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International Conference on Circuits, Power and Intelligent Systems (CCPIS)

Quantum Phase Transition and Entanglement Entropy in DNA Denaturation Dynamics via Heisenberg Spin Model

Subhamoy Singha Roy, Sania Parveen, Saiberi Farhan Khan

Published Sep 5, 2025• 0 citations
Publisher

Abstract

When a DNA molecules conformational characteristics are charted adjacent to a Heisenberg-spin-system, the denaturation shift be able to be expressed in stipulations of a QFT (quantum-phase-transition) brought on through a quench, in which the external field is torsion and the temperature effect is integrated into the quench time. When the spin system's entanglement entropy disappears, the denaturation transition takes place. The energy of torsion includes temperature, stress, and torque, the latter of which is correlated with the twist angle. A DNA molecule put on the Heisenberg spin chain experiences torsion as the outer field. When the EE (entanglement entropy) disappears, the transition to denaturation takes place. The entanglement entropy steadily drops as the proportion of unlock stand pairs gradually increases, the two strands split until the entropy disappears, since the dangerous area corresponding to a 2-boundary actions. The melting profiles of specific DNA molecules have been examined, and the findings show great agreement with biotechnology.

DOI
10.1109/ccpis65231.2025.11234267

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When a DNA molecules conformational characteristics are charted adjacent to a Heisenberg-spin-system, the denaturation shift be able to be expressed in stipulations of a QFT (quantum-phase-transition) brought on through a quench, in which the external field is torsion and the temperature effect is integrated into the quench time. When the spin system's entanglement entropy disappears, the denaturation transition takes place. The energy of torsion includes temperature, stress, and torque, the latter of which is correlated with the twist angle. A DNA molecule put on the Heisenberg spin chain experiences torsion as the outer field. When the EE (entanglement entropy) disappears, the transition to denaturation takes place. The entanglement entropy steadily drops as the proportion of unlock stand pairs gradually increases, the two strands split until the entropy disappears, since the dangerous area corresponding to a 2-boundary actions. The melting profiles of specific DNA molecules have been examined, and the findings show great agreement with biotechnology.
The conformational properties of a DNA molecule when mapped onto a Heisenberg spin system denaturation transition can be formulated in terms of quantum phase transition induced by a quench where the temperature effect is incorporated in the quench time. Here torsion takes on the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes. As the critical region corresponds to a two-limit behaviour the entanglement entropy gradually decreases with the gradual increase in the fraction of open base pairs and when the entropy vanishes the two strands are separated. The sequence heterogeneity interplays with the entropy effects and we have the onset of denaturation bubbles. We have studied the melting profiles for different sequence-specific DNA molecules and the results are found to be in excellent agreement with experiment.
One approach to imagine spins on the axis generating an antiferomagnatic chain is described as simulating a DNA molecule as a Heisenberg spin system. In a DNA molecule, the entanglement entropy of the spin system is shown to be in good agreement with the thermodynamic entropy. At times when the impact of temperature is included during the time of quench, It is shown that denaturation corresponds to a quantum phase change triggered by a quench. The critical point is attained and When the entanglement entropy is eliminated, it equates to a critical torsonal energy. DNA loops now appear as solitonic (skyrmionic) excitations upon base pair opening.
We have considered here that the conformational properties of a DNA molecule can be mapped onto a Heisenberg spin system when spins are located on the axis forming an antiferromagnatic chain.This helps us to study the topological and elastic properties of a DNA molecule in terms of SU(2) gauge fields.The entanglement entropy of the spin system in a supercoil has been determined and it is pointed out that this effectively corresponds to the thermodynamic entropy.The model reproduces salient features of the Rod-Like-Chain model avoiding the "RLC model crisis".
Abstract Here we have study the conceptual properties of DNA molecules that can be mapped in the Heisenberg spin system, and the reduction in the formation of the effect of temperature through the quantum phase transition (QPT) when the refining time occurs. Delayed free rotation of molecules, reverse replication is a complement that uses RNA molecules to produce single-stranded DNA molecules and aids in the diffusion of DNA molecules. This explains the large ternary stress observed near the reverse copy point. We have projected the curve extent which is created to be in good agreement.
Quantum Ising model in one dimension is an exactly solvable example of a quantum phase transition. We investigate its behavior during a quench caused by a gradual turning off of the transverse bias field. The system is then driven at a fixed rate characterized by the quench time ${\ensuremath{\tau}}_{Q}$ across the critical point from a paramagnetic to ferromagnetic phase. In agreement with Kibble-Zurek mechanism (which recognizes that evolution is approximately adiabatic far away, but becomes approximately impulse sufficiently near the critical point), quantum state of the system after the transition exhibits a characteristic correlation length $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$ proportional to the square root of the quench time ${\ensuremath{\tau}}_{Q}$: $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}=\sqrt{{\ensuremath{\tau}}_{Q}}$. The inverse of this correlation length is known to determine average density of defects (e.g., kinks) after the transition. In this paper, we show that this same $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$ controls the entropy of entanglement, e.g., entropy of a block of LLL spins that are entangled with the rest of the system after the transition from the paramagnetic ground state induced by the quench. For large LLL, this entropy saturates at $\frac{1}{6}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}\phantom{\rule{0.2em}{0ex}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$, as might have been expected from the Kibble-Zurek mechanism. Close to the critical point, the entropy saturates when the block size $L\ensuremath{\approx}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$, but---in the subsequent evolution in the ferromagnetic phase---a somewhat larger length scale $l=\sqrt{{\ensuremath{\tau}}_{Q}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\tau}}_{Q}$ develops as a result of a dephasing process that can be regarded as a quantum analog of phase ordering, and the entropy saturates when $L\ensuremath{\approx}l$. We also study the spin-spin correlation using both analytic methods and real time simulations with the Vidal algorithm. We find that at an instant when quench is crossing the critical point, ferromagnetic correlations decay exponentially with the dynamical correlation length $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$, but (as for entropy of entanglement) in the following evolution length scale lll gradually develops. The correlation function becomes oscillatory at distances less than this scale. However, both the wavelength and the correlation length of these oscillations are still determined by $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$. We also derive probability distribution for the number of kinks in a finite spin chain after the transition.
We are here to consider the DNA molecules' spin system to consider when the antiferromagnetic spin chain is formed by the top remains’ axis. It ap-pears that the turning and twist are not two separate entities, not the one the other on the set. This formality assistances us in depicting the thermodynamic entropy as entanglement entropy, and hence the concurrence of two-set entanglement is appraised for transverse Ising model, and antiferromagnetic chain for the assess-ment is that the other methods are to obtain agreements with the excellent deal appeared to be.