report of Tzeng and Yang [26], the transition point and the …”

Section: Haldane-néel Transition Linementioning

confidence: 99%

“…Among these works, only a single study [15] was based on the analysis of the string order, although data from the numerical-diagonalization calculations in this study for small clusters might not be sufficient to show the transition point. Recently, Tzeng and Yang [26] investigated the fidelity susceptibility [27] of the ground state by the DMRG method to detect quantum phase transitions for the system. This work examines only the information of the ground state, a feature that is shared with our present analysis.…”

Section: B Haldane-large-d Transition Linementioning

confidence: 99%

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Finite-size scaling of string order parameters characterizing the Haldane phase

2008

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We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi-point correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S = 1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density matrix renormalization group method. We focus on the gradient of the inversedsystem-size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method to directly observe quantum phase transitions.

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Section: B Haldane-large-d Transition Linementioning

confidence: 99%

“…[9], in which the estimate of c gradually deviates from c = 1 around J z 1. In the report of Tzeng and Yang [26], the transition point and the …”

Section: Haldane-néel Transition Linementioning

confidence: 99%

Section: B Haldane-large-d Transition Linementioning

confidence: 99%

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Finite-size scaling of string order parameters characterizing the Haldane phase

2008

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“…On the other hand for marginal perturbations ∆ λ = d + z i.e., when one is moving along a manifold of critical points, the above scaling formula does not provide a definite prediction as both log-like terms and O(1) might appear. Accordingly moving along a line of gapless point may not give rise to a detectable fidelity drop [6,7].…”

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confidence: 99%

Universal subleading terms in ground-state fidelity from boundary conformal field theory

2009

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The study of the (logarithm of the) fidelity i.e., of the overlap amplitude, between ground states of Hamiltonians corresponding to different coupling constants, provides a valuable insight on critical phenomena. When the parameters are infinitesimally close, it is known that the leading term behaves as O(L α ) (L system size) where α is equal to the spatial dimension d for gapped systems, and otherwise depends on the critical exponents. Here we show that when parameters are changed along a critical manifold, a sub-leading O(1) term can appear. This term, somewhat similar to the topological entanglement entropy, depends only on the system's universality class and encodes non-trivial information about the topology of the system. We relate it to universal g factors and partition functions of (boundary) conformal field theory in d = 1 and d = 2 dimensions. Numerical checks are presented on the simple example of the XXZ chain.

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“…The lowest energy excitations of the D phase which reside in the S z r = ±1 sector, are gapped and consist of pairs of excitons and antiexcitons which can be bound. Numerical studies [45][46][47][48] have established that in the pure spin model the quantum critical point separating the D phase and Haldane phase occurs at D * /J c ∼ 0.96 − 0.971. It has been found that in a pure spin model such as the one discussed here, a quantum phase transition between the Haldane phase and the topologically trivial D phase is signaled by the change in sign of an inversion-symmetry-based order parameter [47] which is a nonlocal topological order parameter.…”

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confidence: 99%

Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes

et al. 2017

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We consider layered decorated honeycomb lattices at two-thirds filling, as realized in some trinuclear organometallic complexes. Localized S = 1 moments with a single-spin anisotropy emerge from the interplay of Coulomb repulsion and spin molecular-orbit coupling (SMOC). Magnetic anisotropies with bond-dependent exchange couplings occur in the honeycomb layers when the direct intracluster exchange and the spin molecular-orbital coupling are both present. We find that the effective spin exchange model within the layers is an XXZ + 120• honeycomb quantum compass model. The intrinsic nonspherical symmetry of the multinuclear complexes leads to very different transverse and longitudinal spin molecular-orbital couplings, which greatly enhances the single-spin and exchange coupling anisotropies. The interlayer coupling is described by an XXZ model with anisotropic biquadratic terms. As the correlation strength increases the system becomes increasingly one-dimensional. Thus, if the ratio of SMOC to the interlayer hopping is small this stabilizes the Haldane phase. However, as the ratio increases there is a quantum phase transition to the topologically trivial "D phase." We also predict a quantum phase transition from a Haldane phase to a magnetically ordered phase at sufficiently strong external magnetic fields.

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Fidelity approach to Gaussian transitions

Cited by 55 publications

References 54 publications

Finite-size scaling of string order parameters characterizing the Haldane phase

Finite-size scaling of string order parameters characterizing the Haldane phase

Universal subleading terms in ground-state fidelity from boundary conformal field theory

Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes

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