Limits...
Signature of a continuous quantum phase transition in non-equilibrium energy absorption: Footprints of criticality on higher excited states.

Bhattacharyya S, Dasgupta S, Das A - Sci Rep (2015)

Bottom Line: Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics.This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them.Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.

View Article: PubMed Central - PubMed

Affiliation: R.R.R. Mahavidyalaya, Radhanagar, Hooghly 712406, India.

ABSTRACT
Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics. Quantum phase transitions concern ground state properties of many-body systems, and hence their signatures are expected to be pronounced in low-energy states. Here we report signature of a quantum critical point manifested in strongly out-of-equilibrium states with finite energy density with respect to the ground state and extensive (subsystem) entanglement entropy, generated by an external pulse. These non-equilibrium states are evidently completely disordered (e.g., paramagnetic in case of a magnetic ordering transition). The pulse is applied by switching a coupling of the Hamiltonian from an initial value (λI) to a final value (λF) for sufficiently long time and back again. The signature appears as non-analyticities (kinks) in the energy absorbed by the system from the pulse as a function of λF at critical-points (i.e., at values of λF corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian H(λF) by increasing the pulse height (/λF - λI/), the non-analyticity grows stronger monotonically with it. This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them. Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.

No MeSH data available.


Contours with poles and branch-point for integrating Eabs (Eq. 4) under different circumstances: The left contour represents the case of crossing the h = 1 line.zF corresponds to the arguments hF, γF and zI for hI, γI. The right contour corresponds to the case of crossing the γ = 0. zF corresponds to the arguments hF, γF and zI for hI, γI. In both the figures red dotted lines represent the branch-cuts.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4644967&req=5

f5: Contours with poles and branch-point for integrating Eabs (Eq. 4) under different circumstances: The left contour represents the case of crossing the h = 1 line.zF corresponds to the arguments hF, γF and zI for hI, γI. The right contour corresponds to the case of crossing the γ = 0. zF corresponds to the arguments hF, γF and zI for hI, γI. In both the figures red dotted lines represent the branch-cuts.

Mentions: First we consider the case of crossing h = 1 critical line from positive γI (Region I to Region III in Fig. 4). The pole z = 0 are always inside in all cases. Of the other four, is always inside and is always outside the contour. However, the pole is inside the unit circle for hF < 1 and outside for hF > 1. The branch points are inside the circle and the contour should be indented to avoid branch lines (Fig. 5, left contour). Since the integral over the indentations are continuous functions of (hF, γF), the non-analyticity in the behaviour of Eabs arises from the restructuring of poles inside the unit circle and we have


Signature of a continuous quantum phase transition in non-equilibrium energy absorption: Footprints of criticality on higher excited states.

Bhattacharyya S, Dasgupta S, Das A - Sci Rep (2015)

Contours with poles and branch-point for integrating Eabs (Eq. 4) under different circumstances: The left contour represents the case of crossing the h = 1 line.zF corresponds to the arguments hF, γF and zI for hI, γI. The right contour corresponds to the case of crossing the γ = 0. zF corresponds to the arguments hF, γF and zI for hI, γI. In both the figures red dotted lines represent the branch-cuts.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4644967&req=5

f5: Contours with poles and branch-point for integrating Eabs (Eq. 4) under different circumstances: The left contour represents the case of crossing the h = 1 line.zF corresponds to the arguments hF, γF and zI for hI, γI. The right contour corresponds to the case of crossing the γ = 0. zF corresponds to the arguments hF, γF and zI for hI, γI. In both the figures red dotted lines represent the branch-cuts.
Mentions: First we consider the case of crossing h = 1 critical line from positive γI (Region I to Region III in Fig. 4). The pole z = 0 are always inside in all cases. Of the other four, is always inside and is always outside the contour. However, the pole is inside the unit circle for hF < 1 and outside for hF > 1. The branch points are inside the circle and the contour should be indented to avoid branch lines (Fig. 5, left contour). Since the integral over the indentations are continuous functions of (hF, γF), the non-analyticity in the behaviour of Eabs arises from the restructuring of poles inside the unit circle and we have

Bottom Line: Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics.This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them.Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.

View Article: PubMed Central - PubMed

Affiliation: R.R.R. Mahavidyalaya, Radhanagar, Hooghly 712406, India.

ABSTRACT
Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics. Quantum phase transitions concern ground state properties of many-body systems, and hence their signatures are expected to be pronounced in low-energy states. Here we report signature of a quantum critical point manifested in strongly out-of-equilibrium states with finite energy density with respect to the ground state and extensive (subsystem) entanglement entropy, generated by an external pulse. These non-equilibrium states are evidently completely disordered (e.g., paramagnetic in case of a magnetic ordering transition). The pulse is applied by switching a coupling of the Hamiltonian from an initial value (λI) to a final value (λF) for sufficiently long time and back again. The signature appears as non-analyticities (kinks) in the energy absorbed by the system from the pulse as a function of λF at critical-points (i.e., at values of λF corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian H(λF) by increasing the pulse height (/λF - λI/), the non-analyticity grows stronger monotonically with it. This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them. Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.

No MeSH data available.