We show that entanglement monotones reveal the pronounced enhancement of entanglement at a quantum phase transition, when they are sensitive to long-range high-order correlations. Such monotones are found to develop a sharp interferometric peak at the critical point, and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlation spectra, and verify that these experimentally accessible quantities encode entanglement information and probe separability. We give a prescription, for mesoscopic scale systems of how to extract the pronounced enhancement of entanglement at a quantum phase transition from limited accessible experimental data.We show that entanglement monotones reveal the pronounced enhancement of entanglement at a quantum phase transition, when they are sensitive to long-range high-order correlations. Such monotones are found to develop a sharp interferometric peak at the critical point, and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlation spectra, and verify that these experimentally accessible quantities encode entanglement information and probe separability. We give a prescription, for mesoscopic scale systems of how to extract the pronounced enhancement of entanglement at a quantum phase transition from limited accessible experimental data.

arXiv:0803.0760Europhysics Letters (EPL)Apr 1, 20099 citations

Scaling of entanglement close to a quantum phase transition

Andreas Osterloh, Luigi Amico A, G. Falci +1 more

arXiv:quant-ph/0202029NatureApr 1, 20021,860 citations

Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction

Fu-Wu Ma, Shengxin Liu, Xiang-Mu Kong

We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin- $1/2$ $XY$ model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-$1/2$ $XY$ model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.

arXiv:1106.0901Physical Review AOct 3, 201187 citations

Probing entanglement scaling across a quantum phase transition on a quantum computer

Qiang Miao, Tianyi Wang, Kenneth R. Brown +2 more

The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase transitions, where quantum fluctuations manifest across all length scales. While quantum simulators give controlled access to a number of strongly correlated systems, the study of critical phenomena has been hampered by finite-size effects arising from diverging correlation lengths. Moreover, the experimental investigation of entanglement in many-body systems has been hindered by limitations in measurement protocols. To address these challenges, we employ the multiscale entanglement renormalization ansatz (MERA) and implement a holographic scheme for subsystem tomography on a fully-connected trapped-ion quantum computer. Our method accurately represents infinite systems and long-range correlations with few qubits, facilitating the efficient extraction of observables and entanglement properties, even at criticality. We observe a quantum phase transition with spontaneous symmetry breaking and reveal the evolution of entanglement properties across the critical point. For the first time, we demonstrate log-law scaling of subsystem entanglement entropies at criticality on a digital quantum computer. This achievement highlights the potential of MERA for the investigation of strongly-correlated many-body systems on quantum computers.The investigation of strongly-correlated quantum matter is difficult due to the curse of dimensionality and intricate entanglement structures. These challenges are particularly pronounced in the vicinity of continuous quantum phase transitions, where quantum fluctuations manifest across all length scales. While quantum simulators give controlled access to a number of strongly correlated systems, the study of critical phenomena has been hampered by finite-size effects arising from diverging correlation lengths. Moreover, the experimental investigation of entanglement in many-body systems has been hindered by limitations in measurement protocols. To address these challenges, we employ the multiscale entanglement renormalization ansatz (MERA) and implement a holographic scheme for subsystem tomography on a fully-connected trapped-ion quantum computer. Our method accurately represents infinite systems and long-range correlations with few qubits, facilitating the efficient extraction of observables and entanglement properties, even at criticality. We observe a quantum phase transition with spontaneous symmetry breaking and reveal the evolution of entanglement properties across the critical point. For the first time, we demonstrate log-law scaling of subsystem entanglement entropies at criticality on a digital quantum computer. This achievement highlights the potential of MERA for the investigation of strongly-correlated many-body systems on quantum computers.

arXiv:2412.18602Nature CommunicationsJul 27, 20260 citations

We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-

1/2

XY

model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.