Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.

arXiv:1801.03495Physical Review LettersSep 24, 20189 citations

GRAVITY AND THE QUANTUM POTENTIAL

WORLD SCIENTIFIC eBooksJan 1, 20100 citations

Detecting the critical point through entanglement in the Schwinger model

Kazuki Ikeda, Dmitri E. Kharzeev, René Meyer +1 more

Using quantum simulations on classical hardware, we study the phase diagram of the massive Schwinger model with a $\ensuremath{\theta}$ term at finite chemical potential $\ensuremath{\mu}$. We find that the quantum critical point in the phase diagram of the model can be detected through the entanglement entropy and entanglement spectrum. As a first step, we chart the phase diagram using conventional methods by computing the dependence of the charge and chiral condensates on the fermion mass $m$ , coupling constant $g$ , and the chemical potential $\ensuremath{\mu}$. At zero density, the Schwinger model possesses a quantum critical point at $\ensuremath{\theta}=\ensuremath{\pi}$ and $m/g\ensuremath{\simeq}0.33$. We find that the position of this quantum critical point depends on the chemical potential. Near this quantum critical point, we observe a sharp maximum in the entanglement entropy. Moreover, we find that the quantum critical point can be located from the entanglement spectrum by detecting the position of the gap closing point.Using quantum simulations on classical hardware, we study the phase diagram of the massive Schwinger model with a $\ensuremath{\theta}$ term at finite chemical potential $\ensuremath{\mu}$. We find that the quantum critical point in the phase diagram of the model can be detected through the entanglement entropy and entanglement spectrum. As a first step, we chart the phase diagram using conventional methods by computing the dependence of the charge and chiral condensates on the fermion mass $m$, coupling constant $g$, and the chemical potential $\ensuremath{\mu}$. At zero density, the Schwinger model possesses a quantum critical point at $\ensuremath{\theta}=\ensuremath{\pi}$ and $m/g\ensuremath{\simeq}0.33$. We find that the position of this quantum critical point depends on the chemical potential. Near this quantum critical point, we observe a sharp maximum in the entanglement entropy. Moreover, we find that the quantum critical point can be located from the entanglement spectrum by detecting the position of the gap closing point.

arXiv:2305.00996Physical review. D/Physical review. D.Nov 9, 202318 citations

Quantum entanglement and criticality in a one-dimensional deconfined quantum critical point

Sheng Yang, Jing-Bo Xu

We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference O_{E} is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between O_{E} and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.We investigate the ground-state quantum entanglement in a one-dimensional incarnation of deconfined quantum critical point by making use of the finite-size density matrix renormalization group method. We observe two distinct behaviors of two-site entanglement calculated on odd and even bonds, and the difference O_{E} is shown to obey conventional scaling relations for order parameters. Accurate deconfined critical point and associated critical exponents are numerically extracted from finite-size scaling analyses. We further notice a close similarity between O_{E} and the valence-bond-solid order parameter and same observations are also obtained for quantum coherence and trace distance. Furthermore, the deconfined critical point is suggested to possess rich quantum entanglement other than the two-site entanglement from the residual entanglement perspective. Our work explores the critical characteristics of the one-dimensional deconfined quantum critical point from the quantum information aspect and provides insights for its ground-state entanglement structure.

Physical review. EDec 16, 202110 citations

Gravity-induced Entanglement under Constrained Dynamics

Hollis Williams

Jan 1, 20260 citations

m

, coupling constant

g

, and the chemical potential $\ensuremath{\mu}$. At zero density, the Schwinger model possesses a quantum critical point at $\ensuremath{\theta}=\ensuremath{\pi}$ and $m/g\ensuremath{\simeq}0.33$. We find that the position of this quantum critical point depends on the chemical potential. Near this quantum critical point, we observe a sharp maximum in the entanglement entropy. Moreover, we find that the quantum critical point can be located from the entanglement spectrum by detecting the position of the gap closing point.