Oscillating fidelity susceptibility near a quantum multicritical point

We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change of either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is put to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

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“…As illustrated in Fig. 7, numerics compares very well to (36) and (37). The prefactor √ 2 is seen in numerical simulations when N ≫ γ/|(1−|c|)δ|.…”

Section: Xy Modelmentioning

confidence: 55%

“…It has been proposed that there are two divergent characteristic length scales that have to be taken into account around it: one characterized by the scaling exponent ν = 1/2 and the other by ν = 1 [37]. We will study here…”

Section: Xy Modelmentioning

confidence: 99%

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Rams

Damski

2011

Phys. Rev. A

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“…Concerning the scaling of fidelity, it is well-known that one can switch from the thermodynamic limit to the fidelity susceptibility (χ F (λ)) limit 27,[37][38][39] (where the notion of the fidelity susceptibility is meaningful) when δ −ν ≫ L. Continuing along the same line of arguments, one can define the heat susceptibility χ E 27 such that W T =0 irr ∼ δ 2 χ E , when δ −ν (i.e, δ → 0) is the largest length scale. In this limit, one expects a scaling W T =0 irr ∼ δ 2 λ −α away from the QCP and on the other hand, close to the QCP, L plays the role of the scaling variable in lieu of λ.…”

Section: Scaling Relations Of Wirr and ∆Sirrmentioning

confidence: 99%

One- and two-dimensional quantum models: Quenches and the scaling of irreversible entropy

Sharma

Dutta

2015

Phys. Rev. E

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Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed; we consider two extreme limits namely, the heat susceptibility limit and the thermodynamic limit. It is then argued that the irreversible entropy generated for a thermal quench at low enough temperatures when the system is initially in a Gibbs state, is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one and two-dimensional Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is indeed possible. Exploiting these exact results, we then establish: (i) the irreversible work at zero temperature indeed shows an appropriate scaling in the thermodynamic limit; (ii) the scaling of the irreversible work in the 1D Dirac model at zero-temperature shows logarithmic corrections to the scaling which is a signature of a marginal situation. (iii) Furthermore, remarkably the logarithmic corrections do indeed appear in the scaling of the entropy generated if temperature is low enough while disappears for high temperatures. For the 2D model, no such logarithmic correction is found to appear.

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“…Compared to local order parameters in the conventional Landau-Ginzburg-Wilson paradigm based on the spontaneous symmetry breaking mechanism, in connections between quantum information and QPTs, quantum entanglement, i.e., a purely quantum correlation being absent in classical systems, can be used as an indicator of QPTs driven by quantum fluctuations in quantum many-body systems 3 . Quantum fidelity, based on the basic notions of quantum mechanics on quantum measurement, has also provided an another way to characterize QPTs [4][5][6][7] . In the last few years, various quantum fidelity approaches such as fidelity per lattice site (FLS) 4 , reduced fidelity 8 , fidelity susceptibility 9 , density-functional fidelity 9 , and operator fidelity 10 , have been suggested and implemented to explore QPTs.…”

Section: Introductionmentioning

confidence: 99%

“…The fact that groundstates in different phases should be orthogonal due to their distinguishability in the thermodynamic limit allows a fidelity between quantum many-body states in different phases signaling QPTs because an abrupt change of the fidelity is expected across a critical point in the thermodynamic limit [4][5][6][7][8][9][10] . Thus, the fidelity has great advantages to characterize the QPTs in a variety of quantum lattice systems because the groundstate of a system undergoes a drastic change in its structure at a critical point, regardless of of what type of internal orders are present in quantum many-body states.…”

Section: Introductionmentioning

confidence: 99%

Quantum fidelity for degenerate ground states in quantum phase transitions

Yao

et al. 2013

Phys. Rev. E

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Spontaneous symmetry breaking mechanism in quantum phase transitions manifests the existence of degenerate groundstates in broken symmetry phases. To detect such degenerate groundstates, we introduce a quantum fidelity as an overlap measurement between system groundstates and an arbitrary reference state. This quantum fidelity is shown a multiple bifurcation as an indicator of quantum phase transitions, without knowing any detailed broken symmetry, between a broken symmetry phase and symmetry phases as well as between a broken symmetry phase and other broken symmetry phases, when a system parameter crosses its critical value (i.e., multiple bifurcation point). Each order parameter, characterizing a broken symmetry phase, from each of degenerate groundstates is shown similar multiple bifurcation behavior. Furthermore, to complete the description of an ordered phase, it is possible to specify how each order parameter from each of degenerate groundstates transforms under a symmetry group that is possessed by the Hamiltonian because each order parameter is invariant under only a subgroup of the symmetry group although the Hamiltonian remains invariant under the full symmetry group. Examples are given in the quantum q-state Potts models with a transverse magnetic field by employing the tensor network algorithms based on infinite-size lattices. For any q, a general relation between the local order parameters is found to clearly show the subgroup of the Z q symmetry group. In addition, we systematically discuss the criticality in the q-state Potts model.

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Oscillating fidelity susceptibility near a quantum multicritical point

Cited by 50 publications

References 65 publications

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

One- and two-dimensional quantum models: Quenches and the scaling of irreversible entropy

Quantum fidelity for degenerate ground states in quantum phase transitions

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