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.


Kink signatures for infinite and finite τ.Plot of Eabs for different types of pulses are shown. Clear signatures (kinks) are visible at critical points marked by vertical dotted lines. (a) Eabs vs λF plot for a general type of pulse (λI → λF → λI) starting from hI = 0, γI = 1 in the direction given by tanδ = −0.5. The critical point occurs at λF = 1.118. (b) Eabs vs γF plot for an anisotropic pulse starting from γI = 1.5 with fixed h = 0.2. (c) Eabs vs hF plot for a field-pulse starting from hI = 0.2 with fixed anisotropy, γ = 0.5. (d) Eabs vs hF plot for a transverse Ising model with a transverse field-pulse 0 → hF → 0. For τ = 50, the plots are almost indistinguishable from the infinite τ result, particularly at and around the critical point.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Kink signatures for infinite and finite τ.Plot of Eabs for different types of pulses are shown. Clear signatures (kinks) are visible at critical points marked by vertical dotted lines. (a) Eabs vs λF plot for a general type of pulse (λI → λF → λI) starting from hI = 0, γI = 1 in the direction given by tanδ = −0.5. The critical point occurs at λF = 1.118. (b) Eabs vs γF plot for an anisotropic pulse starting from γI = 1.5 with fixed h = 0.2. (c) Eabs vs hF plot for a field-pulse starting from hI = 0.2 with fixed anisotropy, γ = 0.5. (d) Eabs vs hF plot for a transverse Ising model with a transverse field-pulse 0 → hF → 0. For τ = 50, the plots are almost indistinguishable from the infinite τ result, particularly at and around the critical point.

Mentions: Here we consider pulses from a general initial point (hI, γI) towards a direction δ such that the Ising transition line is crossed (e.g., in Fig. 2c). Evaluating the integral for Eabs (Eq. 4) following the general outline given above (see the Method section for details) we get, for hF = 1, γF ≠ 0,


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)

Kink signatures for infinite and finite τ.Plot of Eabs for different types of pulses are shown. Clear signatures (kinks) are visible at critical points marked by vertical dotted lines. (a) Eabs vs λF plot for a general type of pulse (λI → λF → λI) starting from hI = 0, γI = 1 in the direction given by tanδ = −0.5. The critical point occurs at λF = 1.118. (b) Eabs vs γF plot for an anisotropic pulse starting from γI = 1.5 with fixed h = 0.2. (c) Eabs vs hF plot for a field-pulse starting from hI = 0.2 with fixed anisotropy, γ = 0.5. (d) Eabs vs hF plot for a transverse Ising model with a transverse field-pulse 0 → hF → 0. For τ = 50, the plots are almost indistinguishable from the infinite τ result, particularly at and around the critical point.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Kink signatures for infinite and finite τ.Plot of Eabs for different types of pulses are shown. Clear signatures (kinks) are visible at critical points marked by vertical dotted lines. (a) Eabs vs λF plot for a general type of pulse (λI → λF → λI) starting from hI = 0, γI = 1 in the direction given by tanδ = −0.5. The critical point occurs at λF = 1.118. (b) Eabs vs γF plot for an anisotropic pulse starting from γI = 1.5 with fixed h = 0.2. (c) Eabs vs hF plot for a field-pulse starting from hI = 0.2 with fixed anisotropy, γ = 0.5. (d) Eabs vs hF plot for a transverse Ising model with a transverse field-pulse 0 → hF → 0. For τ = 50, the plots are almost indistinguishable from the infinite τ result, particularly at and around the critical point.
Mentions: Here we consider pulses from a general initial point (hI, γI) towards a direction δ such that the Ising transition line is crossed (e.g., in Fig. 2c). Evaluating the integral for Eabs (Eq. 4) following the general outline given above (see the Method section for details) we get, for hF = 1, γF ≠ 0,

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.