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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.


Related in: MedlinePlus

(a) Pulse line intersecting two critical lines. This happens for . For this figure, δ = −tan−1 (1.5). (b) Corresponding Eabs vs λF. The present case corresponds to initial point λI = (hI = 0, γI = 1), the pulse direction tanδ = −1.5, and pulse duration τ → ∞. The pulse-line crosses the two critical lines at λF = 0.667 and λF = 1.118 which are the anisotropy critical line and the Ising critical line respectively. The non-analyticity is observed in both the cases.
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f3: (a) Pulse line intersecting two critical lines. This happens for . For this figure, δ = −tan−1 (1.5). (b) Corresponding Eabs vs λF. The present case corresponds to initial point λI = (hI = 0, γI = 1), the pulse direction tanδ = −1.5, and pulse duration τ → ∞. The pulse-line crosses the two critical lines at λF = 0.667 and λF = 1.118 which are the anisotropy critical line and the Ising critical line respectively. The non-analyticity is observed in both the cases.

Mentions: where m = tan(δ). Δ = 0 for any other point on the pulse-line that is not a QPT point. This is of course under the assumption that we are considering the nearest point of intersection between the pulse-line and the critical line from the initial point. If the line intersects more than one critical lines, Eabs shows discontinuity (Δ ≠ 0) at each of those (see Fig. 3). A further simplification occurs if we consider the Ising case, i.e., γ = 1, under the h-pulse 0 → hF → 0, where we can calculate the entire analytical expression: for hF ≤ 1, and for hF ≥ 1 (Fig. 2d).


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)

(a) Pulse line intersecting two critical lines. This happens for . For this figure, δ = −tan−1 (1.5). (b) Corresponding Eabs vs λF. The present case corresponds to initial point λI = (hI = 0, γI = 1), the pulse direction tanδ = −1.5, and pulse duration τ → ∞. The pulse-line crosses the two critical lines at λF = 0.667 and λF = 1.118 which are the anisotropy critical line and the Ising critical line respectively. The non-analyticity is observed in both the cases.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: (a) Pulse line intersecting two critical lines. This happens for . For this figure, δ = −tan−1 (1.5). (b) Corresponding Eabs vs λF. The present case corresponds to initial point λI = (hI = 0, γI = 1), the pulse direction tanδ = −1.5, and pulse duration τ → ∞. The pulse-line crosses the two critical lines at λF = 0.667 and λF = 1.118 which are the anisotropy critical line and the Ising critical line respectively. The non-analyticity is observed in both the cases.
Mentions: where m = tan(δ). Δ = 0 for any other point on the pulse-line that is not a QPT point. This is of course under the assumption that we are considering the nearest point of intersection between the pulse-line and the critical line from the initial point. If the line intersects more than one critical lines, Eabs shows discontinuity (Δ ≠ 0) at each of those (see Fig. 3). A further simplification occurs if we consider the Ising case, i.e., γ = 1, under the h-pulse 0 → hF → 0, where we can calculate the entire analytical expression: for hF ≤ 1, and for hF ≥ 1 (Fig. 2d).

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.


Related in: MedlinePlus