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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2412.02236 |
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| _version_ | 1866916980865368064 |
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| author | Sarkar, Pritam |
| author_facet | Sarkar, Pritam |
| contents | A measure of how sensitive the entanglement entropy is in a quantum system, has been proposed and its information geometric origin is discussed. It has been demonstrated for two exactly solvable spin systems, that thermodynamic criticality is directly \textit{indicated} by finite size scaling of the global maxima and turning points of the susceptibility of entanglement entropy through numerical analysis - obtaining power laws. Analytically we have proved those power laws for $| \ λ_c(N)-λ_c^{\infty}|$ as $N\to \infty$ in the cases of finite 1D transverse field ising model (TFIM) ($λ=h$) and XY chain ($λ=γ$). The integer power law appearing for XY model has been verified using perturbation theory in $\mathcal{O}(\frac{1}{N})$ and the fractional power law appearing in the case of TFIM, is verified by an exact approach involving Chebyshev polynomials, hypergeometric functions and complete elliptic integrals. Furthermore a set of potential applications of this quantity under quantum dynamics and also for non-integrable systems, are briefly discussed. The simplicity of this setup for understanding quantum criticality is emphasized as it takes in only the reduced density matrix of appropriate rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02236 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Susceptibility of entanglement entropy: a universal indicator of quantum criticality Sarkar, Pritam Statistical Mechanics Quantum Physics A measure of how sensitive the entanglement entropy is in a quantum system, has been proposed and its information geometric origin is discussed. It has been demonstrated for two exactly solvable spin systems, that thermodynamic criticality is directly \textit{indicated} by finite size scaling of the global maxima and turning points of the susceptibility of entanglement entropy through numerical analysis - obtaining power laws. Analytically we have proved those power laws for $| \ λ_c(N)-λ_c^{\infty}|$ as $N\to \infty$ in the cases of finite 1D transverse field ising model (TFIM) ($λ=h$) and XY chain ($λ=γ$). The integer power law appearing for XY model has been verified using perturbation theory in $\mathcal{O}(\frac{1}{N})$ and the fractional power law appearing in the case of TFIM, is verified by an exact approach involving Chebyshev polynomials, hypergeometric functions and complete elliptic integrals. Furthermore a set of potential applications of this quantity under quantum dynamics and also for non-integrable systems, are briefly discussed. The simplicity of this setup for understanding quantum criticality is emphasized as it takes in only the reduced density matrix of appropriate rank. |
| title | Susceptibility of entanglement entropy: a universal indicator of quantum criticality |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2412.02236 |