Fidelity and fidelity susceptibility near a quantum critical point

We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'e model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr\'e model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr\'e model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in the near future.We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'e model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr\'e model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr\'e model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in the near future.

arXiv:1902.00200Physical Review AApr 22, 201950 citations

Fidelity susceptibility and general quench near an anisotropic quantum critical point

Victor Mukherjee, Amit Dutta

We study the scaling behavior of fidelity susceptibility density $({\ensuremath{\chi}}_{\mathrm{f}})$ at or close to an anisotropic quantum critical point (AQCP) characterized by two different correlation length exponents ${\ensuremath{\nu}}_{||}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ along parallel and perpendicular spatial directions, respectively. Our studies show that the response of the system due to a small change in the Hamiltonian near an AQCP is different from that seen near an isotropic QCP. In particular, for a finite system with linear dimension ${L}_{||}$ (${L}_{\ensuremath{\perp}}$) in the parallel (perpendicular) directions, the maximum value of ${\ensuremath{\chi}}_{\mathrm{f}}$ is found to increase in a power-law fashion with ${L}_{||}$ for small ${L}_{||}$ , with an exponent depending on both ${\ensuremath{\nu}}_{||}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ and eventually crosses over to a scaling with ${L}_{\ensuremath{\perp}}$ for ${L}_{||}^{1/{\ensuremath{\nu}}_{||}}\ensuremath{\gtrsim}{L}_{\ensuremath{\perp}}^{1/{\ensuremath{\nu}}_{\ensuremath{\perp}}}$. We also propose scaling relations of heat density and defect density generated following a quench starting from an AQCP and connect them to a generalized fidelity susceptibility. These predictions are verified exactly both analytically and numerically taking the example of a Hamiltonian showing a semi-Dirac band-crossing point.We study the scaling behavior of fidelity susceptibility density $({\ensuremath{\chi}}_{\mathrm{f}})$ at or close to an anisotropic quantum critical point (AQCP) characterized by two different correlation length exponents ${\ensuremath{\nu}}_{||}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ along parallel and perpendicular spatial directions, respectively. Our studies show that the response of the system due to a small change in the Hamiltonian near an AQCP is different from that seen near an isotropic QCP. In particular, for a finite system with linear dimension ${L}_{||}$ (${L}_{\ensuremath{\perp}}$) in the parallel (perpendicular) directions, the maximum value of ${\ensuremath{\chi}}_{\mathrm{f}}$ is found to increase in a power-law fashion with ${L}_{||}$ for small ${L}_{||}$, with an exponent depending on both ${\ensuremath{\nu}}_{||}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ and eventually crosses over to a scaling with ${L}_{\ensuremath{\perp}}$ for ${L}_{||}^{1/{\ensuremath{\nu}}_{||}}\ensuremath{\gtrsim}{L}_{\ensuremath{\perp}}^{1/{\ensuremath{\nu}}_{\ensuremath{\perp}}}$. We also propose scaling relations of heat density and defect density generated following a quench starting from an AQCP and connect them to a generalized fidelity susceptibility. These predictions are verified exactly both analytically and numerically taking the example of a Hamiltonian showing a semi-Dirac band-crossing point.

arXiv:1101.1713Physical Review BJun 8, 201120 citations

Fidelity susceptibility probes of dynamical quantum criticality

Niaz Ali Khan

Chaos Solitons & FractalsMay 11, 20245 citations

Fidelity and criticality in the nonreciprocal Aubry-André-Harper model

Changjing Zeng, Zhen Cai, Guang-Heng Wang +1 more

Abstract We study the critical behaviors of the ground and first-excited states in the one-dimensional nonreciprocal Aubry-André-Harper (AAH) model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as N 2 , akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as N 2 . In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law.Abstract We study the critical behaviors of the ground and first-excited states in the one-dimensional nonreciprocal Aubry-André-Harper (AAH) model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as N 2 , akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as N 2 . In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law.

arXiv:2404.16704Europhysics Letters (EPL)Jan 10, 20255 citations

Fidelity susceptibility as a seeker for quantum phase transitions

Wing Chi Yu, Ho-Man Kwok, Junpeng Cao +1 more

Bulletin of the American Physical SocietyMar 19, 20100 citations

{L}_{||}

(${L}_{\ensuremath{\perp}}$) in the parallel (perpendicular) directions, the maximum value of ${\ensuremath{\chi}}_{\mathrm{f}}$ is found to increase in a power-law fashion with

{L}_{||}

for small

{L}_{||}

, with an exponent depending on both ${\ensuremath{\nu}}_{||}$ and ${\ensuremath{\nu}}_{\ensuremath{\perp}}$ and eventually crosses over to a scaling with ${L}_{\ensuremath{\perp}}$ for ${L}_{||}^{1/{\ensuremath{\nu}}_{||}}\ensuremath{\gtrsim}{L}_{\ensuremath{\perp}}^{1/{\ensuremath{\nu}}_{\ensuremath{\perp}}}$. We also propose scaling relations of heat density and defect density generated following a quench starting from an AQCP and connect them to a generalized fidelity susceptibility. These predictions are verified exactly both analytically and numerically taking the example of a Hamiltonian showing a semi-Dirac band-crossing point.